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Chapter 18: Electrochemistry

Summary

This chapter covers electrochemistry including galvanic and electrolytic cells, standard reduction potentials, cell potential calculations, the Nernst equation, Faraday's laws of electrolysis, and practical applications like batteries and corrosion.

Concepts Covered

This chapter covers the following 25 concepts from the learning graph:

  1. Electrochemistry
  2. Galvanic Cells
  3. Voltaic Cell Components
  4. Anode and Cathode
  5. Salt Bridge
  6. Electron Flow Direction
  7. Cell Notation
  8. Standard Reduction Potential
  9. Standard Hydrogen Electrode
  10. Cell Potential Calculation
  11. Spontaneous Cell Reactions
  12. Nernst Equation
  13. Nonstandard Conditions
  14. Concentration Cells
  15. Free Energy and Cell EMF
  16. Delta G and E Relation
  17. Faraday's Constant
  18. Electrolytic Cells
  19. Electrolysis
  20. Electrolysis of Water
  21. Electroplating
  22. Faraday's Laws
  23. Stoichiometry Electrolysis
  24. Batteries and Fuel Cells
  25. Corrosion

Prerequisites

This chapter builds on concepts from:


Welcome, Scientists!

Catalyst welcomes you Every time you charge your phone, start a car, or use a flashlight, you're harnessing electrochemistry. This chapter bridges two of chemistry's grandest themes — thermodynamics and redox reactions — and shows how electron flow can do useful work. Get ready to explore one of the most powerful and practical areas of AP Chemistry. Let's react!

Introduction

Electrochemistry is the study of the relationship between chemical reactions and electrical energy. When electrons flow spontaneously from one substance to another — like when zinc dissolves in copper sulfate solution — that electron flow can be harnessed to do electrical work. Conversely, electrical energy can be used to force non-spontaneous chemical reactions to occur, such as splitting water into hydrogen and oxygen.

These two directions define the two major types of electrochemical cells:

  • Galvanic cells (also called voltaic cells): spontaneous redox reactions generate electrical energy
  • Electrolytic cells: electrical energy is used to drive non-spontaneous redox reactions

Electrochemistry also ties back directly to Chapter 13. Recall that \(\Delta G < 0\) for a spontaneous process. In this chapter, you'll see exactly how the Gibbs free energy change of a redox reaction connects to the voltage (electromotive force, EMF) that a cell produces.

Galvanic (Voltaic) Cells

The Zinc-Copper Cell

The classic demonstration of a galvanic cell uses zinc metal and copper sulfate solution. When a zinc strip is dipped into \(\ce{CuSO4}\) solution, copper metal deposits on the zinc and the blue color of the solution fades:

\[\ce{Zn (s) + Cu^{2+} (aq) -> Zn^{2+} (aq) + Cu (s)}\]

Zinc is oxidized (loses electrons) and copper ion is reduced (gains electrons). In a simple beaker this electron transfer happens by direct contact — useful for demonstrating chemistry but useless for doing electrical work.

In a galvanic cell, the two half-reactions are separated into two compartments (half-cells). Electrons travel through an external wire, doing work as they go.

Voltaic Cell Components

The essential components of a galvanic cell are:

  • Anode: The electrode where oxidation occurs. Metal dissolves, releasing electrons. The anode is the negative terminal (electrons flow out of it).
  • Cathode: The electrode where reduction occurs. Metal deposits (or ions are reduced). The cathode is the positive terminal (electrons flow into it).
  • External circuit: The wire connecting anode to cathode through which electrons flow.
  • Salt bridge: A tube containing an inert electrolyte (often \(\ce{KNO3}\) or \(\ce{KCl}\) in agar gel) that completes the circuit by allowing ion migration between half-cells, maintaining electrical neutrality.
  • Electrolyte solutions: Aqueous solutions containing the ionic species involved in the half-reactions.

Catalyst's Tip

Catalyst shares a tip Remember: AN OX, RED CAT — ANode = OXidation, REDuction = CAThode. This mnemonic never fails. Electrons always flow from anode to cathode through the external wire, and in the opposite direction through the salt bridge (as anions migrate toward the anode).

