Glossary for Advanced Placement Chemistry
A comprehensive reference of terms used throughout this AP Chemistry course, from foundational concepts to electrochemistry. Definitions follow ISO 11179 standards for precision and clarity.
Absorption Spectra
A pattern of dark lines or bands on a continuous spectrum produced when atoms or molecules absorb photons at specific wavelengths, promoting electrons to higher energy levels. Each element has a unique absorption spectrum that serves as a chemical fingerprint.
Example: Hydrogen absorbs light at 410 nm, 434 nm, 486 nm, and 656 nm in the visible range, producing four dark lines in the absorption spectrum.
Accuracy and Precision
Accuracy is the closeness of a measured value to the true or accepted value; precision is the closeness of repeated measurements to one another. A measurement can be precise without being accurate.
Example: Three dart throws landing close together but away from the bullseye are precise but not accurate; throws clustered on the bullseye are both accurate and precise.
Acid Dissociation Ka
The equilibrium constant for the dissociation of a weak acid in water, defined as \(K_a = \frac{[\ce{H+}][\ce{A-}]}{[\ce{HA}]}\). Larger \(K_a\) values indicate stronger acids that dissociate more completely.
Example: Acetic acid (\(\ce{CH3COOH}\)) has \(K_a = 1.8 \times 10^{-5}\), indicating it is a weak acid that dissociates only partially.
Acid Strength Factors
The factors that determine the extent of acid dissociation, including bond strength, bond polarity, electronegativity of surrounding atoms, and the stability of the conjugate base. Stronger conjugate bases correspond to weaker acids.
Example: \(\ce{HF}\) is a weak acid despite fluorine's high electronegativity because the \(\ce{H-F}\) bond is unusually strong and short.
Acid-Base Titration
An analytical procedure in which a solution of known concentration (titrant) is added to a solution of unknown concentration until the reaction reaches the equivalence point, allowing calculation of the unknown concentration.
Example: Titrating 25.0 mL of \(\ce{NaOH}\) solution with standardized \(\ce{HCl}\) to determine the exact concentration of the base.
Acid-Carbonate Reactions
Reactions between an acid and a carbonate or bicarbonate compound producing a salt, water, and carbon dioxide gas. These reactions are a subtype of double replacement reactions characterized by gas evolution.
Acid-Metal Reactions
Reactions in which an active metal reacts with an acid to produce a salt and hydrogen gas. The metal is oxidized and the hydrogen ions are reduced to \(\ce{H2}\).
Example: \(\ce{Zn (s) + 2HCl (aq) -> ZnCl2 (aq) + H2 (g)}\)
Acidic Salts
Salts that produce an acidic solution when dissolved in water, either because the cation is a weak-acid cation (hydrolyzes to produce \(\ce{H+}\)) or the anion is the conjugate base of a strong acid paired with a hydrolyzing cation.
Example: Ammonium chloride (\(\ce{NH4Cl}\)) is an acidic salt; \(\ce{NH4+}\) hydrolyzes to give \(\ce{NH3 + H+}\), lowering the pH below 7.
Acids
Substances that donate protons (\(\ce{H+}\)) to other species (Brønsted-Lowry definition), accept electron pairs (Lewis definition), or increase \(\ce{[H+]}\) in aqueous solution (Arrhenius definition). Acids turn blue litmus red and react with bases in neutralization reactions.
Example: Hydrochloric acid (\(\ce{HCl}\)) is a strong Arrhenius acid that dissociates completely: \(\ce{HCl -> H+ + Cl-}\).
Activated Complex
The unstable, high-energy arrangement of atoms at the peak of the potential energy diagram during a chemical reaction, representing the transition state between reactants and products. The activated complex cannot be isolated.
Example: In the reaction \(\ce{H2 + I2 -> 2HI}\), the activated complex is a four-atom \(\ce{[H2I2]^{\ddagger}}\) structure with partially broken and partially formed bonds.
Activation Energy
The minimum kinetic energy that colliding reactant particles must possess for a reaction to occur. Symbolized \(E_a\), it equals the energy difference between reactants and the transition state on a potential energy diagram.
Example: The decomposition of \(\ce{N2O5}\) has an activation energy of about 103 kJ/mol; molecules with less than this energy cannot react.
Activity Series
A ranked list of metals (and hydrogen) in order of decreasing reactivity, used to predict whether a single replacement reaction will occur. A metal higher on the list will displace the ion of a metal lower on the list from solution.
Example: Since zinc is above copper in the activity series, \(\ce{Zn (s) + CuSO4 (aq) -> ZnSO4 (aq) + Cu (s)}\) proceeds spontaneously.
Actual Yield
The measured mass or moles of product obtained from a chemical reaction under real laboratory or industrial conditions. Actual yield is always less than or equal to the theoretical yield due to side reactions and incomplete reactions.
Example: If a reaction theoretically produces 10.0 g of product but only 8.5 g is collected, the actual yield is 8.5 g.
Adding Inert Gas
The addition of a non-reactive gas to a reaction system at constant volume, which increases total pressure but does not change the partial pressures of reactants or products. Therefore, the equilibrium position does not shift.
Example: Adding argon gas to a \(\ce{N2 + 3H2 <=> 2NH3}\) equilibrium at constant volume has no effect on the position of equilibrium.
Adding Reactions K
The mathematical rule that when two or more chemical equations are added together, their equilibrium constants are multiplied to give the overall equilibrium constant: \(K_{overall} = K_1 \times K_2\).
Example: If reaction 1 has \(K_1 = 0.010\) and reaction 2 has \(K_2 = 50\), the overall reaction has \(K = 0.010 \times 50 = 0.50\).
Amorphous Solids
Solids that lack long-range repeating structural order, possessing only short-range order. Amorphous solids do not have sharp melting points and soften over a temperature range. Examples include glass, rubber, and many plastics.
Example: Window glass is an amorphous solid; when heated, it gradually softens rather than melting sharply at a single temperature.
Amphiprotic Substances
Species capable of acting as either a Brønsted-Lowry acid (proton donor) or a Brønsted-Lowry base (proton acceptor) depending on the reaction partner. Amphiprotic species contain both a transferable proton and a lone pair.
Example: The bicarbonate ion \(\ce{HCO3-}\) is amphiprotic: it donates a proton to form \(\ce{CO3^{2-}}\) or accepts a proton to form \(\ce{H2CO3}\).
Anion Formation
The process by which a neutral atom gains one or more electrons to become a negatively charged ion. Nonmetals typically form anions by gaining electrons to achieve a stable noble gas electron configuration.
Example: A chlorine atom (\(\ce{Cl}\)) gains one electron to form the chloride anion (\(\ce{Cl-}\)) with the electron configuration of argon.
Anode and Cathode
In electrochemical cells, the anode is the electrode where oxidation occurs (loss of electrons) and the cathode is the electrode where reduction occurs (gain of electrons). In galvanic cells the anode is negative; in electrolytic cells it is positive.
Example: In a zinc-copper galvanic cell, zinc is oxidized at the anode (\(\ce{Zn -> Zn^{2+} + 2e-}\)) and copper ions are reduced at the cathode (\(\ce{Cu^{2+} + 2e- -> Cu}\)).
Antibonding Molecular Orbitals
Molecular orbitals formed by the out-of-phase (destructive) combination of atomic orbitals, having higher energy than the original atomic orbitals and a node between the nuclei. Electrons in antibonding orbitals destabilize the bond.
Example: The \(\sigma^*_{1s}\) antibonding orbital in \(\ce{H2}\) is higher in energy than the 1s atomic orbitals and, if occupied, would weaken or eliminate the bond.
Arrhenius Equation
The mathematical relationship between the rate constant \(k\), activation energy \(E_a\), absolute temperature \(T\), and frequency factor \(A\): \(k = Ae^{-E_a/RT}\). It quantifies how temperature and activation energy affect reaction rates.
Example: If \(E_a = 50\) kJ/mol, doubling the rate constant requires raising the temperature from 300 K to about 318 K, as calculated from the Arrhenius equation.
Arrhenius Plot
A graph of \(\ln k\) versus \(1/T\) (reciprocal of absolute temperature), which yields a straight line with slope \(= -E_a/R\) and y-intercept \(= \ln A\). Used to experimentally determine activation energy and the frequency factor.
Example: Plotting \(\ln k\) vs. \(1/T\) for a reaction and finding a slope of \(-6020\) K gives \(E_a = 6020 \times 8.314 = 50.1\) kJ/mol.
Arrhenius Theory
The early acid-base theory stating that acids are substances that produce hydrogen ions (\(\ce{H+}\)) in aqueous solution and bases are substances that produce hydroxide ions (\(\ce{OH-}\)) in aqueous solution. Limited to aqueous systems.
Example: \(\ce{HNO3}\) is an Arrhenius acid because it dissociates in water to give \(\ce{H+}\); \(\ce{KOH}\) is an Arrhenius base because it dissociates to give \(\ce{OH-}\).
Assigning Oxidation Numbers
The process of determining the formal charge each atom in a compound would have if all bonds were completely ionic. Rules include: pure elements = 0; monatomic ions = charge; oxygen = −2 (usually); hydrogen = +1 (usually).
Example: In \(\ce{K2Cr2O7}\): K = +1, O = −2, so \(2(+1) + 2(Cr) + 7(−2) = 0\), giving Cr = +6.
Atmospheric Pressure
The force per unit area exerted by the weight of the Earth's atmosphere on a surface. Standard atmospheric pressure is defined as 101.325 kPa (1 atm = 760 mmHg = 760 torr) at sea level.
Example: A mercury barometer at sea level on a standard day shows a column height of exactly 760 mm, confirming standard atmospheric pressure.
Atomic Mass
The mass of an atom expressed in atomic mass units (amu or u), where 1 amu is defined as exactly 1/12 the mass of a carbon-12 atom. The atomic mass of an element on the periodic table is the weighted average of all naturally occurring isotopes.
Example: Carbon has an atomic mass of 12.011 amu, reflecting the natural mixture of \(\ce{^{12}C}\) (98.89%) and \(\ce{^{13}C}\) (1.11%).
Atomic Number
The number of protons in the nucleus of an atom of an element, denoted Z. The atomic number uniquely identifies an element and determines its position on the periodic table. All neutral atoms of an element have the same atomic number.
Example: Carbon has atomic number Z = 6, meaning every carbon atom has exactly 6 protons in its nucleus.
Atomic Radius
A measure of the size of an atom, typically defined as half the distance between the nuclei of two identical atoms bonded together. Atomic radius decreases across a period (left to right) and increases down a group.
Example: The covalent radius of chlorine is 99 pm, determined as half the bond length in \(\ce{Cl2}\) (198 pm).
Atomic Theory History
The chronological development of models explaining the nature of atoms, progressing from Dalton's solid sphere model (1803), through Thomson's plum pudding model (1897), Rutherford's nuclear model (1911), Bohr's planetary model (1913), to the quantum mechanical model (1926).
Atoms
The smallest unit of an element that retains the chemical identity of that element, consisting of a dense, positively charged nucleus containing protons and neutrons, surrounded by a cloud of negatively charged electrons. Atoms are electrically neutral.
Example: A single gold atom (\(\ce{Au}\)) retains the properties of gold and cannot be further divided by chemical means.
Aufbau Principle
The rule that electrons fill atomic orbitals in order of increasing energy, occupying the lowest available energy level before filling higher levels. The filling order can be determined using the (n + l) rule or the diagonal diagram.
Example: For nitrogen (Z = 7), the configuration is \(\ce{1s^2 2s^2 2p^3}\), filling 1s, then 2s, then three separate 2p orbitals.
Autoionization of Water
The reversible self-ionization reaction in which two water molecules transfer a proton, producing hydronium and hydroxide ions: \(\ce{2H2O (l) <=> H3O+ (aq) + OH- (aq)}\). The equilibrium constant is \(K_w = 1.0 \times 10^{-14}\) at 25°C.
Average Atomic Mass
The weighted average of the atomic masses of all naturally occurring isotopes of an element, calculated by multiplying each isotope's mass by its fractional natural abundance and summing the results. Reported in atomic mass units.
Example: Chlorine has two isotopes: \(\ce{^{35}Cl}\) (75.77%, 34.97 amu) and \(\ce{^{37}Cl}\) (24.23%, 36.97 amu); average mass = \(0.7577(34.97) + 0.2423(36.97) = 35.45\) amu.
Average Rate
The change in concentration of a reactant or product divided by the time interval over which that change occurs: \(\text{rate} = \frac{\Delta[\text{conc}]}{\Delta t}\). Average rate decreases over the course of most reactions as reactants are consumed.
Example: If \(\ce{[A]}\) drops from 0.80 M to 0.60 M in 40 seconds, the average rate = \(\frac{0.20 \text{ M}}{40 \text{ s}} = 0.0050\) M/s.
Avogadro's Law
The principle that equal volumes of all gases at the same temperature and pressure contain equal numbers of particles. Mathematically, \(V \propto n\) at constant T and P, or \(\frac{V_1}{n_1} = \frac{V_2}{n_2}\).
Example: If 1.0 mol of \(\ce{N2}\) occupies 22.4 L at STP, then 2.0 mol of any gas occupies 44.8 L at STP.
Avogadro's Number
The number of particles (atoms, molecules, ions, or formula units) in one mole of a substance, equal to \(6.022 \times 10^{23}\) mol\(^{-1}\). Defined as the number of atoms in exactly 12 grams of carbon-12.
Example: One mole of water contains \(6.022 \times 10^{23}\) water molecules, each composed of 2 hydrogen atoms and 1 oxygen atom.
Back Titration
An analytical technique in which an excess of a known reagent is added to an analyte, the reaction is allowed to complete, and the unreacted excess is titrated with a second standard solution. Used when the analyte does not react directly or quickly with the titrant.
Example: To determine the purity of an antacid tablet (\(\ce{CaCO3}\)), excess \(\ce{HCl}\) is added, then the unreacted \(\ce{HCl}\) is back-titrated with \(\ce{NaOH}\).
Balancing Equations
The process of adjusting stoichiometric coefficients in a chemical equation so that the number of atoms of each element is equal on both the reactant and product sides, satisfying conservation of mass.
Example: The unbalanced equation \(\ce{H2 + O2 -> H2O}\) is balanced by writing \(\ce{2H2 + O2 -> 2H2O}\).
Balancing Redox Equations
The process of balancing oxidation-reduction reactions by ensuring both mass and charge are conserved, using either the half-reaction method (separating oxidation and reduction half-reactions) or the oxidation number change method.
Example: In acidic solution, \(\ce{MnO4- + Fe^{2+} -> Mn^{2+} + Fe^{3+}}\) is balanced to \(\ce{MnO4- + 5Fe^{2+} + 8H+ -> Mn^{2+} + 5Fe^{3+} + 4H2O}\).
Base Dissociation Kb
The equilibrium constant for the reaction of a weak base with water to produce the conjugate acid and hydroxide ion: \(K_b = \frac{[\ce{BH+}][\ce{OH-}]}{[\ce{B}]}\). For a conjugate acid-base pair, \(K_a \times K_b = K_w\).
Example: Ammonia has \(K_b = 1.8 \times 10^{-5}\); its conjugate acid \(\ce{NH4+}\) has \(K_a = K_w/K_b = 5.6 \times 10^{-10}\).
Bases
Substances that accept protons (Brønsted-Lowry), donate electron pairs (Lewis), or produce \(\ce{OH-}\) in aqueous solution (Arrhenius). Bases turn red litmus blue, feel slippery, and react with acids in neutralization reactions.
Example: Sodium hydroxide (\(\ce{NaOH}\)) is a strong Arrhenius base that dissociates completely: \(\ce{NaOH -> Na+ + OH-}\).
Basic Salts
Salts that produce a basic (pH > 7) solution when dissolved in water because the anion is the conjugate base of a weak acid and undergoes hydrolysis to produce \(\ce{OH-}\).
Example: Sodium acetate (\(\ce{CH3COONa}\)) is a basic salt; \(\ce{CH3COO- + H2O <=> CH3COOH + OH-}\), raising the pH above 7.
Batteries and Fuel Cells
Electrochemical devices that convert chemical energy directly into electrical energy. Batteries use finite quantities of reactants sealed within the cell; fuel cells continuously oxidize an external fuel (typically \(\ce{H2}\)) as long as reactants are supplied.
Example: A hydrogen fuel cell combines \(\ce{H2}\) and \(\ce{O2}\) electrochemically to produce electricity and water, with no combustion byproducts.
Beer-Lambert Law
The relationship between the absorbance of a solution, its molar absorptivity, path length, and concentration: \(A = \varepsilon lc\), where \(A\) is absorbance, \(\varepsilon\) is molar absorptivity (L mol\(^{-1}\) cm\(^{-1}\)), \(l\) is path length, and \(c\) is concentration.
Example: A solution with \(\varepsilon = 1500\) L mol\(^{-1}\) cm\(^{-1}\) in a 1.00 cm cell at \(c = 0.010\) M gives \(A = 1500 \times 1.00 \times 0.010 = 15\).
Bent Geometry
A molecular geometry in which a central atom is bonded to two other atoms with one or more lone pairs, producing a bond angle less than 180°. Water (\(\ce{H2O}\)) has a bent geometry with a bond angle of approximately 104.5°.
Example: Sulfur dioxide (\(\ce{SO2}\)) has a bent molecular geometry due to one lone pair on sulfur, giving a bond angle of about 119°.
Bimolecular Reactions
Elementary reaction steps in which two species (atoms or molecules) collide and react simultaneously. The rate law for a bimolecular elementary step is second order overall: rate = \(k[\text{A}][\text{B}]\).
Example: The elementary step \(\ce{NO + O3 -> NO2 + O2}\) is bimolecular; rate = \(k[\ce{NO}][\ce{O3}]\).
Binary Acid Trends
The pattern that acid strength of binary acids (acids with only hydrogen and one other element) increases down a group due to decreasing bond strength, and increases across a period due to increasing electronegativity of the nonmetal.
Example: Acid strength order: \(\ce{HF} < \ce{HCl} < \ce{HBr} < \ce{HI}\) (down Group 17, bond strength decreases); \(\ce{CH4} < \ce{NH3} < \ce{H2O} < \ce{HF}\) (across Period 2).
Bohr Model
The atomic model proposed by Niels Bohr in 1913 in which electrons orbit the nucleus in fixed circular paths (shells) of quantized energy. Electrons emit or absorb photons when transitioning between shells; \(E = -2.18 \times 10^{-18}\) J\((1/n^2)\).
Example: In the Bohr model, the red line (656 nm) in the hydrogen spectrum corresponds to an electron falling from \(n = 3\) to \(n = 2\).
Boiling and Condensation
Boiling is the phase transition from liquid to gas throughout the bulk of the liquid, occurring when vapor pressure equals external pressure. Condensation is the reverse process, gas converting to liquid upon sufficient cooling or increased pressure.
Example: Water boils at 100°C at 1 atm because its vapor pressure reaches 101.325 kPa at that temperature.
Boiling Point Elevation
The colligative property in which the boiling point of a solvent increases upon addition of a nonvolatile solute: \(\Delta T_b = iK_b m\), where \(i\) is the van't Hoff factor, \(K_b\) is the ebullioscopic constant, and \(m\) is molality.
Example: Dissolving 1.00 mol of sucrose (non-electrolyte, \(i = 1\)) in 1.00 kg of water (\(K_b = 0.512\) °C/m) raises the boiling point by \(0.512\)°C to \(100.512\)°C.
Boltzmann Equation
The equation \(S = k_B \ln W\) relating the entropy \(S\) of a system to the number of microstates \(W\) (the number of energetically equivalent arrangements of the system's particles). \(k_B = 1.381 \times 10^{-23}\) J/K is Boltzmann's constant.
Example: A system with \(W = 10^{20}\) microstates has \(S = (1.381 \times 10^{-23})(\ln 10^{20}) = 6.36 \times 10^{-22}\) J/K.
Bond Angles
The angles between adjacent bonds at a central atom in a molecule, determined by the electron geometry and the presence of lone pairs. Lone pairs exert greater repulsion than bonding pairs, compressing bond angles below ideal values.
Example: Methane (\(\ce{CH4}\)) has ideal tetrahedral bond angles of 109.5°; ammonia (\(\ce{NH3}\)) has 107° due to one lone pair; water (\(\ce{H2O}\)) has 104.5° due to two lone pairs.
Bond Energy
The energy required to break one mole of a specified bond in the gas phase, homolytically (each atom receives one electron). Stronger bonds have higher bond energies. Bond energy can be used to estimate \(\Delta H\) for reactions.
Example: The \(\ce{H-H}\) bond energy is 436 kJ/mol; breaking one mole of \(\ce{H2}\) bonds requires 436 kJ of energy input.
Bond Enthalpy
The average energy required to break one mole of a particular type of bond in gaseous molecules, used to estimate reaction enthalpy: \(\Delta H_{rxn} \approx \sum \text{bonds broken} - \sum \text{bonds formed}\). Values are averages over many compounds.
Example: Using bond enthalpies: \(\ce{H2 + Cl2 -> 2HCl}\); \(\Delta H = (436 + 243) - 2(432) = -185\) kJ/mol.
Bond Enthalpy Calculations
The use of tabulated average bond energies to estimate the enthalpy change of a reaction by summing the energies of bonds broken (endothermic, positive) and subtracting the energies of bonds formed (exothermic, negative).
Example: For \(\ce{CH4 + 2O2 -> CO2 + 2H2O}\): bonds broken = 4(C-H) + 2(O=O); bonds formed = 2(C=O) + 4(O-H); \(\Delta H \approx -803\) kJ/mol.
Bond Formation Energy
The energy released when a chemical bond forms between two atoms in the gas phase. Bond formation is always exothermic; the energy released equals the bond dissociation energy. Stronger bonds release more energy upon formation.
Example: When one mole of \(\ce{H-F}\) bonds forms from gaseous H and F atoms, 569 kJ of energy is released.
Bond Length
The average distance between the nuclei of two bonded atoms at their equilibrium (minimum energy) separation. Bond length decreases as bond order increases and as the atoms involved become smaller.
Example: Carbon-carbon bond lengths: C-C single bond = 154 pm; C=C double bond = 134 pm; C≡C triple bond = 120 pm.
Bond Order
The number of bonding electron pairs shared between two atoms in a molecule. A single bond has order 1, double bond order 2, triple bond order 3. Higher bond order means shorter, stronger bonds.
Example: In \(\ce{N2}\), the triple bond has bond order 3, making it very short (110 pm) and very strong (945 kJ/mol).
Bond Order from MO Theory
In molecular orbital theory, bond order is calculated as \(\frac{(\text{bonding electrons}) - (\text{antibonding electrons})}{2}\). A bond order of zero means no stable bond exists; fractional bond orders are possible.
Example: For \(\ce{O2}\): 8 bonding electrons, 4 antibonding electrons; bond order = \((8-4)/2 = 2\), consistent with the observed double bond.
Bond Polarity
The unequal sharing of electrons in a covalent bond due to a difference in electronegativity between the two bonded atoms. The more electronegative atom carries a partial negative charge (\(\delta-\)) and the less electronegative carries a partial positive charge (\(\delta+\)).
Example: In \(\ce{HCl}\), chlorine (electronegativity 3.16) is more electronegative than hydrogen (2.20), so the bond is polar: \(\text{H}^{\delta+}\)-\(\text{Cl}^{\delta-}\).
Bonding Molecular Orbitals
Molecular orbitals formed by the in-phase (constructive) combination of atomic orbitals, having lower energy than the original atomic orbitals. Electrons in bonding molecular orbitals stabilize the bond and hold the atoms together.
Example: The \(\sigma_{1s}\) bonding molecular orbital of \(\ce{H2}\) is lower in energy than the 1s atomic orbitals, so filling it with two electrons stabilizes the molecule.
Bonding Pairs
Pairs of electrons shared between two atoms in a covalent bond. Each bonding pair constitutes one bond; double bonds contain two bonding pairs and triple bonds contain three. Bonding pairs are located between the two bonded nuclei.
Example: In \(\ce{H2O}\), each \(\ce{O-H}\) bond contains one bonding pair of electrons (two electrons shared between oxygen and hydrogen).
Born-Haber Cycle
A thermodynamic cycle that applies Hess's Law to calculate lattice energy of an ionic compound from experimentally measurable quantities: heat of formation, ionization energy, electron affinity, bond dissociation energy, and sublimation energy.
Example: For \(\ce{NaCl}\): lattice energy = \(\Delta H_f - \Delta H_{sub}(\ce{Na}) - \frac{1}{2}D(\ce{Cl2}) - IE_1(\ce{Na}) - EA(\ce{Cl}) = -787\) kJ/mol.
Boyle's Law
The inverse relationship between pressure and volume of a fixed amount of gas at constant temperature: \(P_1V_1 = P_2V_2\). As pressure increases, volume decreases proportionally.
Example: If a gas occupies 2.0 L at 1.0 atm, it will occupy 1.0 L when pressure is doubled to 2.0 atm (at constant T).
Bronsted-Lowry Theory
The acid-base theory defining an acid as a proton (\(\ce{H+}\)) donor and a base as a proton acceptor in a chemical reaction. This theory extends beyond aqueous solutions and explains acid-base behavior of species like \(\ce{NH3}\).
Example: In \(\ce{CH3COOH + H2O <=> CH3COO- + H3O+}\), acetic acid donates a proton (acid) to water (base); water acts as the Brønsted-Lowry base.
Buffer Capacity
The amount of strong acid or strong base that a buffer can neutralize before a significant change in pH occurs. Buffer capacity is greatest when the concentrations of the weak acid and conjugate base are high and equal (pH = pKa).
Example: A buffer with 0.50 M \(\ce{CH3COOH}\) and 0.50 M \(\ce{CH3COO-}\) has greater buffer capacity than one with 0.05 M of each.
Buffer Composition
The pair of chemical species that make up a buffer solution: a weak acid and its conjugate base, or a weak base and its conjugate acid. The optimal pH range is within ±1 pH unit of the weak acid's pKa.
Example: An acetic acid/acetate buffer (\(\ce{CH3COOH}\)/\(\ce{CH3COO-}\), pKa = 4.74) effectively buffers in the range pH 3.74–5.74.
Buffer pH Calculations
The use of the Henderson-Hasselbalch equation to determine the pH of a buffer solution: \(\text{pH} = \text{p}K_a + \log\frac{[\text{A}^-]}{[\text{HA}]}\). Also used to determine the ratio of conjugate base to acid needed for a target pH.
Example: A buffer of 0.30 M \(\ce{CH3COO-}\) and 0.10 M \(\ce{CH3COOH}\) has \(\text{pH} = 4.74 + \log(0.30/0.10) = 4.74 + 0.48 = 5.22\).
Buffer Preparation
The procedure for making a buffer solution of a specified pH by choosing a weak acid with a pKa near the target pH and adjusting the ratio of acid to conjugate base using the Henderson-Hasselbalch equation.
Example: To prepare a pH 5.0 acetate buffer (pKa = 4.74), mix acid and conjugate base in the ratio \(\ce{[CH3COO-]/[CH3COOH]} = 10^{5.0-4.74} = 1.82:1\).
Buffer Region
The portion of a titration curve where pH changes slowly upon addition of small amounts of strong acid or base, corresponding to the region between 10% and 90% completion of the titration of a weak acid (or base) with its strong counterpart.
Example: In the titration of acetic acid with \(\ce{NaOH}\), the buffer region extends from pH ≈ 3.74 to pH ≈ 5.74, centered on pH = 4.74 (the pKa).
Buffer Solutions
Aqueous solutions that resist significant changes in pH upon addition of small amounts of strong acid or base, prepared by combining a weak acid with its conjugate base (or weak base with its conjugate acid) in significant concentrations.
Example: A mixture of \(\ce{NH3}\) and \(\ce{NH4Cl}\) in water forms a buffer that maintains pH near 9.25 even when small amounts of \(\ce{HCl}\) or \(\ce{NaOH}\) are added.
Calorimetry
The experimental technique for measuring the heat exchanged in chemical reactions or physical processes by monitoring temperature changes in a known mass of substance with a known heat capacity. Assumes the calorimeter is thermally isolated.
Example: Burning 1.00 g of glucose in a bomb calorimeter raises the temperature of 1000 g of water by 6.20°C, allowing calculation of the heat of combustion.
Calorimetry Calculations
The mathematical determination of heat absorbed or released using \(q = mc\Delta T\) (for solution calorimetry) or \(q = C_{cal}\Delta T\) (for bomb calorimetry), where \(m\) is mass, \(c\) is specific heat capacity, \(\Delta T\) is temperature change, and \(C_{cal}\) is calorimeter heat capacity.
Example: If 50.0 g of water absorbs heat and rises from 22.0°C to 35.0°C: \(q = (50.0)(4.184)(13.0) = 2720\) J = 2.72 kJ.
Capillary Action
The ability of a liquid to flow in narrow tubes or porous materials against gravity due to the interplay of adhesive forces (liquid-surface attraction) and cohesive forces (liquid-liquid attraction). Stronger adhesion than cohesion causes the liquid to rise.
Example: Water rises in a glass capillary tube because water's adhesion to glass is stronger than water's cohesion to itself, producing a concave meniscus.
Catalyst and Equilibrium
A catalyst increases the rates of both forward and reverse reactions equally, so it does not change the equilibrium constant \(K\) or the equilibrium position. It only decreases the time required to reach equilibrium.
Example: Adding \(\ce{V2O5}\) catalyst to the \(\ce{SO2 + O2 <=> SO3}\) equilibrium reaches the same final concentrations faster but does not change \(K\).
Catalyst Effect on Ea
A catalyst provides an alternative reaction pathway with a lower activation energy than the uncatalyzed reaction. By reducing \(E_a\), the catalyst increases the fraction of collisions that have sufficient energy to react, dramatically increasing the rate.
Example: The enzyme catalase lowers the activation energy for hydrogen peroxide decomposition from 75 kJ/mol to about 8 kJ/mol, making the reaction millions of times faster.
Catalysis
The process of increasing the rate of a chemical reaction by adding a substance (catalyst) that participates in the mechanism but is regenerated at the end, providing a lower-energy alternative pathway. The catalyst is not consumed.
Example: Platinum catalysis in a catalytic converter facilitates rapid oxidation of CO and unburned hydrocarbons at lower temperatures than uncatalyzed combustion.
Catalyzed vs Uncatalyzed
Comparison of reaction pathways with and without a catalyst. A catalyzed pathway has a lower activation energy and different intermediate steps, but the same reactants, products, and overall enthalpy change. The equilibrium position is unaffected.
Example: The uncatalyzed decomposition of \(\ce{H2O2}\) (gas) has \(E_a \approx 75\) kJ/mol; with iodide catalyst, \(E_a\) drops to about 57 kJ/mol, greatly accelerating the reaction.
Cation Formation
The process by which a neutral atom loses one or more electrons to become a positively charged ion. Metals typically form cations by losing valence electrons to achieve a stable electron configuration (often noble gas configuration or pseudo-noble gas).
Example: A sodium atom loses one electron to form the sodium cation: \(\ce{Na -> Na+ + e-}\); \(\ce{Na+}\) has the same electron configuration as neon.
Cell Notation
A shorthand representation of an electrochemical cell using a defined format: anode material | anode solution || cathode solution | cathode material. A single vertical line represents a phase boundary; double vertical lines represent the salt bridge.
Example: The zinc-copper galvanic cell is written as: \(\ce{Zn (s) | Zn^{2+} (aq) || Cu^{2+} (aq) | Cu (s)}\).
Cell Potential Calculation
The calculation of the electromotive force (EMF) of an electrochemical cell as \(E^\circ_{cell} = E^\circ_{cathode} - E^\circ_{anode}\), where each standard reduction potential is looked up from a standard reduction potential table.
Example: For Zn-Cu cell: \(E^\circ_{cell} = E^\circ_{Cu^{2+}/Cu} - E^\circ_{Zn^{2+}/Zn} = +0.34 - (-0.76) = +1.10\) V.
Charles's Law
The direct proportionality between volume and absolute temperature of a fixed amount of gas at constant pressure: \(\frac{V_1}{T_1} = \frac{V_2}{T_2}\). Temperature must be in Kelvin.
Example: A gas at 273 K occupying 1.0 L will expand to 2.0 L when heated to 546 K at constant pressure.
Chemical Analysis
Experimental procedures used to determine the composition, identity, or quantity of substances in a sample. Includes qualitative analysis (identifying components) and quantitative analysis (measuring amounts) using techniques such as titration, spectroscopy, and gravimetry.
Example: Flame tests and precipitation reactions are used in qualitative chemical analysis to identify the cations present in an unknown solution.
Chemical Bonds
Attractive forces between atoms or ions that hold them together in compounds. Primary types include ionic bonds (electrostatic attraction between ions), covalent bonds (shared electron pairs), and metallic bonds (delocalized electron sea in metals).
Example: In \(\ce{NaCl}\), ionic bonds form between \(\ce{Na+}\) and \(\ce{Cl-}\); in \(\ce{Cl2}\), a covalent bond forms by sharing two electrons between chlorine atoms.
Chemical Changes
Processes in which the chemical composition of substances changes, forming new substances with different properties. Indicators include color change, gas production, precipitate formation, energy change, and irreversibility under ordinary conditions.
Example: Burning wood is a chemical change; cellulose reacts with oxygen to form carbon dioxide and water vapor, producing entirely new substances.
Chemical Equations
Symbolic representations of chemical reactions showing the formulas of reactants on the left, an arrow indicating transformation, and formulas of products on the right, with coefficients indicating molar ratios and state symbols indicating physical states.
Example: \(\ce{2H2 (g) + O2 (g) -> 2H2O (l)}\) is a balanced chemical equation for the combustion of hydrogen.
Chemical Equilibrium
The dynamic state of a reversible reaction in which the rate of the forward reaction equals the rate of the reverse reaction, resulting in constant concentrations of reactants and products over time. The system is at equilibrium only in a closed system.
Example: In the reaction \(\ce{N2 (g) + 3H2 (g) <=> 2NH3 (g)}\), equilibrium is reached when the rate of \(\ce{NH3}\) formation equals the rate of its decomposition.
Chemical Properties
Characteristics of a substance that describe its ability to change into different substances through chemical reactions. Chemical properties include reactivity, flammability, acidity, oxidation states, and ability to corrode.
Example: Iron's chemical property of rusting describes its tendency to react with oxygen and water to form iron oxides.
Closed Systems
A thermodynamic system that can exchange energy (heat and work) with its surroundings but cannot exchange matter. Closed systems maintain constant composition while allowing energy flow.
Example: A sealed, rigid reaction vessel is a closed system; energy is exchanged as heat but no matter enters or leaves.
Coefficients
The numbers placed before chemical formulas in a balanced equation indicating the relative number of moles of each substance involved in the reaction. Coefficients can be used as mole ratios in stoichiometric calculations.
Example: In \(\ce{2H2 + O2 -> 2H2O}\), the coefficients 2:1:2 mean that 2 mol of \(\ce{H2}\) reacts with 1 mol of \(\ce{O2}\) to produce 2 mol of \(\ce{H2O}\).
Coffee Cup Calorimeter
A simple constant-pressure calorimeter made from two nested Styrofoam coffee cups, used to measure heat changes in aqueous reactions. Heat is calculated using \(q = mc\Delta T\), assuming the cup absorbs negligible heat.
Example: Mixing 50 mL of 1.0 M \(\ce{HCl}\) and 50 mL of 1.0 M \(\ce{NaOH}\) in a coffee cup calorimeter and measuring the temperature rise determines the enthalpy of neutralization.
Colligative Properties
Properties of solutions that depend on the number of dissolved solute particles rather than the chemical identity of the solute. The four colligative properties are vapor pressure lowering, boiling point elevation, freezing point depression, and osmotic pressure.
Example: Adding 1 mol of \(\ce{NaCl}\) (which produces 2 mol ions) has twice the effect on boiling point elevation as adding 1 mol of glucose.
Collision Theory
The model explaining reaction rates based on the principle that reactions occur only when reactant molecules collide with sufficient energy (at least \(E_a\)) and the correct geometric orientation. Rate depends on collision frequency, collision energy, and orientation.
Example: Increasing temperature increases collision frequency and the fraction of collisions with energy exceeding \(E_a\), both of which increase the reaction rate.
Color of Solutions
The characteristic color of a solution results from the absorption of specific wavelengths of visible light by dissolved species; the observed color is the complementary color of the absorbed wavelength. Transition metal ions and conjugated organic molecules often impart color.
Example: \(\ce{Cu^{2+}(aq)}\) absorbs red/orange light and appears blue; \(\ce{Fe^{3+}(aq)}\) absorbs blue/violet light and appears yellow-orange.
Common Ion Effect
The decrease in solubility of a sparingly soluble salt when a soluble salt sharing a common ion is added to the solution. The additional common ion shifts the solubility equilibrium toward the undissolved solid, consistent with Le Chatelier's Principle.
Example: The molar solubility of \(\ce{AgCl}\) in pure water is \(1.3 \times 10^{-5}\) M, but in 0.10 M \(\ce{NaCl}\) it decreases to \(1.8 \times 10^{-9}\) M due to the common \(\ce{Cl-}\) ion.
Complete Ionic Equations
Chemical equations that show all soluble ionic compounds as separate hydrated ions, covalent molecules and insoluble compounds in their molecular form, and are balanced for both atoms and charges.
Example: \(\ce{Na+ (aq) + OH- (aq) + H+ (aq) + Cl- (aq) -> Na+ (aq) + Cl- (aq) + H2O (l)}\) is the complete ionic equation for \(\ce{NaOH + HCl -> NaCl + H2O}\).
Complex Ion Formation
The reaction in which a metal cation (Lewis acid) combines with ligands (Lewis bases) through coordinate covalent bonds to form a coordination complex. Complex ion formation significantly increases the solubility of sparingly soluble salts.
Example: \(\ce{AgCl (s) + 2NH3 (aq) -> [Ag(NH3)2]+ (aq) + Cl- (aq)}\): silver chloride dissolves in ammonia due to complex ion formation.
Compounds
Pure substances formed when two or more elements combine chemically in fixed, definite mass ratios, with properties entirely different from those of the constituent elements. Compounds can be separated only by chemical means.
Example: Water (\(\ce{H2O}\)) is a compound of hydrogen and oxygen in a fixed 2:1 molar ratio; its properties differ completely from those of hydrogen gas and oxygen gas.
Concentration and Rate
The dependence of reaction rate on the concentrations of reactants, expressed in the rate law \(\text{rate} = k[\text{A}]^m[\text{B}]^n\). Increasing reactant concentration generally increases reaction rate by increasing collision frequency.
Example: For the reaction \(\ce{2NO + Cl2 -> 2NOCl}\) with rate \(= k[\ce{NO}]^2[\ce{Cl2}]\), doubling \(\ce{[NO]}\) quadruples the rate while doubling \(\ce{[Cl2]}\) only doubles the rate.
Concentration Changes
The shift in equilibrium position that occurs when the concentration of a reactant or product is altered in a system at equilibrium. Adding a reactant shifts equilibrium toward products; removing a product also shifts toward products (Le Chatelier's Principle).
Example: Adding more \(\ce{CO2}\) to a \(\ce{CO2 + H2O <=> H2CO3}\) equilibrium shifts it to the right, increasing \(\ce{[H2CO3]}\) until a new equilibrium is established.
Concentration Units
Quantitative measures of the amount of solute dissolved in a given amount of solution or solvent. Common units include molarity (mol/L), molality (mol/kg solvent), mole fraction, mass percent, and parts per million (ppm).
Example: A solution of 0.50 mol \(\ce{NaCl}\) dissolved in 500 mL of solution has a molarity of 1.0 M.
Concentration vs Time
Graphical or mathematical representation of how reactant or product concentrations change over the course of a reaction. The shape of the curve depends on the reaction order: linear for zero order, exponential decay for first order, hyperbolic for second order.
Example: For a first-order reaction, a plot of \(\ln[\text{A}]\) versus time gives a straight line with slope \(= -k\).
Conjugate Acid
The species formed when a Brønsted-Lowry base accepts a proton. The conjugate acid has one more proton than its parent base and a charge that is one unit more positive. Strong bases have very weak conjugate acids.
Example: When \(\ce{NH3}\) acts as a base and accepts a proton, it forms its conjugate acid \(\ce{NH4+}\).
Conjugate Acid-Base Pairs
Two species related by the transfer of a single proton: the acid and the base it produces upon donating a proton (or the base and the acid it produces upon accepting a proton). They differ by exactly one \(\ce{H+}\).
Example: \(\ce{CH3COOH}\)/\(\ce{CH3COO-}\) and \(\ce{H3O+}\)/\(\ce{H2O}\) are two conjugate acid-base pairs in the reaction \(\ce{CH3COOH + H2O <=> CH3COO- + H3O+}\).
Conjugate Base
The species formed when a Brønsted-Lowry acid donates a proton. The conjugate base has one fewer proton than its parent acid and a charge that is one unit more negative. Strong acids have very weak conjugate bases.
Example: When \(\ce{HCl}\) donates a proton, it forms its conjugate base \(\ce{Cl-}\); since \(\ce{HCl}\) is a strong acid, \(\ce{Cl-}\) is an extremely weak base.
Conservation Laws
Fundamental physical laws stating that certain properties of isolated systems remain constant during physical and chemical processes. In chemistry, the most important are conservation of mass (matter is not created or destroyed) and conservation of energy (first law of thermodynamics).
Conservation of Charge
The principle that the total electrical charge of an isolated system remains constant during chemical reactions. In balanced ionic equations, the total charge on the left must equal the total charge on the right.
Example: In \(\ce{Zn + Cu^{2+} -> Zn^{2+} + Cu}\): left side charge = 0 + 2+ = +2; right side = 2+ + 0 = +2. Charge is conserved.
Conservation of Mass
The law that matter is neither created nor destroyed in a chemical reaction; the total mass of reactants equals the total mass of products. This principle underlies the requirement to balance chemical equations.
Example: When 28 g of iron reacts with 16 g of sulfur, exactly 44 g of iron(II) sulfide is produced, confirming conservation of mass.
Combustion Analysis
An analytical method for determining the empirical formula of an organic compound by burning it completely in excess oxygen and measuring the masses of \(\ce{CO2}\) and \(\ce{H2O}\) produced. From these masses, the moles of C, H, and O are calculated.
Example: Burning 0.255 g of a compound produces 0.561 g \(\ce{CO2}\) and 0.306 g \(\ce{H2O}\); this gives the mole ratio C:H and allows determination of the empirical formula.
Combustion Reactions
Reactions in which a substance burns rapidly in oxygen, producing oxides of the elements in the substance. Complete combustion of hydrocarbons produces \(\ce{CO2}\) and \(\ce{H2O}\); incomplete combustion may produce CO or carbon (soot).
Cooling Curves
Graphs of temperature versus time as a substance releases heat and cools. Horizontal portions on cooling curves represent phase transitions (condensation or freezing) where heat is released at constant temperature until the phase change is complete.
Example: As liquid water cools from 50°C, the temperature drops until 0°C, then remains at 0°C while it freezes (releasing 334 J/g), then drops again after all water has frozen.
Core Electrons
Electrons in an atom that occupy filled inner shells below the valence shell. Core electrons are tightly bound to the nucleus, do not participate in chemical bonding, and shield the valence electrons from the full nuclear charge.
Example: In silicon (\(\ce{1s^2 2s^2 2p^6 3s^2 3p^2}\)), the 10 inner electrons (1s, 2s, 2p) are core electrons; the 4 electrons in the 3s and 3p subshells are valence electrons.
Corrosion
The gradual electrochemical degradation of metals through oxidation-reduction reactions with environmental agents such as oxygen and water. Corrosion causes loss of structural integrity and economic damage to metal structures.
Example: Rusting of iron: \(\ce{4Fe (s) + 3O2 (g) + 6H2O (l) -> 4Fe(OH)3 (s)}\); iron is oxidized and oxygen is reduced.
Coulombic Attraction
The electrostatic attractive force between oppositely charged particles, described by Coulomb's law: \(F = k\frac{q_1 q_2}{r^2}\). Coulombic attraction determines the strength of ionic bonds, lattice energy, ionization energy, and the stability of electron configurations.
Example: \(\ce{Mg^{2+}}\) and \(\ce{O^{2-}}\) have stronger coulombic attraction than \(\ce{Na+}\) and \(\ce{F-}\) because the charges are larger, giving MgO a much higher lattice energy.
Critical Point
The endpoint of the liquid-vapor coexistence curve on a phase diagram, defined by the critical temperature (\(T_c\)) and critical pressure (\(P_c\)). Above the critical temperature, a substance cannot be liquefied by pressure alone and exists as a supercritical fluid.
Example: Water has a critical point at \(T_c = 374°C\) and \(P_c = 218\) atm; above these conditions, water exists as a supercritical fluid used in industrial extraction processes.
Crystal Lattice
The regular, repeating three-dimensional arrangement of atoms, ions, or molecules in a crystalline solid. The smallest repeating unit is called the unit cell. The type of lattice determines the physical properties of the solid.
Example: \(\ce{NaCl}\) has a face-centered cubic crystal lattice in which each \(\ce{Na+}\) is surrounded by 6 \(\ce{Cl-}\) ions and each \(\ce{Cl-}\) is surrounded by 6 \(\ce{Na+}\) ions.
Crystalline Solids
Solids characterized by a long-range, repeating three-dimensional arrangement of their constituent particles. Crystalline solids have definite geometric shapes, sharp melting points, and anisotropic physical properties. Types include ionic, metallic, covalent network, and molecular.
Example: Table salt (\(\ce{NaCl}\)) is a crystalline ionic solid that cleaves along flat planes and melts sharply at 801°C.
Dalton's Law
The principle that the total pressure of a mixture of non-reacting gases equals the sum of the partial pressures of each individual gas: \(P_{total} = P_1 + P_2 + P_3 + \ldots\) Each gas behaves independently.
Example: A gas mixture contains \(\ce{N2}\) at 0.78 atm, \(\ce{O2}\) at 0.21 atm, and \(\ce{Ar}\) at 0.01 atm; total pressure = 1.00 atm.
Data Collection
The systematic recording of observations and measurements during an experiment, including quantitative measurements (with units and significant figures), qualitative observations, and conditions of the experiment. Valid data collection is essential for reproducible science.
Decomposition Reactions
Chemical reactions in which a single compound breaks down into two or more simpler substances. Decomposition is typically endothermic and requires energy input such as heat, light, or electricity.
Example: \(\ce{2H2O2 (l) -> 2H2O (l) + O2 (g)}\); hydrogen peroxide decomposes into water and oxygen gas.
Delta G and E Relation
The relationship between Gibbs free energy change and electrochemical cell potential: \(\Delta G = -nFE\), where \(n\) is moles of electrons transferred, \(F\) is Faraday's constant (96,485 C/mol), and \(E\) is cell potential. Spontaneous cells (\(E > 0\)) have \(\Delta G < 0\).
Example: For a cell with \(n = 2\) and \(E = 1.10\) V: \(\Delta G = -2(96485)(1.10) = -212,000\) J = \(-212\) kJ.
Density
The mass per unit volume of a substance, typically expressed in g/mL (for liquids and solids) or g/L (for gases): \(d = m/V\). Density is an intensive physical property that can be used to identify substances.
Example: The density of water at 4°C is exactly 1.000 g/mL; gold has a density of 19.3 g/mL, making it about 19 times denser than water.
Determining Reaction Order
The process of finding the exponents in the rate law experimentally by using the method of initial rates (comparing how rate changes with concentration) or by graphical analysis of concentration-versus-time data.
Example: If doubling \([\ce{A}]\) doubles the rate, the reaction is first order in A; if doubling \([\ce{A}]\) quadruples the rate, it is second order in A.
Deviations from Ideality
The departure of real gas behavior from ideal gas law predictions, most significant at high pressures (where intermolecular repulsions dominate, reducing compressibility) and low temperatures (where intermolecular attractions reduce pressure below ideal).
Example: At 200 atm, \(\ce{CO2}\) occupies significantly less volume than predicted by the ideal gas law due to strong intermolecular attractions between \(\ce{CO2}\) molecules.
Dilute Acid Calculations
The mathematical determination of \(\ce{[H+]}\), pH, or other properties of solutions of weak acids at low concentration, where the quadratic formula or simplifying approximations must be applied carefully to the acid dissociation equilibrium.
Dilution Calculations
The determination of a new concentration when a solution is diluted by adding solvent, using the relationship \(M_1V_1 = M_2V_2\), which states that the number of moles of solute remains constant during dilution.
Example: Diluting 25.0 mL of 6.0 M \(\ce{HCl}\) to 150 mL gives \(M_2 = (6.0)(25.0)/150 = 1.0\) M \(\ce{HCl}\).
Dimensional Analysis
A problem-solving method in which units are treated as algebraic quantities to convert between different unit systems or to set up calculations. Conversion factors are applied so that unwanted units cancel and desired units remain.
Example: Convert 5.0 miles to meters: \(5.0 \text{ mi} \times \frac{1609 \text{ m}}{1 \text{ mi}} = 8045 \text{ m} \approx 8.0 \times 10^3 \text{ m}\).