Why a Salt Bridge Is Needed

Without a salt bridge, the half-cells would quickly become charged — the anode half-cell would build up positive charge (excess \(\ce{Zn^{2+}}\)), and the cathode half-cell would become negatively charged (loss of \(\ce{Cu^{2+}}\)). This charge buildup would stop current flow within seconds. The salt bridge allows anions (\(\ce{NO3-}\) or \(\ce{Cl-}\)) to migrate toward the anode and cations to migrate toward the cathode, maintaining charge balance and allowing continuous current.

In the zinc-copper cell:

  • Anode: \(\ce{Zn (s) -> Zn^{2+} (aq) + 2 e-}\) (oxidation)
  • Cathode: \(\ce{Cu^{2+} (aq) + 2 e- -> Cu (s)}\) (reduction)
  • Overall: \(\ce{Zn (s) + Cu^{2+} (aq) -> Zn^{2+} (aq) + Cu (s)}\)

Cell Notation

Electrochemists use a compact shorthand called cell notation to describe a galvanic cell without drawing a diagram:

\[\ce{Zn (s) | Zn^{2+} (aq) || Cu^{2+} (aq) | Cu (s)}\]

Rules for cell notation:

  • Write the anode on the left, cathode on the right
  • A single vertical line | separates phases (solid from solution)
  • A double vertical line || represents the salt bridge
  • Concentrations are listed in parentheses when known: \(\ce{Zn^{2+}} \text{(1.0 M)}\)
  • If an inert electrode is needed (e.g., platinum), it is included: \(\ce{Pt | H2 (g) | H+ (aq) || ...}\)

Diagram: Galvanic Cell Visualizer MicroSim

Interactive Galvanic Cell Diagram

Type: microsim sim-id: galvanic-cell-visualizer
Library: p5.js
Status: Specified

Learning objective: Students will be able to (Understanding) identify the components of a galvanic cell, describe the direction of electron and ion flow, and interpret cell notation.

Canvas: 860 × 560 px, responsive to window resize.

Visual layout: - Left half-cell: beaker containing a zinc electrode strip (gray rectangle) labeled "Anode (−)". Blue-gray solution labeled "\(\ce{Zn^{2+} (aq)}\)". Small zinc atom particles floating away from the electrode to show oxidation. - Right half-cell: beaker containing a copper electrode strip (orange-brown rectangle) labeled "Cathode (+)". Blue solution labeled "\(\ce{Cu^{2+} (aq)}\)". Copper atom particles depositing onto electrode. - Salt bridge: inverted U-shaped tube connecting the two beakers, labeled "Salt Bridge (\(\ce{KNO3}\))". Animated small dots (anions moving left, cations moving right). - External wire: curved line connecting tops of both electrodes. Animated electron dots (small yellow circles) moving from anode to cathode along the wire. A lightbulb icon in the middle of the wire that glows yellow. - Labels: anode half-reaction below left beaker, cathode half-reaction below right beaker, overall cell reaction centered at bottom.

Controls: - Dropdown: "Select cell": Zn-Cu | Fe-Cu | Zn-Ag | Custom - Slider: Initial \([\ce{Cu^{2+}}]\) 0.001–2.0 M - Slider: Initial \([\ce{Zn^{2+}}]\) 0.001–2.0 M - Display: Cell notation text, cell potential E (standard and actual), spontaneous yes/no

Animation: Particles animate continuously when cell is spontaneous. At non-spontaneous conditions, animation reverses direction and a red "X" appears over the wire.

Implementation: p5.js. Particle positions updated each frame along predefined paths. Cell potential computed using Nernst equation.

Standard Reduction Potentials

What Is Standard Reduction Potential?

Each half-reaction has an intrinsic tendency to occur as a reduction. This tendency is measured as the standard reduction potential, \(E°\) (in volts), measured under standard conditions:

  • All ionic concentrations = 1.0 M
  • Gas pressures = 1 atm
  • Temperature = 25°C

Reduction potentials are always written as reduction half-reactions:

\[\ce{Cu^{2+} (aq) + 2 e- -> Cu (s)} \quad E° = +0.34 \text{ V}\]
\[\ce{Zn^{2+} (aq) + 2 e- -> Zn (s)} \quad E° = -0.76 \text{ V}\]

The more positive the \(E°\), the greater the tendency to be reduced. The more negative the \(E°\), the greater the tendency to be oxidized.