Dipole Moment
A quantitative measure of the polarity of a molecule, defined as the product of the magnitude of partial charges and the distance between them: \(\mu = q \times d\). Expressed in debyes (D); a nonzero net dipole moment indicates a polar molecule.
Example: Water has a dipole moment of 1.85 D due to two polar O-H bonds oriented at 104.5°; their vector sum is nonzero because the molecule is bent.
Dipole-Dipole Forces
Intermolecular attractive forces between the permanent dipoles of polar molecules. The positive end of one polar molecule attracts the negative end of a neighboring molecule. Dipole-dipole forces are stronger than London dispersion forces for molecules of similar size.
Example: \(\ce{HCl}\) molecules experience dipole-dipole forces because each molecule has a permanent dipole; this raises the boiling point compared to noble gases of similar mass.
Diprotic Acid Equilibria
The two-step dissociation equilibria of diprotic acids, each described by its own equilibrium constant: \(K_{a1}\) (first dissociation) and \(K_{a2}\) (second dissociation). Always \(K_{a1} > K_{a2}\) because removing a proton from an anion is harder than from a neutral acid.
Example: For \(\ce{H2SO4}\): \(K_{a1}\) is very large (strong acid, first dissociation complete) and \(K_{a2} = 1.2 \times 10^{-2}\) (second dissociation, weak).
Disproportionation
A redox reaction in which the same element is simultaneously oxidized and reduced, with one species of the element being oxidized and another (or the same molecule) being reduced.
Example: \(\ce{2H2O2 -> 2H2O + O2}\): oxygen in \(\ce{H2O2}\) (oxidation state −1) is both oxidized to 0 (in \(\ce{O2}\)) and reduced to −2 (in \(\ce{H2O}\)).
Double Bonds
Covalent bonds consisting of one sigma (\(\sigma\)) bond and one pi (\(\pi\)) bond between two atoms, sharing four electrons total. Double bonds are shorter and stronger than single bonds between the same atoms but longer and weaker than triple bonds.
Example: The \(\ce{C=C}\) double bond in ethene (\(\ce{C2H4}\)) has a bond length of 134 pm and bond energy of 614 kJ/mol, compared to 154 pm and 347 kJ/mol for a C-C single bond.
Double Replacement
A reaction type in which the cations of two ionic compounds exchange partners, producing two new compounds: \(\ce{AB + CD -> AD + CB}\). Driving forces include precipitate formation, gas evolution, or weak electrolyte formation.
Example: \(\ce{AgNO3 (aq) + NaCl (aq) -> AgCl (s) + NaNO3 (aq)}\); the driving force is formation of the \(\ce{AgCl}\) precipitate.
Driving Force of Reactions
The thermodynamic or chemical factors that cause a reaction to proceed spontaneously: formation of a precipitate, formation of a weak electrolyte (such as water), evolution of a gas, transfer of electrons (redox), or decrease in Gibbs free energy.
Example: The neutralization \(\ce{H+ + OH- -> H2O}\) is driven by the formation of water, a weak electrolyte; the reaction goes essentially to completion.
Dynamic Equilibrium
The state of a reversible reaction in which the forward and reverse reactions occur simultaneously at equal rates, resulting in no net change in concentrations. The system is dynamic (reactions continue) but appears static (macroscopic properties are constant).
Example: In a sealed bottle of liquid water, the rate of evaporation equals the rate of condensation; water molecules continuously move between phases but the vapor pressure remains constant.
Effect of Catalyst on Eq
A catalyst does not change the equilibrium constant \(K\) or the equilibrium concentrations of reactants and products. It lowers the activation energy for both forward and reverse reactions equally, allowing equilibrium to be reached more quickly.
Effective Collisions
Collisions between reactant molecules that result in a chemical reaction, requiring both sufficient energy (greater than or equal to \(E_a\)) and correct geometric orientation of the reactant molecules. Only a small fraction of all collisions are effective.
Example: In the reaction of \(\ce{H2 + I2 -> 2HI}\), molecules must collide along the H-H and I-I bond axes for bonds to break and reform correctly; head-on or sideways collisions are ineffective.
Effective Nuclear Charge
The net nuclear charge experienced by a valence electron after accounting for the shielding effect of core electrons. Calculated approximately as \(Z_{eff} = Z - S\), where \(Z\) is atomic number and \(S\) is the shielding constant.
Example: Sodium (Z = 11) with 10 core electrons has \(Z_{eff} \approx 11 - 10 = +1\) for its valence 3s electron, explaining its relatively large atomic radius.
Electron Affinity
The energy change that occurs when a neutral gaseous atom gains one electron to form a gaseous anion. A negative electron affinity indicates an exothermic process; elements with more negative electron affinities attract electrons more strongly.
Example: Chlorine has an electron affinity of −349 kJ/mol, meaning adding an electron to gaseous \(\ce{Cl}\) releases 349 kJ/mol — explaining its tendency to form \(\ce{Cl-}\).
Electron Config of Ions
The electron configuration of an ion derived from its parent atom by removing (cations) or adding (anions) electrons. For transition metal cations, the \(ns\) electrons are removed before \((n-1)d\) electrons.
Example: \(\ce{Fe}\) (\([Ar]3d^64s^2\)) loses 3 electrons to form \(\ce{Fe^{3+}}\) (\([Ar]3d^5\)), not \([Ar]3d^34s^2\), because the 4s electrons are removed first.
Electron Configuration
The complete description of the distribution of electrons among the atomic orbitals of an atom, written in subshell notation (e.g., \(1s^2 2s^2 2p^6\)) or noble gas shorthand notation. Governed by the Aufbau principle, Pauli exclusion principle, and Hund's rule.
Example: Sulfur (Z = 16) has the electron configuration \(1s^2 2s^2 2p^6 3s^2 3p^4\) or \([\ce{Ne}]3s^2 3p^4\).
Electron Flow Direction
In an electrochemical cell, electrons flow through the external circuit from the anode (where oxidation occurs) to the cathode (where reduction occurs). Conventional current flows in the opposite direction (from cathode to anode in the external circuit).
Electron Transfer
The movement of electrons from one atom or molecule to another, constituting an oxidation-reduction (redox) reaction. The species losing electrons is oxidized; the species gaining electrons is reduced. Electron transfer is the basis of electrochemistry.
Example: In \(\ce{2Na (s) + Cl2 (g) -> 2NaCl (s)}\), each sodium atom transfers one electron to a chlorine atom; sodium is oxidized, chlorine is reduced.
Electrochemistry
The branch of chemistry concerned with the relationship between electrical energy and chemical reactions, including spontaneous galvanic cells that produce electricity and non-spontaneous electrolytic cells that require electrical energy to drive reactions.
Electronegativity
A dimensionless measure of an atom's ability to attract shared bonding electrons toward itself in a covalent bond, using the Pauling scale (range 0.7–4.0). Electronegativity increases across a period and decreases down a group; fluorine is the most electronegative element (4.0).
Example: The electronegativity difference between H (2.20) and F (3.98) is 1.78, indicating a highly polar covalent bond.
Electronegativity Difference
The absolute difference in Pauling electronegativity values between two bonded atoms, used to classify bond type: < 0.4 = nonpolar covalent, 0.4–1.7 = polar covalent, > 1.7 = predominantly ionic.
Example: \(\ce{NaCl}\): electronegativity difference = 3.16 − 0.93 = 2.23, indicating an ionic bond; \(\ce{HCl}\): 3.16 − 2.20 = 0.96, indicating a polar covalent bond.
Electroplating
An electrolytic process in which a thin layer of metal is deposited on the surface of a cathode by reduction of metal cations from solution. The object to be plated is the cathode; the plating metal is often the anode.
Example: To silver-plate a spoon, the spoon is made the cathode in a solution of \(\ce{AgNO3}\); \(\ce{Ag+}\) ions are reduced at the spoon surface: \(\ce{Ag+ + e- -> Ag (s)}\).
Electrolysis
The process of using electrical energy to drive a non-spontaneous chemical reaction in an electrolytic cell. Electrolysis is used in industrial processes such as production of aluminum, chlorine, sodium hydroxide, and electroplating.
Example: Electrolysis of molten \(\ce{NaCl}\) produces sodium metal at the cathode (\(\ce{Na+ + e- -> Na}\)) and chlorine gas at the anode (\(\ce{2Cl- -> Cl2 + 2e-}\)).
Electrolysis of Water
The decomposition of water into hydrogen and oxygen gases by passing electrical current through an electrolyte solution. Hydrogen is produced at the cathode and oxygen at the anode in a 2:1 volume ratio.
Electrolytic Cells
Electrochemical cells in which electrical energy from an external source drives a non-spontaneous chemical reaction. The external power supply forces electrons in the direction opposite to spontaneous flow, reversing the normal galvanic cell reaction.
Example: A rechargeable battery being charged is an electrolytic cell; the charger supplies energy to reverse the discharge reaction.
Elements
Pure substances that cannot be decomposed by ordinary chemical means into simpler substances. Each element consists of atoms with the same atomic number. There are 118 known elements, each represented by a one- or two-letter symbol on the periodic table.
Example: Copper (\(\ce{Cu}\), Z = 29) is an element; it cannot be broken down chemically into simpler substances and all copper atoms have 29 protons.
Emission Spectra
The pattern of bright lines on a dark background produced when excited atoms release photons of specific wavelengths as electrons fall from higher to lower energy levels. Each element produces a unique emission spectrum used for identification.
Example: The hydrogen emission spectrum shows bright lines at 656 nm (red), 486 nm (cyan), 434 nm (violet), and 410 nm (violet) in the visible range (Balmer series).
Empirical Formula
The simplest whole-number ratio of atoms of each element in a compound. The empirical formula is obtained by dividing the mole ratio of elements by the smallest mole ratio. It may or may not be the same as the molecular formula.
Example: The empirical formula of glucose (\(\ce{C6H12O6}\)) is \(\ce{CH2O}\) (ratio C:H:O = 1:2:1).
Empirical Formula from Data
The process of determining the empirical formula of a compound from experimental data (percent composition or combustion analysis) by converting percentages to moles and finding the simplest whole-number ratio.
Example: A compound with 40.0% C, 6.7% H, and 53.3% O: moles are 3.33 C, 6.7 H, 3.33 O; dividing by 3.33 gives ratio 1:2:1 → empirical formula \(\ce{CH2O}\).
Endothermic Diagrams
Energy diagrams for endothermic reactions in which the products are shown at a higher energy level than the reactants. The activation energy barrier rises from the reactants, peaks at the transition state, and falls to a product level above the starting level. \(\Delta H > 0\).
Endothermic Reactions
Chemical reactions in which the system absorbs heat from the surroundings, resulting in a positive enthalpy change (\(\Delta H > 0\)). The products have higher enthalpy than the reactants; the surroundings cool during the reaction.
Example: The dissolution of ammonium nitrate in water is endothermic (\(\Delta H = +25.7\) kJ/mol); the solution cools noticeably as \(\ce{NH4NO3}\) dissolves.
Energy
The capacity to do work or transfer heat, existing in many forms including kinetic energy (energy of motion), potential energy (stored energy), thermal energy, chemical energy, electrical energy, and radiant energy. SI unit: joule (J).
Example: A stretched spring stores potential energy; when released, it converts to kinetic energy; this is analogous to chemical energy stored in bonds being released during exothermic reactions.
Energy Diagrams
Graphical representations (potential energy profiles) of the change in energy along the reaction coordinate as reactants convert to products. They show relative energies of reactants, transition state, any intermediates, and products, as well as \(E_a\) and \(\Delta H\).
Energy Levels
The quantized, discrete values of energy that electrons can possess in an atom, described by the principal quantum number \(n\). Electrons can only occupy these specific energy levels and must absorb or emit photons equal to the energy difference between levels.
Example: In hydrogen, the energy levels are given by \(E_n = -2.18 \times 10^{-18}/n^2\) J; the ground state is \(n = 1\) with energy \(-2.18 \times 10^{-18}\) J.
Endpoint vs Equivalence
The equivalence point is the theoretical point at which stoichiometrically equivalent amounts of acid and base have been mixed; the endpoint is the experimentally observed point at which the indicator changes color. Ideally these coincide; in practice there is a small titration error.
Example: In the titration of acetic acid with \(\ce{NaOH}\), the equivalence point is at pH ≈ 8.7; using phenolphthalein (endpoint at pH 8.2–10.0) introduces minimal error.
Enthalpy
A thermodynamic state function representing the heat content of a system at constant pressure: \(H = U + PV\). Enthalpy changes (\(\Delta H\)) at constant pressure equal the heat transferred to or from the system; negative \(\Delta H\) indicates heat released (exothermic).
Example: The standard enthalpy of formation of liquid water is \(\Delta H_f^\circ = -285.8\) kJ/mol, meaning 285.8 kJ of heat is released when 1 mol of \(\ce{H2O (l)}\) forms from its elements.
Enthalpy Change
The difference in enthalpy between products and reactants: \(\Delta H = H_{products} - H_{reactants}\). Negative \(\Delta H\) (exothermic) means heat is released; positive \(\Delta H\) (endothermic) means heat is absorbed. Measured in kJ per mole of reaction.
Example: \(\ce{H2 (g) + \frac{1}{2}O2 (g) -> H2O (l)}\); \(\Delta H = -285.8\) kJ: 285.8 kJ of heat is released per mole of water formed.
Enthalpy of Combustion
The enthalpy change when one mole of a substance undergoes complete combustion with oxygen under standard conditions. Values are always negative (exothermic). Important for comparing energy content of fuels.
Example: The standard enthalpy of combustion of methane is \(\Delta H_c^\circ = -890\) kJ/mol: \(\ce{CH4 (g) + 2O2 (g) -> CO2 (g) + 2H2O (l)}\); \(\Delta H = -890\) kJ.
Enthalpy of Formation
The enthalpy change when one mole of a compound is formed from its constituent elements in their standard states at 298 K and 1 bar. The standard enthalpy of formation of any element in its standard state is zero by definition.
Example: \(\Delta H_f^\circ[\ce{NH3 (g)}] = -46.1\) kJ/mol means forming 1 mol of ammonia from \(\ce{N2}\) and \(\ce{H2}\) releases 46.1 kJ.
Enthalpy of Reaction
The total enthalpy change for a balanced chemical reaction, calculated using Hess's Law as \(\Delta H_{rxn}^\circ = \sum n\Delta H_f^\circ(\text{products}) - \sum n\Delta H_f^\circ(\text{reactants})\), where \(n\) is the stoichiometric coefficient.
Example: For \(\ce{2SO2 (g) + O2 (g) -> 2SO3 (g)}\): \(\Delta H_{rxn}^\circ = 2(-396) - [2(-297) + 0] = -198\) kJ.
Enthalpy vs Internal Energy
Enthalpy (\(H = U + PV\)) differs from internal energy (\(U\)) by the \(PV\) term, which accounts for work done against the atmosphere. At constant pressure, \(\Delta H = \Delta U + \Delta(PV) = \Delta U + \Delta n_{gas}RT\) for reactions involving gases.
Example: For \(\ce{C(s) + O2(g) -> CO2(g)}\), \(\Delta n_{gas} = 0\), so \(\Delta H = \Delta U\); for \(\ce{N2(g) + 3H2(g) -> 2NH3(g)}\), \(\Delta n_{gas} = -2\), so \(\Delta H \neq \Delta U\).
Entropy
A thermodynamic state function (symbol \(S\)) that measures the dispersal of energy or the number of microstates available to a system. Entropy increases with temperature, with phase transitions to higher disorder, with mixing, and with increasing number of gas molecules.
Example: \(\ce{H2O (l) -> H2O (g)}\) has \(\Delta S > 0\) because the gas phase has far more microstates (greater positional freedom) than the liquid phase.
Entropy and Disorder
The qualitative relationship between entropy and the disorder or randomness of a system. More disordered arrangements correspond to more microstates, hence higher entropy. Entropy is rigorously defined via microstates (\(S = k_B \ln W\)), not just "disorder."
Example: Dissolving a crystal of \(\ce{KNO3}\) in water increases entropy because the ordered crystal lattice (low \(W\)) disperses into randomly distributed ions (high \(W\)).
Entropy Change
The difference in entropy between products and reactants: \(\Delta S = S_{products} - S_{reactants}\). Factors that increase entropy: more moles of gas produced, mixing, phase changes from solid to liquid to gas, increased temperature.
Example: \(\ce{CaCO3 (s) -> CaO (s) + CO2 (g)}\): \(\Delta S > 0\) because a mole of gas (\(\ce{CO2}\)) is produced from a solid.
Entropy of Phase Changes
The change in entropy associated with a phase transition, calculated as \(\Delta S = \Delta H / T\) at the phase transition temperature. Fusion (\(\Delta S_{fus}\)) and vaporization (\(\Delta S_{vap}\)) are both positive; the reverse processes are negative.
Example: For water at 100°C (373 K): \(\Delta S_{vap} = \Delta H_{vap}/T = 40,700/373 = 109\) J/(mol·K).
Entropy Predictions
Qualitative predictions of the sign of \(\Delta S\) for a reaction based on comparing the disorder of products and reactants, considering: change in number of moles of gas, change in phase, dissolution, mixing, and temperature effects.
Example: For \(\ce{2SO3 (g) -> 2SO2 (g) + O2 (g)}\): \(\Delta S > 0\) because 3 mol of gas is produced from 2 mol of gas, increasing disorder.
Equivalence Point
The point in a titration at which stoichiometrically equivalent quantities of acid and base have been added together. For strong acid-strong base titrations, pH = 7 at the equivalence point; for weak acid-strong base titrations, pH > 7.
Example: In the titration of 25.0 mL of 0.10 M \(\ce{HCl}\) with 0.10 M \(\ce{NaOH}\), the equivalence point is reached after adding exactly 25.0 mL of \(\ce{NaOH}\).
Error Propagation
The mathematical procedure for estimating the uncertainty in a calculated result based on the uncertainties of the individual measured quantities used in the calculation. Ensures that reported values honestly reflect the limitations of measurement.
Excess Reagent
The reactant present in an amount greater than stoichiometrically required for the limiting reagent to react completely. The excess reagent remains partially unconsumed after the reaction is complete.
Example: Reacting 4 mol \(\ce{H2}\) with 1 mol \(\ce{N2}\) to form \(\ce{NH3}\) (which requires 3 mol \(\ce{H2}\) per mol \(\ce{N2}\)): \(\ce{N2}\) is limiting and 1 mol \(\ce{H2}\) is the excess reagent.
Exothermic Diagrams
Energy diagrams for exothermic reactions in which the products are at a lower energy level than the reactants. The activation energy hump rises from reactants to the transition state, then falls below the reactant energy level to the products. \(\Delta H < 0\).
Exothermic Reactions
Chemical reactions that release heat to the surroundings, resulting in a negative enthalpy change (\(\Delta H < 0\)). Products are at lower enthalpy than reactants. The surroundings warm during an exothermic reaction.
Example: The combustion of methane (\(\Delta H = -890\) kJ/mol) is highly exothermic; the energy released is used for cooking and heating.
Expanded Octets
A bonding condition in which a central atom accommodates more than eight electrons in its valence shell, possible for elements in Period 3 and beyond due to the availability of empty \(d\) orbitals. Common for P, S, Si, Cl, and Xe.
Example: In \(\ce{PCl5}\), phosphorus has 10 electrons in its valence shell (5 bonding pairs); in \(\ce{SF6}\), sulfur has 12 electrons (6 bonding pairs).
Factors Affecting Rate
The variables that influence the rate of a chemical reaction: concentration of reactants (most reactions), temperature, surface area (for heterogeneous reactions), presence of a catalyst, and physical state of reactants. Each factor can be explained by collision theory.
Faraday's Constant
The charge of one mole of electrons: \(F = 96,485\) C/mol (approximately 96,500 C/mol). Faraday's constant relates moles of electrons transferred in an electrolytic or galvanic cell to electrical charge (coulombs) passed.
Example: Depositing 1 mol of \(\ce{Cu}\) from \(\ce{Cu^{2+}}\) requires \(2F = 2 \times 96,485 = 192,970\) C because each \(\ce{Cu^{2+}}\) requires 2 electrons.
Faraday's Laws
Two laws governing electrolysis: (1) the mass of substance produced at an electrode is proportional to the charge passed; (2) for the same charge, the masses of different substances deposited are proportional to their equivalent masses (\(M/n\), where \(n\) is electrons per ion).
Example: Using \(m = \frac{M \times I \times t}{n \times F}\): passing 9650 C through \(\ce{CuSO4}\) solution deposits \(\frac{63.5 \times 9650}{2 \times 96500} = 3.18\) g of copper.
First Law Thermodynamics
The law of conservation of energy stating that the total energy of the universe is constant: \(\Delta U = q + w\), where \(\Delta U\) is the change in internal energy, \(q\) is heat absorbed by the system, and \(w\) is work done on the system.
Example: If a system absorbs 500 J of heat and has 200 J of work done on it, its internal energy increases by \(\Delta U = 500 + 200 = 700\) J.
First Order Half-Life
The time required for the concentration of a reactant in a first-order reaction to decrease to half its initial value: \(t_{1/2} = \frac{\ln 2}{k} = \frac{0.693}{k}\). The half-life is constant and independent of initial concentration for first-order reactions.
Example: If a first-order reaction has \(k = 0.0231\) min\(^{-1}\), its half-life is \(t_{1/2} = 0.693/0.0231 = 30.0\) min regardless of the starting concentration.
First Order Integrated Law
The integrated rate law for first-order reactions: \(\ln[\text{A}]_t = \ln[\text{A}]_0 - kt\), or equivalently \([\text{A}]_t = [\text{A}]_0 e^{-kt}\). A plot of \(\ln[\text{A}]\) vs. time is linear with slope \(= -k\).
Example: If \([\text{A}]_0 = 0.400\) M and \(k = 0.050\) min\(^{-1}\), after 20 min: \(\ln[\text{A}] = \ln(0.400) - (0.050)(20) = -1.916 - 1.000\); \([\text{A}] = 0.147\) M.
First Order Reactions
Reactions in which the rate depends linearly on the concentration of one reactant: \(\text{rate} = k[\text{A}]\). Overall reaction order is 1. Characterized by an exponential decrease in reactant concentration and a constant half-life.
Example: Radioactive decay and many drug metabolism processes follow first-order kinetics; the concentration decreases exponentially with time.
Flame Tests
A qualitative analytical technique in which a small amount of a substance is introduced into a flame and the color of the flame is used to identify the metal cation present. Different metal ions emit characteristic colors due to their unique emission spectra.
Example: Sodium compounds give an intense yellow-orange flame (589 nm); potassium gives violet; lithium gives crimson red; strontium gives bright red.
Formal Charge
A calculated value assigned to each atom in a Lewis structure representing the charge it would have if all bonding electrons were shared equally: \(FC = (\text{valence electrons}) - (\text{lone pair electrons}) - \frac{1}{2}(\text{bonding electrons})\).
Example: In \(\ce{CO2}\) (O=C=O), each O has \(FC = 6 - 4 - \frac{1}{2}(4) = 0\) and C has \(FC = 4 - 0 - \frac{1}{2}(8) = 0\).
Formal Charge Calculation
The process of calculating the formal charge on each atom in a Lewis structure by subtracting the lone pair electrons and half the bonding electrons from the atom's valence electron count. The sum of formal charges equals the overall charge.
Example: In \(\ce{NO3-}\): nitrogen has formal charge \(+1\) in the structure with one double bond; oxygens have \(0\) (double-bonded) and \(-1\) (single-bonded); sum = \(-1\) = overall charge.
Formation Constants
Equilibrium constants (\(K_f\)) for the formation of complex ions from metal cations and ligands. Large formation constants (often \(10^8\) to \(10^{30}\)) indicate highly stable complexes and effectively complete formation of the complex ion in solution.
Example: \(\ce{Ag+ + 2NH3 <=> [Ag(NH3)2]+}\) has \(K_f = 1.7 \times 10^7\); silver ion forms a very stable complex with ammonia.
Forward Reaction
The reaction that proceeds from left to right as written in a chemical equation. In an equilibrium system, the forward reaction is defined by convention as the reaction producing the products as listed on the right side of the equation.
Free Energy and Cell EMF
The relationship between the standard Gibbs free energy change and the standard cell potential for an electrochemical reaction: \(\Delta G^\circ = -nFE^\circ\). A positive cell potential (\(E^\circ > 0\)) corresponds to a negative \(\Delta G^\circ\) (spontaneous reaction).
Example: A cell with \(E^\circ = 1.10\) V and \(n = 2\) has \(\Delta G^\circ = -(2)(96485)(1.10) = -212\) kJ/mol, indicating a spontaneous reaction.
Free Energy and Work
The maximum useful (non-expansion) work obtainable from a spontaneous process at constant temperature and pressure equals the decrease in Gibbs free energy: \(w_{max} = \Delta G\). For a galvanic cell, the maximum electrical work is \(-\Delta G = nFE\).
Free Energy of Formation
The standard Gibbs free energy change (\(\Delta G_f^\circ\)) for the formation of one mole of a compound from its elements in their standard states. Used to calculate \(\Delta G^\circ\) of reactions using \(\Delta G^\circ_{rxn} = \sum n\Delta G_f^\circ(\text{products}) - \sum n\Delta G_f^\circ(\text{reactants})\).
Example: \(\Delta G_f^\circ[\ce{NH3 (g)}] = -16.5\) kJ/mol; \(\Delta G_f^\circ\) for elements in standard states equals zero by definition.
Freezing Point Depression
The colligative property in which the freezing point of a solvent decreases upon addition of a nonvolatile solute: \(\Delta T_f = iK_f m\), where \(i\) is the van't Hoff factor, \(K_f\) is the cryoscopic constant, and \(m\) is molality.
Example: Adding 1.00 mol of \(\ce{NaCl}\) (\(i = 2\)) to 1.00 kg of water (\(K_f = 1.86\) °C/m) lowers the freezing point by \(2 \times 1.86 \times 1.00 = 3.72\)°C to \(-3.72\)°C.
Frequency Factor
The pre-exponential factor \(A\) in the Arrhenius equation (\(k = Ae^{-E_a/RT}\)), representing the frequency of collisions with the correct orientation. It reflects the collision frequency and the steric (orientation) requirement of the reaction.
Example: A large frequency factor \(A\) means that collisions are frequent and orientational requirements are easily met, contributing to a high rate constant even at lower temperatures.
Galvanic Cells
Electrochemical cells that convert the chemical energy of spontaneous redox reactions into electrical energy. They consist of two half-cells connected by a salt bridge; oxidation occurs at the anode and reduction at the cathode. Also called voltaic cells.
Example: A zinc-copper galvanic cell (\(\ce{Zn | Zn^{2+} || Cu^{2+} | Cu}\)) generates \(E^\circ = 1.10\) V by spontaneous transfer of electrons from zinc to copper ions.
Gas Evolution Reactions
Chemical reactions in which one of the products is a gas, driving the reaction toward completion by removal of a product from the equilibrium. Common evolved gases include \(\ce{CO2}\), \(\ce{H2S}\), \(\ce{SO2}\), \(\ce{NH3}\), and \(\ce{H2}\).
Example: \(\ce{Na2SO3 (aq) + 2HCl (aq) -> 2NaCl (aq) + H2O (l) + SO2 (g)}\); \(\ce{SO2}\) gas evolution drives the reaction to completion.
Gas Pressure
The force per unit area exerted by gas molecules colliding with the walls of their container. Gas pressure is proportional to the number of molecules and temperature, and inversely proportional to volume, as described by the ideal gas law.
Example: Gas in a sealed 1.0 L container at 300 K containing 0.040 mol has \(P = nRT/V = (0.040)(0.08206)(300)/1.0 = 0.985\) atm.
Gas Stoichiometry
The application of stoichiometric calculations to reactions involving gases, using the ideal gas law (\(PV = nRT\)) to convert between volume, pressure, and temperature of gases and moles, allowing calculation of amounts of gas produced or consumed.
Example: At STP, 1 mol of any gas occupies 22.4 L; so producing 44.8 L of \(\ce{CO2}\) at STP requires 2 mol of carbon to be oxidized.
Gibbs and Equilibrium
The relationship between standard Gibbs free energy and the equilibrium constant: \(\Delta G^\circ = -RT \ln K\). Reactions with large \(K\) have large negative \(\Delta G^\circ\); reactions with small \(K\) have large positive \(\Delta G^\circ\). At equilibrium, \(\Delta G = 0\).
Example: If \(K = 1.0 \times 10^5\) at 298 K, \(\Delta G^\circ = -(8.314)(298)\ln(10^5) = -28.5\) kJ/mol.
Gibbs Free Energy
A thermodynamic state function (\(G = H - TS\)) that combines enthalpy and entropy to predict the spontaneity of a process at constant temperature and pressure. A process is spontaneous when \(\Delta G < 0\), nonspontaneous when \(\Delta G > 0\), and at equilibrium when \(\Delta G = 0\).
Example: The combustion of glucose at 298 K has \(\Delta G^\circ = -2880\) kJ/mol, a large negative value confirming it is highly spontaneous.
Gibbs Free Energy Equation
The equation \(\Delta G = \Delta H - T\Delta S\), relating the Gibbs free energy change to enthalpy change, temperature, and entropy change. Allows prediction of spontaneity at any temperature and analysis of how temperature affects spontaneity.
Example: A reaction with \(\Delta H = -100\) kJ and \(\Delta S = -200\) J/K is spontaneous below \(T = 100000/200 = 500\) K (where \(\Delta G\) becomes negative).
Gravimetric Analysis
An analytical technique in which an analyte is converted to an insoluble precipitate, filtered, dried, and weighed. The mass of the precipitate is used to calculate the amount of analyte in the original sample.
Example: To determine \(\ce{[Cl-]}\), silver nitrate is added to precipitate \(\ce{AgCl}\); the dried mass of \(\ce{AgCl}\) is used to calculate the original chloride concentration.
Graphical Rate Analysis
The use of graphs (concentration vs. time, \(\ln[\text{A}]\) vs. time, or \(1/[\text{A}]\) vs. time) to determine the reaction order and rate constant. The graph that yields a straight line identifies the order; the slope gives \(k\) (or \(-k\)).
Example: A plot of \(1/[\text{A}]\) vs. time is linear for a second-order reaction; the slope equals \(+k\) and the y-intercept equals \(1/[\text{A}]_0\).
Graphing Data
The systematic representation of experimental data on a coordinate graph to reveal patterns, relationships, and trends. Best practices include labeling axes with units, including error bars, and using appropriate scales. Linear relationships are most easily analyzed.
Half-Equivalence Point
The point in the titration of a weak acid (or weak base) at which exactly half the original acid (or base) has been neutralized. At this point, \([\text{HA}] = [\text{A}^-]\) and \(\text{pH} = \text{p}K_a\), providing a direct experimental method to determine \(K_a\).
Example: In the titration of acetic acid with \(\ce{NaOH}\), when half the acetic acid has been neutralized, pH = pKa = 4.74.
Half Reactions
The separate oxidation and reduction components of a redox reaction, written as equations showing the electrons transferred. In the half-reaction method of balancing, each half-reaction is balanced separately for atoms, oxygen, hydrogen, and charge, then added together.
Example: Oxidation half-reaction: \(\ce{Zn -> Zn^{2+} + 2e-}\); reduction half-reaction: \(\ce{Cu^{2+} + 2e- -> Cu}\).
Half-Life
The time required for the concentration of a reactant (or amount of a radioactive isotope) to decrease to half its initial value. Symbol \(t_{1/2}\). For first-order processes, \(t_{1/2}\) is constant; for zero-order, it depends on initial concentration; for second-order, it depends on initial concentration.
Example: Carbon-14 has a half-life of 5730 years; after two half-lives (11,460 years), only 25% of the original \(\ce{^{14}C}\) remains.
Heat and Temperature
Heat (\(q\)) is the transfer of thermal energy between objects due to a temperature difference; it flows from hotter to cooler objects. Temperature is an intensive property measuring the average kinetic energy of particles. Heat is path-dependent; temperature is a state function.
Example: Adding 418 J of heat to 100 g of water raises its temperature by exactly 1.00°C, illustrating the distinction between heat transferred and temperature change.
Heat Capacity
The quantity of heat required to raise the temperature of an object by 1°C (or 1 K). Specific heat capacity (\(c\)) is per gram; molar heat capacity is per mole. Water's specific heat capacity (4.184 J g\(^{-1}\) K\(^{-1}\)) is unusually high due to hydrogen bonding.
Example: The specific heat capacity of aluminum is 0.900 J g\(^{-1}\) K\(^{-1}\); raising 50.0 g of Al by 20.0°C requires \(q = (50.0)(0.900)(20.0) = 900\) J.
Heat of Fusion
The enthalpy change when one mole of a solid substance melts at its normal melting point and constant pressure: \(\Delta H_{fus}\). Always positive (endothermic); the heat required to overcome attractive forces holding particles in the solid lattice.
Example: The heat of fusion of water is \(6.01\) kJ/mol; melting 1.00 mol of ice at 0°C requires exactly 6.01 kJ of heat input.
Heat of Vaporization
The enthalpy change when one mole of a liquid substance vaporizes at its normal boiling point and constant pressure: \(\Delta H_{vap}\). Always positive; reflects the energy needed to separate molecules from the liquid phase entirely. Much larger than \(\Delta H_{fus}\).
Example: Water's \(\Delta H_{vap} = 40.7\) kJ/mol at 100°C; vaporizing 18.0 g of water requires 40.7 kJ, which is why steam burns are so severe.
Heat Transfer
The movement of thermal energy from a region of higher temperature to a region of lower temperature by three mechanisms: conduction (through direct contact), convection (through fluid motion), and radiation (through electromagnetic waves).
Heating Curves
Graphs of temperature versus heat added to a substance, showing the phases through which a substance passes as it is heated from below its melting point to above its boiling point. Horizontal plateaus appear at melting and boiling points while phase transitions occur.
Example: A heating curve for water shows slopes during solid, liquid, and gas phases, with flat plateaus at 0°C (melting) and 100°C (boiling) at 1 atm.
Henderson-Hasselbalch
The equation \(\text{pH} = \text{p}K_a + \log\frac{[\text{A}^-]}{[\text{HA}]}\) used to calculate the pH of a buffer solution. It is derived from the \(K_a\) expression and assumes that the concentrations of the weak acid and conjugate base are approximately equal to their initial values.
Example: A buffer of 0.20 M \(\ce{NH3}\) and 0.10 M \(\ce{NH4+}\) (pKa = 9.25): \(\text{pH} = 9.25 + \log(0.20/0.10) = 9.25 + 0.30 = 9.55\).
Henry's Law
The law stating that the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid: \(C = k_H P\), where \(C\) is the concentration of dissolved gas, \(k_H\) is the Henry's law constant, and \(P\) is partial pressure.
Example: At 25°C, oxygen dissolves in water with \(k_H = 1.3 \times 10^{-3}\) mol L\(^{-1}\) atm\(^{-1}\); at \(P_{O_2} = 0.21\) atm, \([\ce{O2}] = 2.7 \times 10^{-4}\) M.
Hess's Law
The principle that the enthalpy change for a reaction is the same regardless of the pathway, as long as the initial and final states are the same. If a reaction can be expressed as the sum of other reactions, \(\Delta H\) for the overall reaction is the sum of their \(\Delta H\) values.
Example: If \(\ce{A -> B}\) has \(\Delta H_1\) and \(\ce{B -> C}\) has \(\Delta H_2\), then \(\ce{A -> C}\) has \(\Delta H = \Delta H_1 + \Delta H_2\).
Hess's Law Calculations
The algebraic manipulation of thermochemical equations (reversing, multiplying by coefficients) to obtain a target equation, then summing the corresponding \(\Delta H\) values. Reversing an equation changes the sign of \(\Delta H\); multiplying by a factor multiplies \(\Delta H\) by the same factor.
Example: To find \(\Delta H\) for \(\ce{C + 2H2 -> CH4}\), combine standard formation reactions for \(\ce{CO2}\), \(\ce{H2O}\), and the combustion of \(\ce{CH4}\), manipulating signs and coefficients appropriately.
Heterogeneous Catalysis
Catalysis in which the catalyst and reactants are in different phases, typically a solid catalyst with gaseous or liquid reactants. The reaction occurs on the surface of the catalyst; key steps include adsorption, surface reaction, and desorption.
Example: The Haber process uses solid iron catalyst to speed up \(\ce{N2 (g) + 3H2 (g) -> 2NH3 (g)}\); nitrogen and hydrogen molecules adsorb onto the iron surface where reaction occurs.
Heterogeneous Equilibrium
An equilibrium system in which reactants and products are present in more than one phase. Pure solids and pure liquids are omitted from the equilibrium expression because their concentrations are constant.
Example: For \(\ce{CaCO3 (s) <=> CaO (s) + CO2 (g)}\): \(K_p = P_{CO_2}\) because solids are excluded from the equilibrium expression.
Homogeneous Catalysis
Catalysis in which the catalyst and all reactants are in the same phase (typically all in solution or all in the gas phase). The catalyst participates in the mechanism to form an intermediate, then is regenerated in a later step.
Example: \(\ce{I-}\) ions catalyze the decomposition of \(\ce{H2O2}\) in aqueous solution; both catalyst and reactant are in the aqueous phase.
Homogeneous Equilibrium
An equilibrium system in which all reactants and products are in the same phase. The equilibrium expression \(K_c\) is written using molar concentrations of all species.
Example: \(\ce{N2 (g) + 3H2 (g) <=> 2NH3 (g)}\) is a homogeneous gaseous equilibrium; \(K_c = \frac{[\ce{NH3}]^2}{[\ce{N2}][\ce{H2}]^3}\).
Hund's Rule
The principle that when electrons occupy orbitals of equal energy (degenerate orbitals), they distribute themselves to maximize the number of unpaired electrons, each with parallel spins, before pairing in any orbital. This minimizes electron-electron repulsion.
Example: Carbon (\(1s^2 2s^2 2p^2\)) has two unpaired electrons in separate 2p orbitals (not two electrons in one 2p orbital), giving carbon two half-filled p orbitals available for bonding.
ICE Table Calculations
The mathematical procedure of substituting equilibrium concentrations from an ICE (Initial, Change, Equilibrium) table into the equilibrium expression and solving for the unknown change \(x\), using either the quadratic formula or the small-\(x\) approximation when valid.
Example: For \(\ce{HA <=> H+ + A-}\) with \(K_a = 1.8 \times 10^{-5}\) and \([\ce{HA}]_0 = 0.10\) M: ICE gives \(K_a = x^2/(0.10-x) \approx x^2/0.10\); \(x = 1.34 \times 10^{-3}\) M.
ICE Tables
A systematic tabular method for solving equilibrium problems, tracking the Initial concentrations, the Change in concentrations (in terms of an unknown \(x\)), and the Equilibrium concentrations of all species. The equilibrium row is substituted into the \(K\) expression.
Example: For \(\ce{A <=> B + C}\), an ICE table lists: Initial (given concentrations), Change (\(-x\), \(+x\), \(+x\)), Equilibrium (initial ± change), then \(K = [B][C]/[A]\) is solved for \(x\).
Ideal Gas Constant
The proportionality constant \(R\) in the ideal gas law \(PV = nRT\). Its value depends on the units used: \(R = 8.314\) J mol\(^{-1}\) K\(^{-1}\) = \(8.314\) Pa·m\(^3\) mol\(^{-1}\) K\(^{-1}\) = \(0.08206\) L·atm mol\(^{-1}\) K\(^{-1}\).
Example: When pressure is in atm and volume is in liters, use \(R = 0.08206\) L·atm mol\(^{-1}\) K\(^{-1}\); when working with energy (joules), use \(R = 8.314\) J mol\(^{-1}\) K\(^{-1}\).
Ideal Gas Law
The equation of state for an ideal gas: \(PV = nRT\), where \(P\) is pressure, \(V\) is volume, \(n\) is moles, \(R\) is the ideal gas constant, and \(T\) is absolute temperature. Assumes no intermolecular forces and negligible particle volume.
Example: Find the volume of 2.00 mol of an ideal gas at 300 K and 1.50 atm: \(V = nRT/P = (2.00)(0.08206)(300)/1.50 = 32.8\) L.
IMF Strength Comparison
The relative strengths of intermolecular forces from weakest to strongest: London dispersion forces < dipole-dipole forces < hydrogen bonding < ion-dipole forces. Stronger IMFs lead to higher boiling points, greater viscosity, and lower vapor pressures.
Example: \(\ce{HF}\) (hydrogen bonding, bp −19°C) > \(\ce{HCl}\) (dipole-dipole, bp −85°C) > \(\ce{Ar}\) (London only, bp −186°C).
IMF vs Chemical Bonds
Intermolecular forces (IMFs) act between molecules and are much weaker (typically 1–50 kJ/mol) than intramolecular covalent or ionic bonds (typically 150–1000 kJ/mol). IMFs determine physical properties; intramolecular bonds determine chemical identity.
Example: Boiling water (breaking IMFs between \(\ce{H2O}\) molecules, \(\Delta H_{vap} = 40.7\) kJ/mol) requires far less energy than breaking O-H covalent bonds (\(\sim 460\) kJ/mol each).
Incomplete Octets
A bonding situation in which a central atom has fewer than eight electrons in its valence shell. Common for beryllium (4 electrons, 2 bonds) and boron (6 electrons, 3 bonds) in compounds. These species are electron deficient and act as Lewis acids.
Example: \(\ce{BF3}\) has only 6 electrons around boron; it acts as a Lewis acid by accepting an electron pair from a Lewis base like \(\ce{NH3}\) to form \(\ce{F3B-NH3}\).
Indicator Selection
The process of choosing an appropriate acid-base indicator whose color-change range (transition interval, typically pKa ± 1) encompasses the pH at the equivalence point of the titration. Incorrect indicator selection causes systematic endpoint error.
Example: For a strong acid-strong base titration (equivalence point pH = 7), phenolphthalein (range 8.2–10.0) is a poor choice; bromothymol blue (range 6.0–7.6) is better.
Indicators and pH Range
Acid-base indicators are weak acids or bases that have different colors in their acid form (HIn) and conjugate base form (In\(^-\)). They change color over a pH range of approximately \(\text{p}K_a(\text{In}) \pm 1\).
Example: Phenolphthalein (\(\text{p}K_a \approx 9.1\)) is colorless below pH 8.2 and pink above pH 10.0; it changes color in the range 8.2–10.0.
Industrial Equilibrium
The application of Le Chatelier's Principle and thermodynamic analysis to optimize industrial chemical processes. Key considerations include temperature, pressure, concentration, and catalyst choice to maximize yield and rate while minimizing cost.
Example: The Haber process (\(\ce{N2 + 3H2 <=> 2NH3}\), \(\Delta H < 0\)) uses moderate temperature (400–500°C) to balance yield (favored by low T) and rate (favored by high T), and high pressure (150–300 atm).
Initial Rate
The instantaneous rate of a reaction measured at the very beginning of the reaction, before significant concentration changes occur. Initial rates are used in the method of initial rates to determine the rate law exponents without solving complex integrated equations.
Example: Measuring the rate of \(\ce{[H2O2]}\) decrease in the first few seconds of its decomposition gives the initial rate, unaffected by buildup of products.
Instantaneous Rate
The rate of a chemical reaction at a specific moment in time, calculated as the slope of the tangent line to the concentration-versus-time curve at that moment. Contrast with average rate, which is calculated over a finite time interval.
Example: The instantaneous rate at \(t = 50\) s is found by drawing a tangent to the \([\text{A}]\) vs. \(t\) graph at \(t = 50\) s and calculating the slope of that tangent.
Integrated Rate Laws
Mathematical equations relating the concentration of a reactant to time, obtained by integrating the differential rate law. Different orders give different equations: zero order (\([\text{A}] = [\text{A}]_0 - kt\)), first order (\(\ln[\text{A}] = \ln[\text{A}]_0 - kt\)), second order (\(1/[\text{A}] = 1/[\text{A}]_0 + kt\)).
Intermolecular Forces
Attractive and repulsive forces between adjacent molecules or atoms. Types include London dispersion forces (all molecules), dipole-dipole forces (polar molecules), hydrogen bonding (N-H, O-H, F-H), and ion-dipole forces (ions in polar solvents). IMFs govern physical properties.
Example: Water's high boiling point (100°C) relative to \(\ce{H2S}\) (−60°C) results from strong hydrogen bonding between \(\ce{H2O}\) molecules.
Intramolecular Forces
Forces that exist within a molecule, holding its atoms together: covalent bonds (shared electrons), ionic bonds (electrostatic attraction), and metallic bonds (delocalized electrons). Much stronger than intermolecular forces; determine molecular identity and chemical reactivity.
Example: The O-H intramolecular covalent bonds in water have a bond energy of ~460 kJ/mol, far stronger than the hydrogen bonds between water molecules (~20 kJ/mol).
Internal Energy
The total energy of all particles within a system, including the kinetic energy of molecular motion and the potential energy from intermolecular and intramolecular interactions. Symbol \(U\); changes are calculated as \(\Delta U = q + w\).
Ion Product
The product of the concentrations of the ions in a solution, raised to the powers of their stoichiometric coefficients: \(Q_{sp} = [\text{cation}]^a[\text{anion}]^b\). Comparing \(Q_{sp}\) to \(K_{sp}\) predicts whether precipitation will occur.
Example: If \([\ce{Ca^{2+}}] = 0.01\) M and \([\ce{SO4^{2-}}] = 0.01\) M, then \(Q_{sp} = (0.01)(0.01) = 10^{-4}\); if \(K_{sp}(\ce{CaSO4}) = 4.9 \times 10^{-5}\), precipitation occurs (\(Q > K_{sp}\)).
Ion Product of Water Kw
The equilibrium constant for the autoionization of water: \(K_w = [\ce{H3O+}][\ce{OH-}] = 1.0 \times 10^{-14}\) at 25°C. At all temperatures, the product of \([\ce{H+}]\) and \([\ce{OH-}]\) equals \(K_w\); neutral solution has \([\ce{H+}] = [\ce{OH-}] = 1.0 \times 10^{-7}\) M at 25°C.
Ion-Dipole Forces
Intermolecular attractive forces between an ion and the partial charge on a polar molecule. Ion-dipole forces are the strongest intermolecular interactions and are responsible for the dissolution of ionic compounds in polar solvents such as water.
Example: When \(\ce{NaCl}\) dissolves in water, \(\ce{Na+}\) is attracted to the negative oxygen end of water molecules, and \(\ce{Cl-}\) is attracted to the positive hydrogen end.
Ionic Bonds
Chemical bonds formed by the electrostatic attraction between oppositely charged ions. Ionic bonds result from the complete transfer of one or more electrons from a metal (forming a cation) to a nonmetal (forming an anion). Strong bonds with high lattice energies.
Example: In \(\ce{NaCl}\), one electron transfers from Na to Cl, forming \(\ce{Na+}\) and \(\ce{Cl-}\); the resulting electrostatic attraction is the ionic bond.
Ionic Compounds
Compounds consisting of positively charged cations and negatively charged anions held together by ionic bonds in a regular crystal lattice. Ionic compounds have high melting points, conduct electricity when dissolved or molten, and tend to be brittle.
Example: Calcium fluoride (\(\ce{CaF2}\)) is an ionic compound with a melting point of 1418°C; it conducts electricity when dissolved in water as \(\ce{Ca^{2+}}\) and \(\ce{F-}\) ions.
Ionic Radius
The radius of an ion in a crystal, determined from X-ray crystallography. Cations are smaller than their parent atoms (loss of electrons, increased \(Z_{eff}\)); anions are larger (gain of electrons, decreased \(Z_{eff}\)). Ionic radius increases down a group.
Example: \(\ce{Na+}\) radius = 102 pm; \(\ce{Na}\) atom radius = 186 pm; \(\ce{Cl-}\) radius = 181 pm; \(\ce{Cl}\) atom radius = 99 pm.
Ionization Energy
The minimum energy required to remove an electron from a gaseous neutral atom (or ion) in its ground state: \(\ce{A (g) -> A+ (g) + e-}\). Ionization energy increases across a period and decreases down a group. First IE < second IE < third IE.
Example: The first ionization energy of sodium is 496 kJ/mol; the second is 4562 kJ/mol (much larger, because it requires removing a core electron).
Isolated Systems
A thermodynamic system that cannot exchange either energy or matter with its surroundings. A perfectly insulated, sealed container approximates an isolated system. The total energy and mass of an isolated system are constant.
Example: A thermos bottle approximates an isolated system; it minimizes heat transfer (insulation) and prevents matter exchange (sealed lid).
Isotopes
Atoms of the same element (same number of protons) that have different numbers of neutrons, and therefore different mass numbers. Isotopes have the same chemical properties but different nuclear properties. Most elements have multiple naturally occurring isotopes.
Example: Carbon has three isotopes: \(\ce{^{12}C}\) (6 neutrons, 98.89%), \(\ce{^{13}C}\) (7 neutrons, 1.11%), and \(\ce{^{14}C}\) (8 neutrons, radioactive, trace amounts).
Kinetic Molecular Theory
A model explaining the behavior of ideal gases in terms of the properties of their molecules: particles are in constant random motion; collisions are elastic; there are no attractive forces between particles; the average kinetic energy is proportional to absolute temperature.
Example: Kinetic molecular theory explains why gas pressure increases with temperature: faster-moving molecules collide with container walls more frequently and with greater force.
Kinetic Stability
The persistence of a chemical species over time due to a high activation energy barrier, even if thermodynamically unstable (high \(\Delta G\)). A substance may be thermodynamically unstable but kinetically stable if the rate of its decomposition is extremely slow.
Example: Diamond is thermodynamically less stable than graphite at 25°C and 1 atm (\(\Delta G > 0\) for diamond → graphite), but kinetically stable because the activation energy for conversion is enormous.
Kinetics Experiments
Laboratory procedures designed to measure reaction rates and determine rate laws, including methods such as monitoring absorbance (spectrophotometry), measuring gas pressure, tracking color changes, and using initial rate comparisons across experimental trials.
Laboratory Safety
The set of procedures and precautions followed in a chemistry laboratory to prevent injury and accidents, including proper use of personal protective equipment (PPE: goggles, gloves, lab coat), safe chemical handling, proper waste disposal, and knowledge of emergency procedures.
Lattice Energy
The energy released when one mole of an ionic solid forms from its gaseous ions at infinite separation. Lattice energy is always negative (exothermic) and is the primary reason ionic compounds are stable. Magnitude increases with charge and decreases with ionic radius.
Example: Lattice energy of \(\ce{NaCl} = -787\) kJ/mol; of \(\ce{MgO} = -3791\) kJ/mol (\(\ce{Mg^{2+}}\) and \(\ce{O^{2-}}\) have greater charges, giving stronger coulombic attraction).
Le Chatelier's Principle
The principle stating that when a system at equilibrium is subjected to a stress (change in concentration, pressure, or temperature), the equilibrium shifts in the direction that partially relieves the stress and establishes a new equilibrium position.
Example: Adding \(\ce{H2}\) to a \(\ce{N2 + 3H2 <=> 2NH3}\) equilibrium shifts it toward products (\(\ce{NH3}\)) to consume the added \(\ce{H2}\) and partially restore equilibrium.
Lewis Acid-Base Theory
The broadest acid-base theory, defining a Lewis acid as an electron-pair acceptor and a Lewis base as an electron-pair donor. Lewis acid-base reactions involve the formation of a coordinate covalent bond; this theory encompasses all Brønsted-Lowry reactions and more.
Example: In \(\ce{BF3 + :NH3 -> F3B-NH3}\), \(\ce{BF3}\) is the Lewis acid (accepts electron pair) and \(\ce{NH3}\) is the Lewis base (donates electron pair).
Lewis Dot Symbols
Representations of atoms or ions showing valence electrons as dots surrounding the element symbol. Each side of the symbol can hold up to two dots; valence electrons are first distributed one per side, then paired. Used as building blocks for Lewis structures.
Example: Nitrogen (5 valence electrons) is drawn as \(\cdot\overset{\cdot}{\underset{\cdot}{\text{N}}}\cdot\) — one lone pair and two single electrons (or three lone pairs and one pair, depending on arrangement).
Lewis Structures
Structural diagrams of molecules and polyatomic ions showing all valence electrons as bonding pairs (lines) and lone pairs (dots). Drawn following rules: count valence electrons, connect atoms, complete octets, minimize formal charges.
Example: The Lewis structure of \(\ce{H2O}\) shows oxygen with two bonding pairs (to H atoms) and two lone pairs, totaling 8 electrons around oxygen.
Like Dissolves Like
The empirical rule that polar solvents dissolve polar and ionic solutes, while nonpolar solvents dissolve nonpolar solutes. Dissolution is favored when solute-solvent interactions are similar in strength to solute-solute and solvent-solvent interactions.
Example: Ethanol (\(\ce{C2H5OH}\)) dissolves in water (both polar, can hydrogen bond), but iodine (\(\ce{I2}\)) dissolves much better in hexane (both nonpolar).
Limiting Reagent
The reactant that is completely consumed first in a chemical reaction, determining the maximum amount of product that can form. After the limiting reagent is exhausted, the reaction stops even if other reagents remain.
Example: Reacting 3 mol \(\ce{H2}\) with 3 mol \(\ce{N2}\) to produce \(\ce{NH3}\): the reaction requires 3 mol \(\ce{H2}\) per mol \(\ce{N2}\); \(\ce{H2}\) is limiting (only 1 mol \(\ce{NH3}\) forms, leaving 2.33 mol \(\ce{N2}\) unreacted).
Linear Geometry
A molecular geometry in which a central atom is bonded to exactly two other atoms with no lone pairs, producing a bond angle of exactly 180°. Linear geometry results from two electron domains (two bonding pairs and zero lone pairs) around the central atom.
Example: Carbon dioxide (\(\ce{CO2}\)) has linear geometry: O=C=O with a bond angle of 180° and two double bonds to carbon.
Linearization Rate Data
The mathematical transformation of concentration-time data into a form that gives a straight line, allowing determination of reaction order and rate constant. Plotting \([\text{A}]\) vs. \(t\), \(\ln[\text{A}]\) vs. \(t\), or \(1/[\text{A}]\) vs. \(t\) gives a straight line for zero, first, or second order, respectively.
Liquids
A state of matter with definite volume but no definite shape, taking the shape of its container. Liquid particles are close together but able to move past one another. Liquids exhibit surface tension, viscosity, capillary action, and vapor pressure.
Example: Water at room temperature is a liquid; it takes the shape of any container (unlike solids) but maintains a definite volume (unlike gases).
London Dispersion Forces
Weak, temporary intermolecular attractive forces that arise from instantaneous dipoles caused by random fluctuations in electron distribution. All atoms and molecules experience London forces; their strength increases with molecular size (more electrons, greater polarizability).
Example: Noble gases such as xenon (Xe) are held in the liquid state only by London dispersion forces; because Xe is large and polarizable, it has a higher boiling point (−108°C) than helium (−269°C).
Lone Pair Repulsion
The stronger repulsive force exerted by lone pairs compared to bonding pairs in VSEPR theory, because lone pair electrons are held closer to the central nucleus and spread over a larger angular region. Lone pairs compress adjacent bond angles below their ideal values.
Example: Each lone pair on the central atom of \(\ce{NH3}\) repels the bonding pairs, compressing the H-N-H angle from the ideal 109.5° (tetrahedral) to 107°.
Lone Pairs
Pairs of valence electrons on an atom that are not shared with another atom in a covalent bond. Lone pairs participate in hydrogen bonding and Lewis base behavior, occupy space in VSEPR geometry, and affect molecular shape and polarity.
Example: The nitrogen atom in \(\ce{NH3}\) has one lone pair, which makes it a Lewis base and causes the molecule to have a pyramidal shape rather than planar.
Manipulating K Expressions
The algebraic rules for modifying equilibrium constants when chemical equations are reversed, multiplied by a coefficient, or added together: reversing gives \(K' = 1/K\); multiplying by \(n\) gives \(K' = K^n\); adding reactions gives \(K_{total} = K_1 \times K_2\).
Example: If \(\ce{A <=> B}\) has \(K_1 = 0.5\), then \(\ce{B <=> A}\) has \(K = 1/0.5 = 2.0\); and \(\ce{2A <=> 2B}\) has \(K = 0.5^2 = 0.25\).
Mass Number
The total number of protons and neutrons (nucleons) in the nucleus of an atom, denoted \(A\). Mass number is always a whole number and approximates (but does not equal) the atomic mass in amu. \(A = Z + N\), where \(N\) is the number of neutrons.
Example: Carbon-14 (\(\ce{^{14}C}\)) has mass number 14, with 6 protons and 8 neutrons.
Mass Spectrometry
An analytical technique in which a sample is vaporized, ionized, and the ions are separated by their mass-to-charge ratio (\(m/z\)) in a magnetic or electric field. The resulting mass spectrum shows the relative abundances of ions at different \(m/z\) values.
Example: The mass spectrum of \(\ce{Cl2}\) shows peaks at \(m/z = 70\), \(72\), and \(74\) in a 1:2:1 ratio, corresponding to \(\ce{^{35}Cl^{35}Cl}\), \(\ce{^{35}Cl^{37}Cl}\), and \(\ce{^{37}Cl^{37}Cl}\).
Mass Spectrum Analysis
The interpretation of mass spectrometry data to determine atomic masses, natural isotope abundances, or molecular fragments. The molecular ion peak (\(\ce{M+}\)) gives the molecular mass; fragment peaks reveal structural information.
Example: Neon's mass spectrum shows peaks at \(m/z = 20\) (90.48%, \(\ce{^{20}Ne}\)), 21 (0.27%, \(\ce{^{21}Ne}\)), and 22 (9.25%, \(\ce{^{22}Ne}\)); the weighted average gives the atomic mass of 20.18 amu.
Mass-to-Mass Calculations
Stoichiometric calculations that convert the mass of a given substance (reactant or product) to the mass of another substance in the same reaction, using the sequence: mass → moles (÷ molar mass) → moles (× mole ratio) → mass (× molar mass).
Example: How many grams of \(\ce{CO2}\) form from 44 g of \(\ce{C}\)? \(44 \text{ g C} \div 12 \text{ g/mol} = 3.67 \text{ mol C} \times 1 \text{ mol CO}_2/\text{mol C} \times 44 \text{ g/mol} = 161 \text{ g CO}_2\).
Matter
Anything that has mass and occupies space. Matter exists in three common states (solid, liquid, gas) and can be classified as pure substances (elements and compounds) or mixtures (homogeneous and heterogeneous). Matter is neither created nor destroyed in chemical reactions.
Measurement
The quantitative determination of a property using a calibrated instrument, resulting in a numerical value with units. Good measurements are both accurate (close to true value) and precise (reproducible). All measurements have some degree of uncertainty.
Mechanism Validation
The process of confirming that a proposed reaction mechanism is consistent with experimental data, particularly the observed rate law. A valid mechanism must: (1) sum to the overall equation; (2) have a rate-determining step consistent with the observed rate law.
Example: If the proposed mechanism gives rate \(= k[\text{A}]^2[\text{B}]\) and the experimental rate law is rate \(= k[\text{A}][\text{B}]\), the mechanism is invalid.
Melting and Freezing
Melting is the endothermic phase transition from solid to liquid at the melting point, when thermal energy overcomes the attractive forces of the crystal lattice. Freezing is the exothermic reverse process. Both occur at the same temperature (melting point).
Example: Water melts at 0°C and 1 atm; adding 6.01 kJ of heat to 1 mol of ice at 0°C completely converts it to liquid water at 0°C.
Metallic Bonds
Chemical bonds in metals formed by the electrostatic attraction between positive metal cations (in a fixed lattice) and a delocalized "sea" of valence electrons that move freely throughout the metal. Metallic bonds explain electrical/thermal conductivity, malleability, and luster.
Example: In copper metal, each atom contributes approximately 1 electron to the delocalized electron sea; these free electrons conduct heat and electricity.
Metathesis Reactions
Reactions in which the ions of two compounds exchange partners to form two new compounds. Metathesis reactions are driven by formation of a precipitate, a gas, or a weak electrolyte (such as water). Also called double replacement reactions.
Example: \(\ce{Pb(NO3)2 (aq) + 2KI (aq) -> PbI2 (s) + 2KNO3 (aq)}\); a yellow precipitate of \(\ce{PbI2}\) forms as the driving force.
Method of Initial Rates
An experimental technique for determining the rate law in which the initial rate of a reaction is measured at several initial concentrations. By comparing how the rate changes when one reactant concentration is changed while others are held constant, each order can be determined.
Example: If doubling \([\text{A}]\) (at constant \([\text{B}]\)) doubles the rate, then the reaction is first order in A. If quadrupling occurs, it is second order in A.
Microstates
The number of distinct ways the particles and energy of a system can be arranged while maintaining the same macroscopic properties (temperature, pressure, volume). More microstates means higher entropy: \(S = k_B \ln W\).
Example: A gas expanded into a larger container has more microstates (more positions available to each molecule), so its entropy increases.
Mixtures
Two or more substances physically combined in no definite ratio, retaining their individual properties. Homogeneous mixtures (solutions) have uniform composition throughout; heterogeneous mixtures have nonuniform composition and distinguishable regions.
Example: Air is a homogeneous mixture of \(\ce{N2}\), \(\ce{O2}\), \(\ce{Ar}\), \(\ce{CO2}\), and other gases; sand and gravel is a heterogeneous mixture.
MO Energy Diagrams
Molecular orbital diagrams showing the relative energies of bonding and antibonding molecular orbitals, with electrons filled according to the Aufbau principle, Pauli exclusion, and Hund's rule. Used to predict bond order, paramagnetism, and stability.
Example: The MO energy diagram for \(\ce{O2}\) shows two electrons in degenerate antibonding \(\pi^*\) orbitals (one per orbital, by Hund's rule), predicting that \(\ce{O2}\) is paramagnetic — confirmed experimentally.
Molarity
The concentration of a solution expressed as moles of solute per liter of solution: \(M = n/V\). Molarity is temperature-dependent because solution volume changes with temperature. Symbol: M (mol/L).
Example: Dissolving 0.500 mol of \(\ce{NaOH}\) in enough water to make 250.0 mL of solution gives a concentration of \(0.500/0.250 = 2.00\) M \(\ce{NaOH}\).
Molar Mass
The mass of one mole of a substance, expressed in grams per mole (g/mol). Numerically equal to the atomic mass (for elements) or the sum of atomic masses of all atoms in the formula (for compounds). Used to convert between grams and moles.
Example: Molar mass of \(\ce{H2SO4}\): \(2(1.008) + 32.06 + 4(16.00) = 98.07\) g/mol; 98.07 g of \(\ce{H2SO4}\) is 1 mole.
Molar Ratios in Solutions
The stoichiometric ratios derived from balanced chemical equations used in solution stoichiometry calculations, relating moles of reactants and products. Combined with molarity and volume, they enable calculation of concentrations, volumes, or masses needed for reactions.
Example: In \(\ce{2HCl + Ca(OH)2 -> CaCl2 + 2H2O}\), the mole ratio of \(\ce{HCl}\) to \(\ce{Ca(OH)2}\) is 2:1.
Molar Solubility
The concentration of dissolved solute (in mol/L) in a saturated solution at a given temperature. Related to the solubility product constant: for \(\ce{AB <=> A+ + B-}\), molar solubility \(s = \sqrt{K_{sp}}\).
Example: For \(\ce{AgCl}\) (\(K_{sp} = 1.8 \times 10^{-10}\)): molar solubility \(s = \sqrt{1.8 \times 10^{-10}} = 1.3 \times 10^{-5}\) mol/L.
Molar Volume
The volume occupied by one mole of a substance at specified conditions. For an ideal gas at STP (0°C, 1 atm), the molar volume is 22.414 L/mol. At SATP (25°C, 1 bar), the molar volume is 24.79 L/mol.
Example: At STP, 1 mol of \(\ce{O2}\) occupies 22.4 L; 11.2 L of \(\ce{O2}\) at STP contains 0.500 mol and has a mass of \(0.500 \times 32.00 = 16.0\) g.
Mole Calculations
Calculations that convert between mass (g), moles (mol), number of particles, and volume (for gases at STP) using molar mass, Avogadro's number, and molar volume as conversion factors.
Example: How many atoms are in 12.0 g of carbon? \(12.0 \text{ g} \div 12.01 \text{ g/mol} = 0.999 \text{ mol} \times 6.022 \times 10^{23} = 6.01 \times 10^{23}\) atoms.
Mole Concept
The fundamental SI unit for the amount of substance, defined such that one mole contains exactly \(6.02214076 \times 10^{23}\) elementary entities (atoms, molecules, ions, electrons, etc.). The mole is the chemist's counting unit for atoms and molecules.
Example: 1 mol of \(\ce{H2O}\) contains \(6.022 \times 10^{23}\) water molecules, \(1.204 \times 10^{24}\) hydrogen atoms, and \(6.022 \times 10^{23}\) oxygen atoms.
Mole Fraction
The dimensionless ratio of moles of a component to the total moles of all components in a mixture: \(\chi_A = n_A / n_{total}\). Mole fractions are used in Dalton's Law (\(P_A = \chi_A P_{total}\)) and Raoult's Law.
Example: A mixture of 2 mol \(\ce{N2}\) and 3 mol \(\ce{O2}\): \(\chi_{N_2} = 2/5 = 0.40\); \(\chi_{O_2} = 3/5 = 0.60\).
Mole-to-Mole Ratios
The stoichiometric ratios between substances in a balanced chemical equation, expressed in moles. These ratios are derived directly from the coefficients and used as conversion factors in stoichiometric calculations.
Example: In \(\ce{2Al + 3Cl2 -> 2AlCl3}\), the mole ratio of \(\ce{Al}\) to \(\ce{Cl2}\) is 2:3; reacting 0.60 mol \(\ce{Al}\) requires \(0.60 \times (3/2) = 0.90\) mol \(\ce{Cl2}\).
Molecular Equations
Chemical equations written showing complete formulas of all reactants and products without indicating the ionic nature of dissolved species. Also called formula equations. Less informative than complete ionic or net ionic equations for aqueous reactions.
Example: \(\ce{NaOH (aq) + HCl (aq) -> NaCl (aq) + H2O (l)}\) is a molecular equation; it does not show that \(\ce{NaOH}\), \(\ce{HCl}\), and \(\ce{NaCl}\) exist as ions in solution.
Molecular Formula
The exact formula giving the actual number of atoms of each element present in one molecule of a compound. The molecular formula is a whole-number multiple of the empirical formula.
Example: Glucose has the molecular formula \(\ce{C6H12O6}\) (empirical formula \(\ce{CH2O}\); molecular formula = 6 × empirical formula).
Molecular Geometry
The three-dimensional arrangement of the atoms of a molecule in space, determined by the positions of bonded atoms (not lone pairs). Described by terms such as linear, bent, trigonal planar, tetrahedral, trigonal pyramidal, and octahedral.
Example: \(\ce{NH3}\) has a tetrahedral electron geometry (4 electron domains) but a trigonal pyramidal molecular geometry (3 bonded atoms + 1 lone pair), with H-N-H angles of 107°.
Molecular Orbital Theory
A quantum mechanical model of bonding in which atomic orbitals combine mathematically to form molecular orbitals that are delocalized over the entire molecule. Electrons are placed in molecular orbitals from lowest to highest energy, predicting bond order and magnetic properties.
Example: MO theory correctly predicts that \(\ce{O2}\) is paramagnetic (has unpaired electrons in degenerate \(\pi^*_{2p}\) orbitals), which valence bond theory fails to predict.
Molecular Polarity
The overall polarity of a molecule, determined by both the polarity of individual bonds (from electronegativity differences) and the geometry of the molecule. A molecule is polar if it has polar bonds arranged asymmetrically so that bond dipoles do not cancel.
Example: \(\ce{CCl4}\) has 4 polar C-Cl bonds, but they are arranged tetrahedrally and cancel; the molecule is nonpolar. \(\ce{CHCl3}\) is polar because the geometry is unsymmetrical.
Molecularity
The number of reactant molecules or atoms that collide and react in an elementary reaction step. Unimolecular (one species), bimolecular (two species), and termolecular (three species, rare) are the only meaningful molecularities.
Example: The decomposition of \(\ce{N2O5 -> NO2 + NO3}\) is unimolecular (molecularity = 1); \(\ce{NO + O3 -> NO2 + O2}\) is bimolecular (molecularity = 2).
Naming Covalent Compounds
The systematic IUPAC naming of binary covalent compounds using Greek prefixes (mono-, di-, tri-, tetra-, penta-...) to indicate the number of atoms of each element. The first element is named, then the second with the suffix "-ide."
Example: \(\ce{N2O4}\) is dinitrogen tetraoxide; \(\ce{PCl3}\) is phosphorus trichloride; \(\ce{SO3}\) is sulfur trioxide (the prefix mono- is omitted for the first element).
Naming Ionic Compounds
The systematic naming of ionic compounds: the cation name is given first (metal name, with Roman numeral for variable-charge metals), followed by the anion name (nonmetal with "-ide" suffix, or polyatomic ion name).
Example: \(\ce{FeCl3}\) = iron(III) chloride; \(\ce{Cu2SO4}\) = copper(I) sulfate; \(\ce{Na3PO4}\) = sodium phosphate.
Nernst Equation
The equation relating the cell potential to standard cell potential and the reaction quotient under non-standard conditions: \(E = E^\circ - \frac{RT}{nF}\ln Q\), or at 25°C: \(E = E^\circ - \frac{0.0592}{n}\log Q\).
Example: For a \(\ce{Zn/Cu}\) cell with \([\ce{Zn^{2+}}] = 0.10\) M and \([\ce{Cu^{2+}}] = 1.0\) M: \(E = 1.10 - (0.0592/2)\log(0.10/1.0) = 1.10 + 0.030 = 1.13\) V.
Net Ionic Acid-Base
The simplified ionic equation for acid-base neutralization reactions, showing only the species that actually change during the reaction. For strong acid-strong base reactions, the net ionic equation is always \(\ce{H+ (aq) + OH- (aq) -> H2O (l)}\).
Example: For \(\ce{HNO3 + KOH -> KNO3 + H2O}\), the net ionic equation is \(\ce{H+ + OH- -> H2O}\); \(\ce{K+}\) and \(\ce{NO3-}\) are spectator ions.
Net Ionic Equations
Chemical equations that include only the species that are directly involved in the chemical change, omitting spectator ions. Soluble ionic compounds are written as separated ions; insoluble compounds, gases, and weak electrolytes are written in molecular form.
Example: For the reaction \(\ce{AgNO3 (aq) + NaCl (aq) -> AgCl (s) + NaNO3 (aq)}\), the net ionic equation is \(\ce{Ag+ (aq) + Cl- (aq) -> AgCl (s)}\).
Network Covalent Solids
Solids in which atoms are covalently bonded to their neighbors throughout the entire crystal in a three-dimensional network, with no discrete molecules. They have extremely high melting points, are very hard, and are poor electrical conductors (unless there is electron delocalization).
Example: Diamond (carbon) and silicon dioxide (\(\ce{SiO2}\), quartz) are network covalent solids; diamond is the hardest natural substance due to its strong, directional C-C bonds throughout the entire crystal.
Neutral Salts
Salts that produce a solution with pH = 7 when dissolved in water, formed from the combination of a strong acid and a strong base. Neither the cation nor the anion undergoes hydrolysis.
Example: Sodium chloride (\(\ce{NaCl}\)), formed from \(\ce{NaOH}\) (strong base) and \(\ce{HCl}\) (strong acid), produces a neutral solution (pH = 7) in water.
Neutralization Reactions
Reactions in which an acid and a base react to produce a salt and (in aqueous solution) water. Complete neutralization of a strong acid with a strong base gives a neutral salt solution; incomplete neutralization or weak acid/base involvement gives other products.
Noble Gas Notation
Abbreviated electron configuration notation that uses the symbol of the preceding noble gas in brackets to represent the core electrons, followed by the configuration of the valence electrons. Saves writing complete configurations for heavier elements.
Example: Chlorine's full configuration is \(1s^2 2s^2 2p^6 3s^2 3p^5\); in noble gas notation, this is written \([\ce{Ne}]3s^2 3p^5\).
Nonpolar Covalent Bonds
Covalent bonds between two atoms with identical (or very similar) electronegativities (difference < 0.4), resulting in equal sharing of electrons and no partial charges. The bonding electrons are centered between the nuclei.
Example: The \(\ce{Cl-Cl}\) bond in \(\ce{Cl2}\) and the \(\ce{C-H}\) bond in methane (electronegativity difference 0.35) are considered nonpolar covalent bonds.
Nonpolar Molecules
Molecules with no net dipole moment, either because all bonds are nonpolar or because polar bonds are arranged symmetrically so their dipoles cancel. Nonpolar molecules dissolve in nonpolar solvents and experience only London dispersion forces.
Example: \(\ce{CO2}\) has two polar C=O bonds, but they point in opposite directions (linear geometry); the dipoles cancel, making \(\ce{CO2}\) a nonpolar molecule.
Nonspontaneous Processes
Processes that do not occur spontaneously under given conditions because they require a continuous input of free energy (\(\Delta G > 0\)). Nonspontaneous processes can be driven by coupling them to a spontaneous process that provides the required energy.
Example: The electrolysis of water (\(\ce{2H2O -> 2H2 + O2}\)) is nonspontaneous (\(\Delta G^\circ = +474\) kJ); it requires a continuous electrical energy input.
Octet Rule
The tendency of main-group atoms to form bonds so that each atom acquires 8 electrons in its valence shell, achieving the stable electron configuration of the nearest noble gas. Exceptions include species with incomplete octets, odd-electron species, and expanded octets.
Example: Carbon forms four bonds in \(\ce{CH4}\), achieving an octet: \(4 \text{ (bonding pairs)} \times 2 = 8\) electrons around C.
Open Systems
A thermodynamic system that can exchange both energy and matter with its surroundings. Open systems are common in living organisms and industrial processes where mass and energy flow continuously.
Example: A beaker of boiling water is an open system; water vapor (matter) and heat (energy) both transfer to the surroundings.
Orbital Hybridization
A quantum mechanical concept in which standard atomic orbitals (s, p, d) are mathematically combined to form new, equivalent hybrid orbitals with specific geometries, explaining the observed bond angles and shapes of molecules.
Example: Carbon in methane (\(\ce{CH4}\)) forms four equivalent \(sp^3\) hybrid orbitals (from one 2s and three 2p orbitals), giving tetrahedral geometry with 109.5° bond angles.
Orbital Shapes
The three-dimensional regions of space defined by each type of atomic orbital, described by angular momentum quantum number \(l\): s orbitals are spherical (\(l=0\)); p orbitals are dumbbell-shaped (\(l=1\)); d orbitals have more complex shapes (\(l=2\)).
Example: The 2p orbital has a dumbbell shape with two lobes of electron density on opposite sides of the nucleus, separated by a nodal plane where electron density is zero.
Orbitals
Regions of space around an atomic nucleus where the probability of finding an electron is 90% or greater, described by a wave function with specific quantum numbers (n, l, ml). Each orbital holds at most two electrons with opposite spins.
Example: The \(3d_{xy}\) orbital is one of five equivalent 3d orbitals; it has four lobes of electron density in the xy plane between the x and y axes.
Orientation Factor
The probability factor (steric factor, \(p\)) in the modified collision theory rate expression that accounts for the requirement that reactant molecules must collide with the correct geometric orientation for a reaction to occur. \(0 < p \leq 1\).
Example: Linear molecules reacting end-to-end have a small orientation factor; reactions requiring specific orbital overlap (like \(S_N2\) reactions) are particularly orientation-sensitive.
Oxidation
The loss of electrons by an atom, ion, or molecule in a redox reaction, resulting in an increase in the oxidation state of the element. Oxidation always occurs simultaneously with reduction (they are paired in every redox reaction).
Example: In \(\ce{Zn -> Zn^{2+} + 2e-}\), zinc is oxidized; its oxidation state increases from 0 to +2.
Oxidation States
Formal numbers assigned to each atom in a compound or ion indicating the charge it would have if all electrons were assigned to the more electronegative atom in each bond. Used to track electron transfer in redox reactions. Also called oxidation numbers.
Example: In \(\ce{KMnO4}\): K = +1, O = −2; so \(+1 + Mn + 4(-2) = 0\), giving Mn an oxidation state of +7.
Oxidizing Agents
Substances that cause oxidation of another species by accepting electrons from it, thereby being reduced themselves in a redox reaction. Strong oxidizing agents include \(\ce{F2}\), \(\ce{Cl2}\), \(\ce{O2}\), \(\ce{MnO4-}\), and \(\ce{Cr2O7^{2-}}\).
Example: In \(\ce{Cu + 2AgNO3 -> Cu(NO3)2 + 2Ag}\), \(\ce{Ag+}\) is the oxidizing agent; it accepts electrons from copper and is reduced to silver metal.
Oxyacid Strength
The relative strength of oxyacids (acids containing oxygen), which increases with the number of oxygen atoms bonded to the central nonmetal and with the electronegativity of the central atom. More electronegative atoms and more oxygen atoms stabilize the conjugate base.
Example: Acid strength order: \(\ce{HClO4}\) > \(\ce{HClO3}\) > \(\ce{HClO2}\) > \(\ce{HClO}\); each additional oxygen atom increases the electronegativity around Cl, weakening the O-H bond and strengthening the acid.
Paramagnetism and Diamagnetism
Paramagnetism is the property of substances with unpaired electrons being weakly attracted into a magnetic field. Diamagnetism is the property of substances with all electrons paired being weakly repelled by a magnetic field. Paramagnetism is predicted by counting unpaired electrons.
Example: \(\ce{O2}\) is paramagnetic (has 2 unpaired electrons in \(\pi^*\) MOs) and is attracted to magnets; \(\ce{N2}\) is diamagnetic (all electrons paired) and is slightly repelled.
Partial Pressures
The pressure that each individual gas in a mixture would exert if it alone occupied the entire volume of the container at the same temperature. Partial pressure is calculated as \(P_A = \chi_A P_{total}\), where \(\chi_A\) is the mole fraction.
Example: In a 1.0 L container at 300 K with 0.4 mol \(\ce{N2}\) and 0.6 mol \(\ce{O2}\): \(P_{total} = 24.6\) atm; \(P_{N_2} = 0.4 \times 24.6 = 9.85\) atm; \(P_{O_2} = 0.6 \times 24.6 = 14.8\) atm.
Path Functions
Thermodynamic quantities whose values depend on the specific path taken between two states, not just on the initial and final states. Heat (\(q\)) and work (\(w\)) are path functions; they are not state functions because their values change depending on how the process occurs.
Example: Expanding a gas isothermally against a constant external pressure versus expanding into a vacuum gives the same \(\Delta U\) (state function) but different values of \(w\) (path function).
Pauli Exclusion Principle
The quantum mechanical rule stating that no two electrons in an atom can have identical sets of all four quantum numbers (\(n\), \(l\), \(m_l\), \(m_s\)). As a consequence, each orbital can hold at most two electrons and they must have opposite spins.
Example: The two electrons in the 1s orbital of helium have quantum numbers (1,0,0,+½) and (1,0,0,−½); they differ only in spin quantum number \(m_s\).
Percent Composition
The percent by mass of each element in a compound, calculated as \(\%\text{ element} = \frac{\text{mass of element in one formula unit}}{\text{molar mass of compound}} \times 100\). Used to verify compound identity and calculate empirical formulas.
Example: In \(\ce{H2O}\): \(\%\text{H} = (2 \times 1.008)/18.02 \times 100 = 11.19\%\); \(\%\text{O} = 16.00/18.02 \times 100 = 88.81\%\).
Percent Error
A measure of the accuracy of an experimental measurement relative to an accepted value: \(\%\text{ error} = \frac{|\text{experimental} - \text{accepted}|}{|\text{accepted}|} \times 100\). Smaller percent error indicates higher accuracy.
Example: Measuring the density of aluminum as 2.59 g/mL (accepted: 2.70 g/mL) gives \(\%\text{ error} = |2.59-2.70|/2.70 \times 100 = 4.1\%\).
Percent Ionization
The percentage of a weak acid (or base) that ionizes in solution: \(\%\text{ ionization} = \frac{[\ce{H+}]_{eq}}{[\text{HA}]_0} \times 100\). Percent ionization increases as concentration decreases for a weak acid with constant \(K_a\).
Example: Acetic acid (\(K_a = 1.8 \times 10^{-5}\)) at 0.10 M: \([\ce{H+}] = 1.34 \times 10^{-3}\) M; \(\%\text{ ionization} = 1.34 \times 10^{-3}/0.10 \times 100 = 1.3\%\).
Percent Purity
The percentage of a desired substance in a sample that may contain impurities: \(\%\text{ purity} = \frac{\text{mass of pure substance}}{\text{mass of sample}} \times 100\). Determined experimentally and used in industrial quality control.
Example: A 5.0 g sample of \(\ce{NaHCO3}\) reacts with excess \(\ce{HCl}\) and produces 2.1 g \(\ce{CO2}\) (theoretical for pure: 2.5 g); purity = \(2.1/2.5 \times 100 = 84\%\).
Percent Yield
The ratio of actual yield to theoretical yield, expressed as a percentage: \(\%\text{ yield} = (\text{actual yield}/\text{theoretical yield}) \times 100\). Always between 0 and 100% for a single reaction; below 100% due to incomplete reactions, side reactions, and product loss.
Example: If a reaction theoretically produces 15.0 g of product but only 12.3 g is collected, \(\%\text{ yield} = 12.3/15.0 \times 100 = 82.0\%\).
Periodic Table Organization
The arrangement of elements in order of increasing atomic number into horizontal rows (periods) and vertical columns (groups), placing elements with similar valence electron configurations and chemical properties in the same group.
Example: Group 1 (alkali metals: Li, Na, K, Rb, Cs, Fr) all have the valence configuration \(ns^1\) and all react vigorously with water to form metal hydroxides and hydrogen gas.
Periodic Trends
The systematic variations in physical and chemical properties of elements as atomic number increases across a period or down a group. Key trends include atomic radius, ionization energy, electron affinity, electronegativity, and metallic character.
Example: Across Period 3: atomic radius decreases (Na > Mg > Al > Si > P > S > Cl > Ar); ionization energy generally increases; electronegativity increases.
Periods and Groups
Periods are horizontal rows of the periodic table (numbered 1–7); elements in the same period have the same highest principal quantum number for valence electrons. Groups are vertical columns (numbered 1–18); elements in the same group have the same valence electron configuration and similar properties.
Example: Period 2 contains Li, Be, B, C, N, O, F, Ne — all with \(n = 2\) as the highest shell; Group 17 (halogens) all have \(ns^2np^5\) valence configuration.
PES Data Interpretation
The analysis of photoelectron spectroscopy (PES) data showing relative intensities and binding energies of electrons removed from atoms. Peak position (binding energy) identifies which subshell electrons came from; peak height reflects the relative number of electrons in that subshell.
Example: The PES spectrum of neon shows three peaks: a large peak (lower binding energy, 2p — 6 electrons), a medium peak (2s — 2 electrons), and a small-area peak (1s — 2 electrons, highest binding energy).
pH and pOH Relationship
At 25°C, the sum of pH and pOH equals 14.00 (from \(K_w = 10^{-14}\)): \(\text{pH} + \text{pOH} = 14.00\). This relationship allows calculation of pOH from pH and vice versa for any aqueous solution at 25°C.
Example: A solution with pH = 3.50 has pOH = \(14.00 - 3.50 = 10.50\); \([\ce{OH-}] = 10^{-10.50} = 3.16 \times 10^{-11}\) M.
pH Calculation
The determination of the hydrogen ion concentration and pH of a solution from known information. For strong acids: \(\text{pH} = -\log[\text{HA}]\) (complete dissociation); for weak acids: use the ICE table and \(K_a\) expression.
Example: For 0.050 M \(\ce{HCl}\) (strong acid): \([\ce{H+}] = 0.050\) M; \(\text{pH} = -\log(0.050) = 1.30\).
pH of Mixed Solutions
The calculation of the pH resulting from mixing two acidic or basic solutions, or an acid solution with a basic solution, accounting for dilution and any neutralization reactions before calculating the final \([\ce{H+}]\).
Example: Mixing 50 mL of 0.20 M \(\ce{HCl}\) with 30 mL of 0.20 M \(\ce{NaOH}\): moles \(\ce{HCl}\) = 0.010, moles \(\ce{NaOH}\) = 0.006; excess \(\ce{HCl}\) = 0.004 mol in 80 mL; \([\ce{H+}] = 0.050\) M; pH = 1.30.
pH Scale
A logarithmic scale (0–14 at 25°C, but can extend beyond) measuring the acidity or basicity of an aqueous solution: \(\text{pH} = -\log[\ce{H+}]\). pH < 7 is acidic, pH = 7 is neutral, pH > 7 is basic at 25°C. Each unit represents a 10-fold change in \([\ce{H+}]\).
Example: Lemon juice has pH ≈ 2 (\([\ce{H+}] \approx 0.01\) M); blood has pH ≈ 7.4; bleach has pH ≈ 12 (\([\ce{H+}] \approx 10^{-12}\) M).
Phase Changes
The transitions between the three states of matter: melting (solid → liquid), freezing (liquid → solid), vaporization (liquid → gas), condensation (gas → liquid), sublimation (solid → gas), and deposition (gas → solid). Each change occurs at a characteristic temperature and pressure.
Example: Dry ice (\(\ce{CO2}\)) sublimes at −78°C at atmospheric pressure, transitioning directly from solid to gas without passing through the liquid phase.
Phase Diagrams
Graphs showing the conditions of temperature and pressure under which the solid, liquid, and gas phases of a substance are stable. Key features include the triple point (all three phases coexist), critical point, and phase boundaries (coexistence curves).
Example: Water's phase diagram shows a triple point at 0.006 atm and 0.01°C; the unusual negative slope of the solid-liquid boundary explains why ice melts under pressure.
Photoelectric Effect
The emission of electrons from a metal surface when light of sufficient frequency shines on it. Einstein explained that light consists of photons with energy \(E = h\nu\); electrons are ejected only when photon energy exceeds the metal's work function, regardless of light intensity.
Example: Cesium metal has a work function of 2.1 eV; light with \(\nu < 5.1 \times 10^{14}\) Hz cannot eject electrons regardless of how bright it is.
Photoelectron Spectroscopy
An analytical technique in which a sample is bombarded with high-energy photons (X-rays or UV), causing photoionization of electrons. The kinetic energies of ejected electrons are measured to determine electron binding energies, providing information about atomic subshell structure.
Example: PES confirms that the first ionization energy of carbon corresponds to removal of a 2p electron (least tightly bound), with 2s electrons bound more tightly and 1s electrons most tightly bound.
Photon Energy
The energy of a single quantum of electromagnetic radiation (photon), calculated by Planck's equation: \(E = h\nu = hc/\lambda\), where \(h = 6.626 \times 10^{-34}\) J·s is Planck's constant, \(\nu\) is frequency, \(c\) is speed of light, and \(\lambda\) is wavelength.
Example: A photon of red light with \(\lambda = 700\) nm has energy \(E = (6.626 \times 10^{-34})(3.00 \times 10^8)/(700 \times 10^{-9}) = 2.84 \times 10^{-19}\) J.
Physical Changes
Changes in the form or appearance of matter that do not alter the chemical composition. Physical changes are generally reversible and include changes of state, dissolution, changes in shape, and mixing.
Example: Dissolving sugar in water, melting ice, and crushing a can are physical changes; the chemical identity of the substances is unchanged.
Physical Properties
Characteristics of a substance that can be measured or observed without changing the substance's chemical composition, including density, boiling point, melting point, color, hardness, electrical conductivity, and solubility.
Example: Water's physical properties include a boiling point of 100°C, density of 1.000 g/mL at 4°C, and colorless appearance; these can be measured without decomposing water.
Pi Bonds
Covalent bonds formed by the sideways (lateral) overlap of parallel \(p\) orbitals on adjacent atoms, creating a region of electron density above and below the internuclear axis. Pi bonds are weaker than sigma bonds and restrict rotation around the bond axis.
Example: Ethene (\(\ce{C2H4}\)) has one sigma bond and one pi bond between the two carbons; the pi bond prevents rotation around the C=C double bond, making cis-trans isomers possible.
Planck's Equation
The equation \(E = h\nu\) relating the energy of a photon to its frequency, where \(h = 6.626 \times 10^{-34}\) J·s is Planck's constant and \(\nu\) is frequency in Hz. This equation quantizes electromagnetic radiation and is fundamental to quantum mechanics.
Example: A photon of UV light with \(\nu = 1.00 \times 10^{15}\) Hz has energy \(E = (6.626 \times 10^{-34})(1.00 \times 10^{15}) = 6.626 \times 10^{-19}\) J.
Polar Covalent Bonds
Covalent bonds between two atoms with different electronegativities (difference 0.4–1.7), in which the shared electrons are pulled toward the more electronegative atom, creating partial positive (\(\delta+\)) and partial negative (\(\delta-\)) charges on opposite ends.
Example: In \(\ce{H2O}\), the O-H bonds are polar covalent (electronegativity difference: 3.44 − 2.20 = 1.24); oxygen bears a \(\delta-\) charge and each hydrogen a \(\delta+\) charge.
Polar Molecules
Molecules with a net (nonzero) dipole moment, resulting from polar bonds arranged asymmetrically. Polar molecules have a positive end and a negative end, interact more strongly with each other and with polar solvents, and experience dipole-dipole forces.
Example: Water (\(\ce{H2O}\)) is polar (dipole moment = 1.85 D) because its two polar O-H bonds are oriented at 104.5° and their dipoles do not cancel.
Polarizability
The ease with which the electron cloud of an atom or molecule can be distorted by an external electric field or nearby charge. Polarizability increases with atomic size and number of electrons. Highly polarizable atoms form stronger London dispersion forces.
Example: Iodine (\(\ce{I2}\)) is much more polarizable than fluorine (\(\ce{F2}\)) due to its larger, more diffuse electron cloud; this explains why \(\ce{I2}\) is a solid (strong London forces) while \(\ce{F2}\) is a gas.
Polyatomic Ions
Ions composed of two or more covalently bonded atoms that carry a net charge. Common examples include \(\ce{SO4^{2-}}\), \(\ce{NO3-}\), \(\ce{NH4+}\), \(\ce{OH-}\), \(\ce{CO3^{2-}}\), and \(\ce{PO4^{3-}}\). Their formulas and charges must be memorized.
Example: The sulfate ion \(\ce{SO4^{2-}}\) consists of one sulfur atom covalently bonded to four oxygen atoms, carrying an overall charge of 2−; it behaves as a unit in ionic compounds.
Polyprotic Acids
Acids capable of donating more than one proton per molecule. Each successive proton is harder to remove, so \(K_{a1} > K_{a2} > K_{a3}\). The pH is dominated by the first dissociation; subsequent dissociations contribute negligibly to \([\ce{H+}]\).
Example: Phosphoric acid (\(\ce{H3PO4}\)) is triprotic: \(K_{a1} = 7.5 \times 10^{-3}\), \(K_{a2} = 6.2 \times 10^{-8}\), \(K_{a3} = 4.8 \times 10^{-13}\).
pOH
A logarithmic measure of the hydroxide ion concentration in a solution: \(\text{pOH} = -\log[\ce{OH-}]\). At 25°C, \(\text{pH} + \text{pOH} = 14.00\). Lower pOH indicates a more basic solution.
Example: A 0.010 M \(\ce{NaOH}\) solution: \([\ce{OH-}] = 0.010\) M; \(\text{pOH} = -\log(0.010) = 2.00\); \(\text{pH} = 14.00 - 2.00 = 12.00\).
Precipitate Identification
The use of solubility rules, selective precipitation, or qualitative analysis tests to identify anions or cations in a solution based on the formation of characteristic insoluble precipitates with specific reagents.
Example: Adding \(\ce{BaCl2}\) to an unknown solution: a white precipitate forming indicates \(\ce{SO4^{2-}}\) (insoluble \(\ce{BaSO4}\)); no precipitate indicates \(\ce{SO4^{2-}}\) is absent.
Precipitation Reactions
Double replacement reactions in which mixing two aqueous solutions produces an insoluble solid product (precipitate) that falls out of solution. Driving force is the formation of an insoluble ionic compound.
Example: \(\ce{Pb(NO3)2 (aq) + 2NaI (aq) -> PbI2 (s) + 2NaNO3 (aq)}\); the bright yellow lead(II) iodide precipitate forms immediately upon mixing.
Predicting Direction
The use of the reaction quotient \(Q\) compared to the equilibrium constant \(K\) to determine which direction an equilibrium reaction will shift: if \(Q < K\), the reaction shifts toward products; if \(Q > K\), toward reactants; if \(Q = K\), the system is at equilibrium.
Predicting Precipitation
The use of the ion product \(Q_{sp}\) (concentration product) compared to \(K_{sp}\) to predict whether a precipitate will form: precipitation occurs when \(Q_{sp} > K_{sp}\); no precipitation when \(Q_{sp} < K_{sp}\); saturated solution when \(Q_{sp} = K_{sp}\).
Example: Mixing 1.0 × 10\(^{-3}\) M \(\ce{Ca^{2+}}\) with 1.0 × 10\(^{-4}\) M \(\ce{F-}\): \(Q_{sp} = (10^{-3})(10^{-4})^2 = 10^{-11} > K_{sp}(\ce{CaF2}) = 3.9 \times 10^{-11}\)? If yes, \(\ce{CaF2}\) precipitates.
Pressure Changes
Changes in total pressure on a gaseous equilibrium system, which shift the equilibrium toward the side with fewer moles of gas (if pressure increases) or more moles of gas (if pressure decreases). Pressure changes have no effect on equilibria with equal moles of gas on both sides.
Example: Increasing pressure on \(\ce{N2 (g) + 3H2 (g) <=> 2NH3 (g)}\) (4 mol gas → 2 mol gas) shifts equilibrium toward \(\ce{NH3}\) to reduce total moles of gas.
Primary Standards
High-purity, stable, nonhygroscopic solids of known molar mass used to prepare standard solutions of accurately known concentration in titrimetry. Examples include potassium hydrogen phthalate (KHP) for standardizing bases and sodium oxalate for permanganate.
Example: Potassium hydrogen phthalate (\(\ce{KHC8H4O4}\), KHP) is a primary standard for \(\ce{NaOH}\); its exact mass is weighed, dissolved, and titrated to determine the exact concentration of \(\ce{NaOH}\).
Principal Quantum Number
The quantum number \(n\) (positive integer: 1, 2, 3, …) that describes the energy level (shell) of an electron in an atom. Larger \(n\) values correspond to higher energy and larger average distance from the nucleus. Also called the shell number.
Example: Electrons with \(n = 1\) (K shell) are closest to the nucleus and most tightly bound; \(n = 4\) electrons (N shell) are farther from the nucleus and less tightly bound.
PV Work
Work done on or by a system through volume changes against an external pressure: \(w = -P_{ext}\Delta V\). When a gas expands against external pressure, the system does work on the surroundings (\(w < 0\)); when compressed, surroundings do work on the system (\(w > 0\)).
Example: A gas expanding from 2.0 L to 5.0 L at constant external pressure of 1.5 atm: \(w = -(1.5)(3.0) = -4.5\) L·atm = \(-456\) J (system does work on surroundings).
Q vs K Comparison
The comparison of the reaction quotient \(Q\) (calculated using current concentrations) with the equilibrium constant \(K\) (using equilibrium concentrations) to predict the direction of reaction. \(Q < K\): forward reaction favored; \(Q > K\): reverse reaction favored; \(Q = K\): at equilibrium.
Example: For \(\ce{N2 + 3H2 <=> 2NH3}\) with \(K = 0.50\), if \(Q = 2.0 > K\), the reaction will proceed in reverse (decomposing \(\ce{NH3}\)) until equilibrium is restored.
Qualitative Analysis
The branch of analytical chemistry concerned with identifying the components of a chemical sample, rather than measuring their amounts. Methods include flame tests, precipitation reactions, color observations, and gas tests to identify specific ions or compounds.
Example: A systematic qualitative analysis scheme separates and identifies common cations (\(\ce{Ag+}\), \(\ce{Pb^{2+}}\), \(\ce{Cu^{2+}}\), \(\ce{Fe^{3+}}\), etc.) using a series of selective precipitating agents.
Quadratic in Equilibrium
The use of the quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\) to solve equilibrium problems when the small-\(x\) approximation is invalid (typically when \(K_a/C > 1 \times 10^{-3}\) or less than 5% ionization cannot be assumed).
Example: For \(\ce{HA <=> H+ + A-}\) with \(K_a = 4.0 \times 10^{-3}\) and \([\text{HA}]_0 = 0.100\) M: solving \(4.0 \times 10^{-3} = x^2/(0.100-x)\) requires the quadratic formula because the approximation is invalid (\(K_a/C = 4\%\), borderline).
Quantum Mechanical Model
The modern model of the atom based on the Schrödinger equation and the Heisenberg uncertainty principle, describing electrons as wave functions (probability distributions) in atomic orbitals. Electrons have quantized energies and cannot be assigned definite position and momentum simultaneously.
Example: The quantum mechanical model correctly predicts atomic emission spectra, explains the periodic table, and describes bonding in terms of orbital overlap — none of which the Bohr model could do.
Rate Constant
The proportionality constant \(k\) in the rate law, specific to a particular reaction at a particular temperature. Units of \(k\) depend on the overall reaction order. Increasing temperature increases \(k\) (Arrhenius equation); catalysts change \(k\) by lowering \(E_a\).
Example: For a second-order reaction (rate = \(k[\text{A}]^2\)), \(k\) has units of L mol\(^{-1}\) s\(^{-1}\); a larger value of \(k\) means a faster reaction at the same concentration.
Rate Law
A mathematical expression relating the rate of a chemical reaction to the concentrations of reactants: \(\text{rate} = k[\text{A}]^m[\text{B}]^n \ldots\), where \(k\) is the rate constant and \(m\), \(n\) are the reaction orders. Determined experimentally, not from the balanced equation.
Example: For \(\ce{2NO + Cl2 -> 2NOCl}\), the experimentally determined rate law is \(\text{rate} = k[\ce{NO}]^2[\ce{Cl2}]\); the second order in NO reflects the elementary mechanism.
Rate of Appearance
The rate at which the concentration of a product increases with time: \(\text{rate} = +\frac{\Delta[\text{product}]}{\Delta t}\). Always positive. Related to the rate of disappearance by the stoichiometric coefficients.
Example: For \(\ce{2SO2 + O2 -> 2SO3}\): rate of appearance of \(\ce{SO3}\) = \(+\frac{\Delta[\ce{SO3}]}{\Delta t}\) = rate of disappearance of \(\ce{SO2}\) = \(2 \times\) rate of disappearance of \(\ce{O2}\).
Rate of Disappearance
The rate at which the concentration of a reactant decreases with time: \(\text{rate} = -\frac{\Delta[\text{reactant}]}{\Delta t}\). Always positive because concentration decreases. Related to rate of appearance by stoichiometric ratios.
Example: For \(\ce{N2 + 3H2 -> 2NH3}\): \(-\frac{\Delta[\ce{N2}]}{\Delta t} = -\frac{1}{3}\frac{\Delta[\ce{H2}]}{\Delta t} = \frac{1}{2}\frac{\Delta[\ce{NH3}]}{\Delta t}\).
Rate-Determining Step
The slowest elementary step in a reaction mechanism, which controls the overall reaction rate. The rate law for the overall reaction is determined by the rate law of the rate-determining step, using concentrations of species that appear up to and including that step.
Example: If the mechanism has a slow first step \(\ce{A + B -> C}\) and a fast second step \(\ce{C -> D}\), the rate-determining step gives rate = \(k[\text{A}][\text{B}]\), which matches the overall rate law.
Reaction Intermediates
Species produced in one elementary step of a reaction mechanism and consumed in a subsequent step. Intermediates appear in the mechanism but not in the overall balanced equation. They are distinct from catalysts, which are regenerated.
Example: In the ozone depletion mechanism, \(\ce{Cl}\) atoms are intermediates: \(\ce{Cl + O3 -> ClO + O2}\) (forms ClO) then \(\ce{ClO + O -> Cl + O2}\) (consumes ClO, regenerates Cl). \(\ce{ClO}\) is the intermediate; \(\ce{Cl}\) is the catalyst.
Reaction Mechanisms
Step-by-step sequences of elementary reactions by which reactants are converted to products. A valid mechanism must sum to the overall reaction equation, be consistent with the experimentally determined rate law, and have reasonable elementary steps.
Example: The mechanism for \(\ce{NO2 + CO -> NO + CO2}\) involves two steps: (1) slow \(\ce{NO2 + NO2 -> NO3 + NO}\); (2) fast \(\ce{NO3 + CO -> NO2 + CO2}\); overall: \(\ce{NO2 + CO -> NO + CO2}\).
Reaction Order
The exponent of a reactant's concentration in the rate law, indicating how the rate depends on that concentration. Overall reaction order is the sum of all individual orders. Orders are determined experimentally and are usually small integers (0, 1, 2) or simple fractions.
Example: In rate = \(k[\ce{A}]^1[\ce{B}]^2\), the reaction is first order in A, second order in B, and third order overall.
Reaction Prediction
The use of activity series, solubility rules, acid-base theory, and redox potentials to predict whether a particular chemical reaction will occur and what products will form.
Example: Predicting whether \(\ce{Mg + CuSO4 ->}\) occurs: Mg is above Cu in the activity series, so Mg will displace Cu; products are \(\ce{MgSO4 + Cu}\).
Reaction Quotient Q
A value calculated using the same expression as the equilibrium constant \(K\) but using the actual (non-equilibrium) concentrations or pressures at any point in time. Comparison of \(Q\) with \(K\) predicts the direction of the net reaction.
Example: For \(\ce{A <=> B + C}\) at some time, if \([\text{A}] = 0.5\), \([\text{B}] = 0.2\), \([\text{C}] = 0.3\), then \(Q = (0.2)(0.3)/0.5 = 0.12\); if \(K = 0.50\), since \(Q < K\), reaction proceeds forward.
Reaction Rate
The speed at which reactants are consumed or products are formed in a chemical reaction, expressed as the change in concentration per unit time. Units: M/s (mol L\(^{-1}\) s\(^{-1}\)). Rate depends on concentration, temperature, catalysts, and surface area.
Example: If \([\ce{A}]\) decreases from 0.80 M to 0.20 M in 60 s, the average rate of disappearance of A = \((0.80-0.20)/60 = 0.010\) M/s.
Reaction Types Overview
A classification of chemical reactions into five main types: synthesis (combination), decomposition, single replacement, double replacement, and combustion. Some sources add acid-base (neutralization), precipitation, and redox as additional categories.
Example: \(\ce{Fe + S -> FeS}\) (synthesis); \(\ce{H2O2 -> H2O + O2}\) (decomposition); \(\ce{Zn + HCl -> ZnCl2 + H2}\) (single replacement); \(\ce{HCl + NaOH -> NaCl + H2O}\) (double replacement/neutralization).
Real Gases
Actual gases that deviate from ideal behavior because gas particles have finite volume and experience intermolecular attractive forces. Deviations are most pronounced at high pressure and low temperature, described by the van der Waals equation.
Example: At very high pressures, real gases are more compressible than ideal predictions (at moderate pressures, intermolecular attractions reduce volume) and less compressible at extreme pressures (particle volumes matter).
Redox Reactions
Chemical reactions in which electrons are transferred from one species (which is oxidized) to another (which is reduced). Oxidation and reduction always occur simultaneously. Identified by changes in oxidation states. Basis of electrochemistry, corrosion, and combustion.
Example: \(\ce{2Fe^{3+} + Sn^{2+} -> 2Fe^{2+} + Sn^{4+}}\): \(\ce{Fe^{3+}}\) is reduced (gains electrons, oxidation state decreases from +3 to +2); \(\ce{Sn^{2+}}\) is oxidized.
Reducing Agents
Substances that cause reduction of another species by donating electrons to it, thereby being oxidized themselves. Strong reducing agents include active metals (Li, Na, K, Mg, Al, Zn), hydrogen, and carbon monoxide.
Example: In \(\ce{Zn + CuSO4 -> ZnSO4 + Cu}\), zinc is the reducing agent; it donates electrons to \(\ce{Cu^{2+}}\) and is oxidized from 0 to +2.
Reduction
The gain of electrons by an atom, ion, or molecule in a redox reaction, resulting in a decrease in the oxidation state of the element. Reduction always occurs simultaneously with oxidation.
Example: \(\ce{Cu^{2+} + 2e- -> Cu}\): copper(II) ion gains electrons and its oxidation state decreases from +2 to 0; copper ion is reduced to copper metal.
Relative Abundance
The percentage of each naturally occurring isotope of an element, used to calculate the weighted average atomic mass. Relative abundances sum to 100% across all isotopes of an element.
Example: Boron: \(\ce{^{10}B}\) (19.9%, 10.013 amu) and \(\ce{^{11}B}\) (80.1%, 11.009 amu); average mass = \(0.199(10.013) + 0.801(11.009) = 10.81\) amu.
Resonance Hybrid
The actual structure of a molecule or ion that cannot be accurately represented by a single Lewis structure, described as a superposition (blend) of all contributing resonance structures. The resonance hybrid is more stable than any individual resonance structure.
Example: The \(\ce{CO3^{2-}}\) ion is a resonance hybrid with three equivalent C-O bonds (bond order 1.33), rather than two single bonds and one double bond as any single Lewis structure shows.
Resonance Structures
Two or more Lewis structures for the same species that have the same atomic connectivity but differ in the placement of electrons (pi bonds and lone pairs). All resonance structures are contributing forms of the actual resonance hybrid.
Example: The nitrate ion \(\ce{NO3-}\) has three equivalent resonance structures, each showing a different oxygen as double-bonded to nitrogen; the actual ion has three equivalent N-O bonds.
Reverse Reaction
The reaction that proceeds from right to left in a chemical equation, representing the conversion of products back to reactants. In an equilibrium system, the reverse reaction and forward reaction occur simultaneously at equal rates at equilibrium.
Reversing Reactions K
When a chemical equation is reversed, the equilibrium constant of the reversed reaction is the reciprocal of the original: \(K_{reverse} = 1/K_{forward}\). This follows from the definition of \(K\) as a ratio of products to reactants concentrations.
Example: If \(\ce{A + B <=> C}\) has \(K = 10^3\), then \(\ce{C <=> A + B}\) has \(K = 1/10^3 = 10^{-3}\).
Salt Bridge
An electrolyte-filled tube or porous plug connecting the two half-cells of a galvanic cell, allowing ions to migrate between half-cells to maintain electrical neutrality without direct mixing of the solutions. Without it, charge buildup would halt the reaction.
Example: In a zinc-copper galvanic cell, a \(\ce{KNO3}\) salt bridge allows \(\ce{K+}\) ions to flow toward the cathode compartment and \(\ce{NO3-}\) ions toward the anode to balance the charge buildup.
Salt Hydrolysis
The reaction of an anion or cation of a salt with water, producing an acidic or basic solution. Cations of weak bases hydrolyze to give \(\ce{H+}\) (acidic); anions of weak acids hydrolyze to give \(\ce{OH-}\) (basic); salts of strong acids and strong bases do not hydrolyze.
Example: \(\ce{NH4Cl}\) hydrolyzes: \(\ce{NH4+ + H2O <=> NH3 + H3O+}\); the solution is acidic because \(\ce{NH4+}\) donates a proton to water.
Saturated Solutions
Solutions that contain the maximum amount of dissolved solute at a given temperature and pressure, in equilibrium with undissolved solute. Any additional solute added to a saturated solution will not dissolve.
Example: At 20°C, a saturated \(\ce{NaCl}\) solution contains approximately 36 g of \(\ce{NaCl}\) per 100 g of water; adding more \(\ce{NaCl}\) produces a visible solid at the bottom.
Scientific Method
The systematic process of asking questions and using evidence to develop and test explanations: observation, hypothesis, experimental design, data collection, analysis, conclusion, and peer review. The cornerstone of scientific knowledge-building.
Scientific Notation
A way of expressing very large or very small numbers as a coefficient between 1 and 10 multiplied by a power of 10: \(a \times 10^n\) where \(1 \leq a < 10\) and \(n\) is an integer. Essential in chemistry where quantities span many orders of magnitude.
Example: Avogadro's number = \(6.022 \times 10^{23}\); the mass of a proton = \(1.673 \times 10^{-27}\) kg.
Second Law Thermodynamics
The law stating that the total entropy of the universe increases for any spontaneous process: \(\Delta S_{universe} = \Delta S_{system} + \Delta S_{surroundings} > 0\). A process is spontaneous if it increases the total entropy of the universe; reversible processes have \(\Delta S_{universe} = 0\).
Example: Heat spontaneously flows from hot to cold (increasing the entropy of the universe); the reverse process (cold to hot spontaneously) would decrease universal entropy and never occurs.
Second Order Integrated Law
The integrated rate law for second-order reactions (in one reactant): \(\frac{1}{[\text{A}]_t} = \frac{1}{[\text{A}]_0} + kt\). A plot of \(1/[\text{A}]\) vs. time is linear with slope \(= +k\) and y-intercept \(= 1/[\text{A}]_0\).
Example: If \([\text{A}]_0 = 2.00\) M and \(k = 0.050\) L mol\(^{-1}\) s\(^{-1}\), after 10 s: \(1/[\text{A}] = 1/2.00 + (0.050)(10) = 1.0\); \([\text{A}] = 1.00\) M.
Second Order Reactions
Reactions in which the rate depends on the square of one reactant's concentration or on the product of two different reactants' concentrations: \(\text{rate} = k[\text{A}]^2\) or \(k[\text{A}][\text{B}]\). Half-life depends on initial concentration: \(t_{1/2} = 1/(k[\text{A}]_0)\).
Example: The reaction \(\ce{2HI (g) -> H2 (g) + I2 (g)}\) is second order overall: rate = \(k[\ce{HI}]^2\); doubling \([\ce{HI}]\) quadruples the rate.
Selective Precipitation
A technique used to separate mixtures of cations by adding a precipitating agent that selectively precipitates one ion while leaving others in solution, based on differences in their \(K_{sp}\) values.
Example: Adding dilute \(\ce{HCl}\) to a solution containing \(\ce{Ag+}\), \(\ce{Pb^{2+}}\), and \(\ce{Cu^{2+}}\) precipitates \(\ce{AgCl}\) and \(\ce{PbCl2}\) (insoluble) while \(\ce{CuCl2}\) remains dissolved (soluble).
Serial Dilutions
A stepwise dilution technique in which a solution is diluted by the same factor in multiple successive steps, producing a geometric series of concentrations. Used to prepare standards for calibration curves and to reduce highly concentrated samples to measurable levels.
Example: A 1:10 serial dilution of a 1.0 M solution: step 1 → 0.10 M; step 2 → 0.010 M; step 3 → 0.0010 M (each step uses \(M_1V_1 = M_2V_2\)).
SI Units
The International System of Units (Système International), the modern standardized metric system. The seven base SI units include: meter (m, length), kilogram (kg, mass), second (s, time), kelvin (K, temperature), mole (mol, amount), ampere (A, current), and candela (cd, luminous intensity).
Example: Pressure in SI is the pascal (Pa = N/m\(^2\)); in chemistry, kilopascals (kPa) and atmospheres (1 atm = 101.325 kPa) are common.
Sigma Bonds
Covalent bonds formed by the head-on (end-to-end) overlap of atomic orbitals along the internuclear axis, creating a cylindrically symmetric region of electron density. Sigma bonds are the first bond formed between two atoms; all single bonds are sigma bonds. Free rotation is possible around sigma bonds.
Example: In ethane (\(\ce{C2H6}\)), the C-C and all C-H bonds are sigma bonds; free rotation around the C-C sigma bond allows different conformations.
Significant Figures
The digits in a measurement that convey meaningful information about the precision of the measurement, including all certain digits plus one uncertain (estimated) digit. Rules govern which zeros are significant and how significant figures propagate through calculations.
Example: 0.00350 has 3 significant figures (the leading zeros are not significant; the trailing zero after 5 is significant); \(4.500 \times 10^3\) has 4 significant figures.
Single Bonds
Covalent bonds formed by one shared pair of electrons (one sigma bond) between two atoms. Single bonds have the longest bond length and lowest bond energy compared to double and triple bonds between the same pair of atoms. Free rotation is possible.
Example: The C-C single bond in ethane (\(\ce{C2H6}\)) has a length of 154 pm and bond energy of 347 kJ/mol, while the C=C double bond in ethene is 134 pm and 614 kJ/mol.
Single Replacement
A reaction type in which one element displaces another element from a compound: \(\ce{A + BC -> AC + B}\). Whether the reaction occurs depends on the activity series (for metals) or the halogen reactivity trend (for halogens).
Example: \(\ce{Fe (s) + CuSO4 (aq) -> FeSO4 (aq) + Cu (s)}\); iron displaces copper because iron is above copper in the activity series.
Small K Approximation
A simplifying assumption used in equilibrium calculations when \(K\) is very small (typically \(K < 1 \times 10^{-3}\)): the change in concentration \(x\) is negligible compared to the initial concentration, so \((C - x) \approx C\). Validity is checked by confirming \(x < 5\%\) of \(C\).
Example: For \(K_a = 1.8 \times 10^{-5}\) and \([\text{HA}]_0 = 0.10\) M: assuming \(0.10 - x \approx 0.10\), then \(x = \sqrt{K_a \times 0.10} = 1.34 \times 10^{-3}\) M; checking: \(1.34 \times 10^{-3}/0.10 = 1.34\% < 5\%\), so the approximation is valid.
Solids
A state of matter with definite shape and definite volume, in which particles are closely packed in fixed positions and vibrate about equilibrium positions. Solids are nearly incompressible. Types include crystalline (ordered) and amorphous (disordered).
Example: Ice is a crystalline solid with a regular hexagonal crystal lattice; glass is an amorphous solid with no long-range order.
Solubility
The maximum amount of a solute that dissolves in a given amount of solvent at a specified temperature and pressure to form a stable homogeneous solution. Expressed in g/100 mL solvent, mol/L (molar solubility), or other units.
Example: The solubility of \(\ce{NaCl}\) in water at 25°C is 36.0 g/100 mL; the solubility of \(\ce{AgCl}\) is only \(1.9 \times 10^{-4}\) g/100 mL (sparingly soluble).
Solubility Equilibria
The dynamic equilibrium between dissolved ions and undissolved ionic solid in a saturated solution, described by the solubility product constant \(K_{sp}\): for \(\ce{AB (s) <=> A+ (aq) + B- (aq)}\), \(K_{sp} = [\ce{A+}][\ce{B-}]\).
Solubility Product Ksp
The equilibrium constant for the dissolution of a sparingly soluble ionic compound. It equals the product of the concentrations of the dissolved ions, each raised to the power of its stoichiometric coefficient. Smaller \(K_{sp}\) indicates lower solubility.
Example: \(K_{sp}(\ce{AgCl}) = [\ce{Ag+}][\ce{Cl-}] = 1.8 \times 10^{-10}\) at 25°C; molar solubility \(s = \sqrt{1.8 \times 10^{-10}} = 1.3 \times 10^{-5}\) M.
Solubility Rules
Empirical guidelines for predicting the solubility of ionic compounds in water. Key rules: all alkali metal salts are soluble; all nitrates (\(\ce{NO3-}\)) and acetates (\(\ce{CH3COO-}\)) are soluble; most chlorides are soluble except \(\ce{AgCl}\), \(\ce{PbCl2}\), \(\ce{HgCl2}\); most sulfates are soluble except \(\ce{BaSO4}\), \(\ce{PbSO4}\), \(\ce{SrSO4}\).
Solution Stoichiometry
Stoichiometric calculations involving reactions in solution, using molarity and volume to determine moles of reactants and products. The key relation is \(n = M \times V\).
Example: How many mL of 0.250 M \(\ce{NaOH}\) is needed to neutralize 20.0 mL of 0.150 M \(\ce{H2SO4}\)? Moles \(\ce{H2SO4}\) = 0.00300 mol; needs 0.00600 mol \(\ce{NaOH}\); volume = 0.00600/0.250 = 24.0 mL.
Solutions
Homogeneous mixtures of two or more substances in which the solute is uniformly distributed at the molecular level throughout the solvent. Solutions can be liquid, gaseous, or solid. Properties depend on both solute and solvent identities and concentrations.
Example: Seawater is a liquid solution of many dissolved salts (primarily \(\ce{NaCl}\)) in water; the dissolved ions give seawater its characteristic conductivity and taste.
Solvent and Solute
In a solution, the solvent is the component present in the greatest amount (usually the liquid) that dissolves the solute. The solute is the substance that is dissolved, present in smaller amounts. A solution always has one solvent and may have multiple solutes.
Example: In a 1.0 M \(\ce{NaCl}\) aqueous solution, water is the solvent and \(\ce{NaCl}\) is the solute; water makes up the bulk of the mixture.
sp Hybridization
The hybridization of one s orbital and one p orbital on a central atom to produce two equivalent \(sp\) hybrid orbitals oriented at 180° from each other, with two unhybridized p orbitals perpendicular to the hybrid axis. Associated with linear geometry and triple bonds.
Example: Carbon in acetylene (\(\ce{HC#CH}\)) is \(sp\) hybridized; the two \(sp\) orbitals form sigma bonds to H and the other C, while two unhybridized p orbitals form the two pi bonds of the triple bond.
sp2 Hybridization
The hybridization of one s orbital and two p orbitals to produce three equivalent \(sp^2\) hybrid orbitals in the same plane (trigonal planar, 120° apart), with one unhybridized p orbital perpendicular to the plane. Associated with double bonds and trigonal planar geometry.
Example: Carbon in ethene (\(\ce{C2H4}\)) is \(sp^2\) hybridized; the three \(sp^2\) orbitals form the sigma framework, while the unhybridized p orbitals on each carbon overlap sideways to form the pi bond.
sp3 Hybridization
The hybridization of one s orbital and three p orbitals to produce four equivalent \(sp^3\) hybrid orbitals directed toward the corners of a tetrahedron (109.5° apart). Associated with single bonds and tetrahedral geometry.
Example: Carbon in methane (\(\ce{CH4}\)) is \(sp^3\) hybridized; each of the four \(sp^3\) orbitals overlaps with a hydrogen 1s orbital to form one of the four equivalent C-H sigma bonds.
Spectator Ions
Ions present in a reaction mixture that do not participate in the actual chemical change; they appear in identical form on both the reactant and product sides of the ionic equation. Spectator ions are omitted from the net ionic equation.
Example: In \(\ce{Na+ + OH- + H+ + Cl- -> Na+ + Cl- + H2O}\), \(\ce{Na+}\) and \(\ce{Cl-}\) are spectator ions; the net ionic equation is \(\ce{H+ + OH- -> H2O}\).
Spectrophotometry
An analytical technique that measures the absorbance of a solution at a specific wavelength of light to determine the concentration of an absorbing species, based on the Beer-Lambert Law (\(A = \varepsilon lc\)). Used with a calibration curve.
Example: The concentration of \(\ce{Cu^{2+}}\) in solution can be determined spectrophotometrically by measuring absorbance at 634 nm and comparing to a calibration curve.
Spontaneity
The tendency of a process to occur without continuous external energy input. Spontaneity at constant temperature and pressure is determined by the sign of \(\Delta G\): spontaneous if \(\Delta G < 0\), nonspontaneous if \(\Delta G > 0\). Spontaneous does not imply fast.
Example: Rusting of iron (\(\Delta G < 0\)) is spontaneous but very slow without catalysts; the decomposition of diamond to graphite is also spontaneous but occurs immeasurably slowly.
Spontaneous Cell Reactions
Redox reactions in galvanic cells that occur spontaneously, releasing free energy as electrical work. Spontaneous cells have a positive standard cell potential (\(E^\circ_{cell} > 0\)) and negative \(\Delta G^\circ\). The zinc-copper cell is a classic example.
Example: \(\ce{Zn (s) + Cu^{2+} (aq) -> Zn^{2+} (aq) + Cu (s)}\); \(E^\circ = +1.10\) V, \(\Delta G^\circ = -212\) kJ/mol; spontaneous.
Standard Enthalpy
The enthalpy of a substance measured under standard state conditions: pure substance at 1 bar (100 kPa) pressure and a specified temperature (usually 298 K). Standard enthalpies of formation, combustion, and reaction are all measured under these conditions.
Example: The standard enthalpy of formation of \(\ce{H2O (l)}\) is \(\Delta H_f^\circ = -285.8\) kJ/mol, measured for the formation at exactly 298 K and 1 bar.
Standard Entropy
The absolute entropy of one mole of a substance at standard conditions (298 K, 1 bar), denoted \(S^\circ\). Unlike enthalpy, absolute entropy values can be determined (from the third law: \(S = 0\) at 0 K for a perfect crystal). Units: J mol\(^{-1}\) K\(^{-1}\).
Example: \(S^\circ[\ce{H2O (l)}] = 69.9\) J mol\(^{-1}\) K\(^{-1}\); \(S^\circ[\ce{H2O (g)}] = 188.8\) J mol\(^{-1}\) K\(^{-1}\); the gas has much higher entropy than the liquid.
Standard Formation Values
Tabulated thermodynamic quantities (\(\Delta H_f^\circ\), \(\Delta G_f^\circ\), \(S^\circ\)) measured or calculated for formation of one mole of a compound from its elements in standard states. Used with Hess's Law to calculate thermodynamic properties of reactions.
Standard Free Energy
The Gibbs free energy change for a reaction when all reactants and products are in their standard states (1 bar, 298 K, 1 M for solutions). \(\Delta G^\circ = \Delta H^\circ - T\Delta S^\circ\) and relates to \(K\) by \(\Delta G^\circ = -RT \ln K\).
Example: For \(\ce{N2 + 3H2 -> 2NH3}\) at 298 K: \(\Delta G^\circ = -33.0\) kJ/mol, corresponding to \(K = e^{33000/(8.314 \times 298)} = 5.8 \times 10^5\).
Standard Hydrogen Electrode
The reference electrode (SHE) assigned a standard reduction potential of exactly 0 V, consisting of a platinum electrode in contact with 1 M \(\ce{H+}\) solution with \(\ce{H2}\) gas at 1 atm bubbled over it: \(\ce{2H+ + 2e- <=> H2}\), \(E^\circ = 0.000\) V.
Standard Reduction Potential
The voltage measured for a half-reaction under standard conditions (all solutions 1 M, all gases 1 atm, 25°C) relative to the standard hydrogen electrode (SHE = 0.000 V). More positive values indicate stronger oxidizing agents.
Example: \(\ce{F2 + 2e- -> 2F-}\), \(E^\circ = +2.87\) V (strongest oxidizing agent); \(\ce{Li+ + e- -> Li}\), \(E^\circ = -3.05\) V (strongest reducing agent).
Standard Solutions
Solutions of accurately known concentration prepared by dissolving a primary standard or by standardizing against one. Used as titrants in volumetric analysis to determine the concentration of unknown solutions.
Example: A 0.1000 M \(\ce{NaOH}\) standard solution is prepared by dissolving \(\ce{NaOH}\) and standardizing its concentration against KHP primary standard before use.
State Functions
Thermodynamic quantities whose values depend only on the current state of the system (defined by temperature, pressure, composition) and not on the path by which the state was reached. Examples: \(U\), \(H\), \(S\), \(G\), \(T\), \(P\), \(V\).
Example: The enthalpy change (\(\Delta H\)) for melting ice is always +6.01 kJ/mol at 0°C and 1 atm, regardless of whether the ice was heated slowly or quickly.
State Symbols
Symbols placed after chemical formulas in equations to indicate the physical state of each substance: (s) for solid, (l) for liquid, (g) for gas, (aq) for aqueous solution. Essential for complete thermodynamic equations and net ionic equations.
Example: \(\ce{NaCl (s) -> Na+ (aq) + Cl- (aq)}\) shows that solid NaCl dissolves to give aqueous ions; the enthalpy change differs from other state combinations.
States of Matter
The three principal physical forms of matter: solid (definite shape and volume, closely packed, low energy), liquid (definite volume but not shape, intermediate energy), and gas (neither definite shape nor volume, high energy, widely separated particles).
Stoichiometry
The branch of chemistry dealing with the quantitative relationships between reactants and products in chemical reactions, based on balanced chemical equations and the law of conservation of mass. Enables calculation of amounts of substances involved in reactions.
Example: From \(\ce{2H2 + O2 -> 2H2O}\): stoichiometry tells us 4.0 g of \(\ce{H2}\) reacts with 32.0 g of \(\ce{O2}\) to produce 36.0 g of \(\ce{H2O}\).
Stoichiometry Electrolysis
The application of Faraday's laws to calculate the mass of a substance deposited or dissolved at an electrode during electrolysis: \(m = \frac{M \times I \times t}{n \times F}\), where \(M\) is molar mass, \(I\) is current (A), \(t\) is time (s), \(n\) is moles of electrons per mole of product, and \(F\) is Faraday's constant.
Example: Depositing silver from \(\ce{AgNO3}\) at 2.00 A for 1930 s: \(m = \frac{107.87 \times 2.00 \times 1930}{1 \times 96485} = 4.31\) g of Ag.
Strong Acid pH
The calculation of pH for a strong acid solution (one that dissociates completely): \([\ce{H+}] = [\text{acid}]_0\) (for monoprotic) and \(\text{pH} = -\log[\ce{H+}]\).
Example: 0.025 M \(\ce{HCl}\): since \(\ce{HCl}\) is a strong acid, \([\ce{H+}] = 0.025\) M; \(\text{pH} = -\log(0.025) = 1.60\).
Strong Acid-Strong Base
The titration of a strong acid with a strong base (or vice versa), producing a neutral salt and water at the equivalence point (pH = 7). The pH curve shows an abrupt change near the equivalence point with no buffering region.
Example: Titrating \(\ce{HCl}\) with \(\ce{NaOH}\): \(\ce{HCl + NaOH -> NaCl + H2O}\); equivalence point at pH = 7.00; the pH jumps sharply from ~4 to ~10 in the vicinity of the equivalence point.
Strong Acid-Weak Base
The titration of a strong acid with a weak base (or a weak base with a strong acid), producing a salt whose cation is the conjugate acid of the weak base. The equivalence point pH is below 7 because the conjugate acid hydrolyzes.
Example: Titrating \(\ce{HCl}\) with \(\ce{NH3}\): \(\ce{HCl + NH3 -> NH4Cl}\); at the equivalence point, \(\ce{NH4+}\) hydrolyzes to give pH < 7 (approximately pH ≈ 5.1 for 0.1 M solutions).
Strong Acids
Acids that ionize completely in aqueous solution, with \(K_a \gg 1\). The seven common strong acids are: \(\ce{HCl}\), \(\ce{HBr}\), \(\ce{HI}\), \(\ce{HNO3}\), \(\ce{H2SO4}\) (first proton), \(\ce{HClO4}\), and \(\ce{HClO3}\).
Example: \(\ce{HNO3 (aq) -> H+ (aq) + NO3- (aq)}\) is complete; a 0.10 M \(\ce{HNO3}\) solution has \([\ce{H+}] = 0.10\) M and pH = 1.00.
Strong Base pH
The calculation of pH for a strong base solution (one that dissociates completely): \([\ce{OH-}] = [\text{base}]_0 \times n\) (where \(n\) is the number of \(\ce{OH-}\) per formula unit), then \(\text{pOH} = -\log[\ce{OH-}]\) and \(\text{pH} = 14.00 - \text{pOH}\).
Example: 0.050 M \(\ce{Ca(OH)2}\): \([\ce{OH-}] = 2 \times 0.050 = 0.100\) M; pOH = 1.00; pH = 13.00.
Strong Bases
Bases that dissociate completely in aqueous solution, producing stoichiometric \(\ce{OH-}\). Common strong bases include: \(\ce{LiOH}\), \(\ce{NaOH}\), \(\ce{KOH}\), \(\ce{RbOH}\), \(\ce{CsOH}\), \(\ce{Ca(OH)2}\), \(\ce{Sr(OH)2}\), and \(\ce{Ba(OH)2}\).
Example: \(\ce{Ba(OH)2 -> Ba^{2+} + 2OH-}\) is complete; 0.025 M \(\ce{Ba(OH)2}\) gives \([\ce{OH-}] = 0.050\) M; pH = 12.70.
Subatomic Particles
The three fundamental constituents of atoms: protons (positive charge, mass 1.0073 amu, in nucleus), neutrons (no charge, mass 1.0087 amu, in nucleus), and electrons (negative charge, mass 0.000549 amu, in orbitals surrounding nucleus).
Example: A neutral carbon-12 atom contains 6 protons, 6 neutrons, and 6 electrons; the protons and neutrons are confined to the nucleus while electrons occupy the 1s and 2s2p orbitals.
Subshells
Subdivisions of principal energy levels (shells), identified by the azimuthal quantum number \(l\): s (\(l = 0\)), p (\(l = 1\)), d (\(l = 2\)), f (\(l = 3\)). Each subshell contains a specific number of orbitals: s has 1, p has 3, d has 5, f has 7.
Example: The \(n = 3\) shell contains three subshells: 3s (1 orbital, 2 electrons max), 3p (3 orbitals, 6 electrons max), and 3d (5 orbitals, 10 electrons max).
Sublimation and Deposition
Sublimation is the endothermic phase change from solid directly to gas without passing through the liquid phase. Deposition is the reverse exothermic process (gas → solid directly). Both occur when the vapor pressure of the solid exceeds atmospheric pressure.
Example: Solid iodine sublimes at room temperature (vapor pressure measurable at 25°C); the purple vapor deposits as solid crystals on cool surfaces.
Successive Ionization Energy
The energy required to remove electrons from an atom one at a time; each successive ionization energy is larger than the previous one because the remaining electrons are held more tightly. A large jump in ionization energies signals removal of a core electron, revealing the number of valence electrons.
Example: Aluminum: IE1 = 577, IE2 = 1817, IE3 = 2745, IE4 = 11,578 kJ/mol; the large jump between IE3 and IE4 confirms Al has 3 valence electrons.
Surface Area and Rate
The effect of the total exposed surface area of a solid reactant on reaction rate: increasing surface area (by crushing or grinding) increases the rate by exposing more reactant molecules to contact with the other reactant, increasing collision frequency.
Example: Powdered calcium carbonate reacts with \(\ce{HCl}\) much faster than a marble chip of equal mass because the powder has enormously greater surface area.
Surface Tension
The energy per unit area (or force per unit length) at the surface of a liquid, arising from the net inward intermolecular attractive forces experienced by surface molecules. Liquids with stronger IMFs have higher surface tension.
Example: Water has a very high surface tension (72.8 mN/m at 25°C) due to hydrogen bonding; small insects can walk on water because the surface tension supports their weight.
System and Surroundings
In thermodynamics, the system is the part of the universe under study (e.g., the reaction flask and its contents); the surroundings is everything else. Energy and (for open systems) matter can be exchanged between system and surroundings.
Example: In a calorimetry experiment, the reaction mixture is the system; the water bath and calorimeter are the surroundings; heat flows between them.
Temperature and Rate
The effect of temperature on reaction rate, explained by the Arrhenius equation: increasing temperature increases the rate constant \(k\) by increasing the fraction of molecules with energy exceeding \(E_a\) and increasing collision frequency. A 10°C rise often doubles or triples the rate.
Example: A reaction with \(E_a = 50\) kJ/mol at 300 K: raising temperature to 310 K increases \(k\) by approximately \(e^{(50000/8.314)(1/300 - 1/310)} \approx 1.9\) times.
Temperature and Solubility
The effect of temperature on the solubility of solutes: for most ionic and solid solutes, solubility increases with temperature; for gases, solubility decreases with increasing temperature (Henry's Law — more thermal energy overcomes gas-liquid interactions).
Example: \(\ce{KNO3}\) solubility increases from 13.3 g/100 mL at 0°C to 246 g/100 mL at 100°C; but \(\ce{O2}\) solubility decreases from 14.6 mg/L at 0°C to 7.6 mg/L at 30°C.
Temperature Changes on K
The effect of temperature on the equilibrium constant \(K\). For exothermic reactions (\(\Delta H < 0\)), increasing temperature decreases \(K\) (shifts equilibrium toward reactants). For endothermic reactions (\(\Delta H > 0\)), increasing temperature increases \(K\) (shifts equilibrium toward products).
Example: For \(\ce{N2O4 (g) <=> 2NO2 (g)}\) (\(\Delta H = +57\) kJ/mol, endothermic): increasing temperature increases \(K\) and the proportion of \(\ce{NO2}\) at equilibrium; the mixture becomes darker brown.
Temperature Dependence
The variation of a chemical or physical property with temperature. In kinetics, rate constants are exponentially dependent on temperature (Arrhenius). Equilibrium constants depend on temperature through \(\ln K = -\Delta H^\circ/RT + \Delta S^\circ/R\) (van't Hoff equation).
Temperature Scales
The three common temperature scales: Celsius (°C, water freezes at 0°, boils at 100°), Fahrenheit (°F, water freezes at 32°, boils at 212°), and Kelvin (K, absolute zero = 0 K = −273.15°C). All gas law calculations require Kelvin.
Example: Room temperature 25°C = 298.15 K = 77°F; absolute zero 0 K = −273.15°C; conversion: \(T(\text{K}) = T(°\text{C}) + 273.15\).
Theoretical Yield
The maximum mass or moles of product that could form from given amounts of reactants based on the limiting reagent and stoichiometry of the balanced equation, assuming complete reaction with no side reactions or losses.
Example: From 5.00 g of magnesium reacting with excess \(\ce{O2}\): \(5.00/24.31 = 0.206\) mol Mg → \(0.206\) mol \(\ce{MgO}\) → \(0.206 \times 40.30 = 8.30\) g \(\ce{MgO}\) theoretical yield.
Thermodynamic Stability
The stability of a substance relative to its decomposition products as determined by the sign of \(\Delta G\) for decomposition. A substance is thermodynamically stable if \(\Delta G > 0\) for its decomposition (i.e., formation is spontaneous).
Example: \(\ce{CO2}\) is thermodynamically stable because \(\Delta G_f^\circ[\ce{CO2 (g)}] = -394\) kJ/mol; its decomposition to \(\ce{C}\) and \(\ce{O2}\) is highly nonspontaneous.
Thermodynamics
The branch of chemistry and physics dealing with the energy changes accompanying chemical and physical processes, including enthalpy, entropy, and Gibbs free energy. Thermodynamics predicts the direction and extent of chemical reactions.
Third Law Thermodynamics
The law stating that the entropy of a perfect crystal at absolute zero (0 K) is exactly zero: \(S(0\text{ K}) = 0\). This provides an absolute reference point from which absolute entropies of substances at other temperatures can be calculated.
Example: The absolute standard molar entropy of diamond at 298 K is 2.4 J mol\(^{-1}\) K\(^{-1}\); it is small because diamond is very ordered (nearly perfect crystal structure).
Titration
A volumetric analytical procedure in which a solution of known concentration (titrant) is carefully added from a burette to a known volume of analyte solution until the reaction reaches the equivalence point. The volume used determines the unknown concentration.
Example: Adding 23.15 mL of 0.1000 M \(\ce{NaOH}\) from a burette to 25.00 mL of \(\ce{HCl}\) until the phenolphthalein endpoint: moles \(\ce{NaOH}\) = 0.002315 mol = moles \(\ce{HCl}\); \([\ce{HCl}] = 0.002315/0.02500 = 0.09260\) M.
Titration Calculations
Mathematical calculations to determine the concentration of an unknown solution from titration data, using the relationship between moles of titrant and analyte at the equivalence point and the stoichiometric ratio from the balanced equation.
Example: For \(\ce{H2SO4 + 2NaOH -> Na2SO4 + 2H2O}\): if 25.0 mL of \(\ce{NaOH}\) (0.200 M) neutralizes \(\ce{H2SO4}\), moles \(\ce{NaOH}\) = 0.00500 mol → moles \(\ce{H2SO4}\) = 0.00250 mol.
Titration Curve Analysis
The interpretation of a pH-versus-volume-of-titrant graph to identify the equivalence point, buffer region, half-equivalence point (where pH = pKa), and to determine \(K_a\) (or \(K_b\)), the nature of the acid/base, and the appropriate indicator to use.
Example: On a weak acid-strong base titration curve: the half-equivalence point gives pH = pKa; the equivalence point pH is above 7; the flat buffering region confirms weak acid character.
Titration Curves
Graphs of pH (y-axis) versus volume of titrant added (x-axis) during a titration. The shape depends on the types of acid and base: strong acid-strong base curves show a symmetric S-shape; weak acid-strong base curves are asymmetric with a buffering region.
Example: The titration curve of \(\ce{CH3COOH}\) with \(\ce{NaOH}\) shows an initial slow pH rise, a flat buffering region centered at pH = 4.74 (= pKa), a steep rise at the equivalence point (pH ≈ 8.7), then a slow rise.
Transition Metal Ions
Cations formed from transition metals (d-block elements), which can have multiple stable oxidation states because d electrons are close in energy to valence s electrons. Many transition metal ions are colored and paramagnetic due to partially filled d subshells.
Example: Iron forms \(\ce{Fe^{2+}}\) (\([\text{Ar}]3d^6\), pale green) and \(\ce{Fe^{3+}}\) (\([\text{Ar}]3d^5\), yellow-orange); copper forms \(\ce{Cu^+}\) (\([\text{Ar}]3d^{10}\), colorless) and \(\ce{Cu^{2+}}\) (\([\text{Ar}]3d^9\), blue).
Transition State
The highest-energy, unstable configuration of atoms along the reaction coordinate, existing at the peak of the potential energy diagram. Also called the activated complex. Transition states cannot be isolated; they exist for approximately \(10^{-13}\) seconds.
Example: In the reaction \(\ce{A + BC -> AB + C}\), the transition state \([\ce{A---B---C}]^{\ddagger}\) has partially broken B-C and partially formed A-B bonds simultaneously.
Triple Bonds
Covalent bonds consisting of one sigma (\(\sigma\)) bond and two pi (\(\pi\)) bonds between two atoms, sharing six electrons total. Triple bonds are shorter and stronger than double or single bonds between the same atoms.
Example: Nitrogen gas (\(\ce{N2}\)) has a triple bond with bond length 110 pm and bond energy 945 kJ/mol — the strongest and shortest common diatomic bond.
Triple Point
The unique temperature and pressure at which all three phases (solid, liquid, gas) of a substance coexist in thermodynamic equilibrium. Defined precisely by temperature and pressure coordinates on the phase diagram.
Example: Water's triple point is at 0.01°C and 611.7 Pa (0.006 atm); this is the internationally accepted temperature calibration point for the Kelvin scale.
Unimolecular Reactions
Elementary reaction steps in which a single species decomposes or rearranges to form products. The rate law is first order: rate = \(k[\text{A}]\). Unimolecular processes often involve bond breaking through thermal excitation.
Example: \(\ce{N2O5 -> NO2 + NO3}\) is a unimolecular elementary step; rate = \(k[\ce{N2O5}]\), and the rate depends only on the concentration of \(\ce{N2O5}\).
Van der Waals Equation
A modified ideal gas law that corrects for intermolecular attractions (by adding \(an^2/V^2\) to pressure) and finite molecular volume (by subtracting \(nb\) from volume): \(\left(P + \frac{an^2}{V^2}\right)(V-nb) = nRT\), where \(a\) and \(b\) are gas-specific constants.
Example: For \(\ce{CO2}\): \(a = 3.640\) L\(^2\)·atm/mol\(^2\) (large, strong attractions) and \(b = 0.04267\) L/mol (significant molecular volume); these corrections make predictions more accurate at high pressure.
Valence Electrons
Electrons in the outermost principal energy level (highest \(n\)) of an atom, which participate in chemical bonding. Valence electrons determine the chemical properties of an element and equal the group number for main-group elements.
Example: Oxygen has 6 valence electrons (\(2s^2 2p^4\)), forms 2 bonds to complete its octet, and is in Group 16; sulfur also has 6 valence electrons and similar chemistry.
Vapor Pressure
The pressure exerted by the vapor of a liquid (or solid) in equilibrium with its condensed phase at a given temperature in a closed container. Vapor pressure increases with temperature; liquids boil when their vapor pressure equals external pressure.
Example: At 25°C, water's vapor pressure is 23.8 mmHg; at 100°C, it rises to 760 mmHg (= 1 atm), which is why water boils at 100°C at standard pressure.
Viscosity
A measure of a liquid's resistance to flow, resulting from intermolecular friction between layers of moving liquid. Liquids with stronger intermolecular forces or larger, more entangled molecules have higher viscosity. Viscosity generally decreases with increasing temperature.
Example: Glycerol (many -OH groups, strong hydrogen bonding) has viscosity 1490 mPa·s at 20°C; water has viscosity 1.002 mPa·s; glycerol is about 1500 times more viscous.
Voltaic Cell Components
The parts of a galvanic (voltaic) cell: two electrodes (anode for oxidation, cathode for reduction), two electrolyte solutions containing the ion pairs, a salt bridge or porous partition to allow ion migration, and an external circuit for electron flow.
Example: A zinc-copper voltaic cell components: Zn anode in \(\ce{ZnSO4}\) solution | salt bridge (\(\ce{KNO3}\)) | \(\ce{CuSO4}\) solution | Cu cathode; connected by a wire with a voltmeter.
Volume Changes
Changes in the volume of a gas phase reaction system at constant pressure, which can shift equilibrium according to Le Chatelier's Principle. Decreasing volume increases pressure, shifting equilibrium toward the side with fewer moles of gas; increasing volume shifts the opposite way.
Example: Compressing the \(\ce{2SO2 + O2 <=> 2SO3}\) equilibrium (3 mol gas → 2 mol gas) shifts it toward \(\ce{SO3}\), the side with fewer gas moles, which partially counteracts the pressure increase.
Volumetric Analysis
A quantitative analytical method that measures volume of solution rather than mass, including titration techniques. Relies on accurately known concentrations and volumes to determine the amount of analyte.
Example: Acid-base titration, redox titration (permanganimetry), and EDTA complexometric titration are all forms of volumetric analysis.
VSEPR Theory
Valence Shell Electron Pair Repulsion theory: a model for predicting the three-dimensional shape of molecules based on the principle that electron pairs (bonding and lone pairs) around a central atom repel each other and arrange themselves to minimize repulsion.
Example: \(\ce{SF4}\) has 5 electron domains around S (4 bonding pairs + 1 lone pair) → trigonal bipyramidal electron geometry → see-saw molecular geometry, with bond angles of approximately 102° and 186°.
Weak Acid pH Calculation
The determination of the pH of a weak acid solution using an ICE table and the \(K_a\) expression. The equilibrium \(\ce{HA <=> H+ + A-}\) is set up with initial concentration, change (\(-x\), \(+x\), \(+x\)), and \(K_a = x^2/([\text{HA}]_0 - x)\) is solved for \(x = [\ce{H+}]\).
Example: For 0.10 M formic acid (\(K_a = 1.8 \times 10^{-4}\)): ICE gives \(x = \sqrt{1.8 \times 10^{-4} \times 0.10} = 4.2 \times 10^{-3}\) M; pH = \(-\log(4.2 \times 10^{-3}) = 2.38\).
Weak Acid-Strong Base
The titration of a weak acid with a strong base, producing the conjugate base of the weak acid at the equivalence point. The solution at the equivalence point is basic (pH > 7) because the conjugate base undergoes hydrolysis.
Example: Titrating acetic acid with \(\ce{NaOH}\): \(\ce{CH3COOH + NaOH -> CH3COONa + H2O}\); at the equivalence point, \(\ce{CH3COO-}\) hydrolyzes, giving pH ≈ 8.7 for 0.1 M solutions.
Weak Acids
Acids that partially ionize in aqueous solution, reaching a dynamic equilibrium with their conjugate base: \(\ce{HA <=> H+ + A-}\), with \(K_a < 1\). Most acids are weak acids. pH is calculated using \(K_a\) and an ICE table.
Example: Acetic acid (\(K_a = 1.8 \times 10^{-5}\)): only 1.3% of a 0.10 M solution ionizes, giving pH = 2.87, much higher (less acidic) than 0.10 M HCl (pH = 1.00).
Weak Base pH Calculation
The determination of the pH of a weak base solution using an ICE table and the \(K_b\) expression. For \(\ce{B + H2O <=> BH+ + OH-}\): \(K_b = x^2/([\text{B}]_0 - x)\) is solved for \(x = [\ce{OH-}]\), then pOH and pH are calculated.
Example: For 0.10 M ammonia (\(K_b = 1.8 \times 10^{-5}\)): \(x = [\ce{OH-}] = \sqrt{1.8 \times 10^{-5} \times 0.10} = 1.34 \times 10^{-3}\) M; pOH = 2.87; pH = 11.13.
Weak Bases
Bases that partially ionize (react with water to a limited extent) in aqueous solution, establishing equilibrium: \(\ce{B + H2O <=> BH+ + OH-}\), with \(K_b < 1\). Examples include ammonia, amines, and the conjugate bases of weak acids.
Example: Methylamine (\(\ce{CH3NH2}\), \(K_b = 4.4 \times 10^{-4}\)) is a weak base; in 0.10 M solution, only about 6.6% reacts with water to produce \(\ce{OH-}\).
Writing Ionic Formulas
The procedure for writing the correct formula of an ionic compound by combining the cation and anion in the ratio that makes the overall compound electrically neutral. The cation is written first, followed by the anion.
Example: Combining \(\ce{Al^{3+}}\) with \(\ce{SO4^{2-}}\): need 2 Al\(^{3+}\) (charge 6+) and 3 \(\ce{SO4^{2-}}\) (charge 6−) to achieve neutrality → formula is \(\ce{Al2(SO4)3}\).
Writing K Expressions
The construction of the equilibrium constant expression for a reaction, with the concentrations of products in the numerator and reactants in the denominator, each raised to the power of its stoichiometric coefficient. Pure solids and liquids are excluded.
Example: For \(\ce{aA + bB <=> cC + dD}\): \(K_c = \frac{[\text{C}]^c[\text{D}]^d}{[\text{A}]^a[\text{B}]^b}\); for \(\ce{PCl5 (g) <=> PCl3 (g) + Cl2 (g)}\): \(K_c = \frac{[\ce{PCl3}][\ce{Cl2}]}{[\ce{PCl5}]}\).
Zero Order Integrated Law
The integrated rate law for zero-order reactions: \([\text{A}]_t = [\text{A}]_0 - kt\). A plot of \([\text{A}]\) versus time is linear with slope \(= -k\). The half-life depends on initial concentration: \(t_{1/2} = [\text{A}]_0/(2k)\).
Example: If \([\text{A}]_0 = 0.80\) M and \(k = 0.020\) M/s, after 30 s: \([\text{A}] = 0.80 - (0.020)(30) = 0.20\) M.
Zero Order Reactions
Reactions in which the rate is independent of the concentration of any reactant: \(\text{rate} = k\). Concentration decreases linearly with time. Common for reactions occurring on catalyst surfaces at saturation or in certain enzyme-catalyzed reactions.
Example: The decomposition of \(\ce{N2O}\) on a platinum surface at high \([\ce{N2O}]\) is zero order; the rate depends only on the number of active sites on the catalyst surface, not on \([\ce{N2O}]\).