The Standard Hydrogen Electrode (SHE)

All reduction potentials are measured relative to the standard hydrogen electrode (SHE):

\[\ce{2 H+ (aq) + 2 e- -> H2 (g)} \quad E° = 0.00 \text{ V (by definition)}\]

The SHE consists of a platinum electrode immersed in 1.0 M \(\ce{HCl}\) with \(\ce{H2}\) gas bubbling at 1 atm over it. This arbitrary zero point defines the entire reduction potential scale.

Selected standard reduction potentials (from most positive to most negative):

Half-reaction \(E°\) (V)
\(\ce{F2 (g) + 2 e- -> 2 F- (aq)}\) +2.87
\(\ce{MnO4- + 8 H+ + 5 e- -> Mn^{2+} + 4 H2O}\) +1.51
\(\ce{Cl2 (g) + 2 e- -> 2 Cl- (aq)}\) +1.36
\(\ce{O2 (g) + 4 H+ + 4 e- -> 2 H2O}\) +1.23
\(\ce{Cu^{2+} (aq) + 2 e- -> Cu (s)}\) +0.34
\(\ce{2 H+ (aq) + 2 e- -> H2 (g)}\) 0.00
\(\ce{Fe^{2+} (aq) + 2 e- -> Fe (s)}\) −0.44
\(\ce{Zn^{2+} (aq) + 2 e- -> Zn (s)}\) −0.76
\(\ce{Al^{3+} (aq) + 3 e- -> Al (s)}\) −1.66
\(\ce{Li+ (aq) + e- -> Li (s)}\) −3.04

Calculating Standard Cell Potential

The standard cell potential \(E°_{\text{cell}}\) is:

\[E°_{\text{cell}} = E°_{\text{cathode}} - E°_{\text{anode}}\]

or equivalently:

\[E°_{\text{cell}} = E°_{\text{reduction (cathode)}} + E°_{\text{oxidation (anode)}}\]

(where \(E°_{\text{oxidation}} = -E°_{\text{reduction}}\) for the same half-reaction)

Example: Calculate \(E°_{\text{cell}}\) for the Zn-Cu cell.

  • Cathode (reduction): \(\ce{Cu^{2+} + 2 e- -> Cu}\), \(E° = +0.34\) V
  • Anode (oxidation): \(\ce{Zn -> Zn^{2+} + 2 e-}\), \(E°_{\text{ox}} = +0.76\) V
\[E°_{\text{cell}} = 0.34 - (-0.76) = 0.34 + 0.76 = +1.10 \text{ V}\]

A positive \(E°_{\text{cell}}\) indicates a spontaneous cell reaction.

Predicting Spontaneity

From the table of reduction potentials, you can immediately predict which half-reaction will be the cathode and which will be the anode:

  • The more positive \(E°\) half-reaction will be reduced (cathode)
  • The more negative \(E°\) half-reaction will be oxidized (anode)
  • If \(E°_{\text{cell}} > 0\), the forward reaction is spontaneous
  • If \(E°_{\text{cell}} < 0\), the reverse reaction is spontaneous

Catalyst's Key Insight

Catalyst is thinking Here's the deep connection: \(E°_{\text{cell}} > 0\) means \(\Delta G° < 0\) (spontaneous). \(E°_{\text{cell}} < 0\) means \(\Delta G° > 0\) (non-spontaneous). The reduction potential table is really a spontaneity table in disguise — the strongest oxidizing agents (most positive \(E°\)) will spontaneously oxidize anything below them in the table.

Connecting Cell EMF to Thermodynamics

The ΔG and E Relationship

Gibbs free energy and cell potential are directly related:

\[\Delta G° = -nFE°_{\text{cell}}\]

where:

  • \(n\) = number of moles of electrons transferred in the balanced equation
  • \(F\) = Faraday's constant = 96,485 C/mol e⁻ ≈ 96,500 C/mol e⁻
  • \(E°_{\text{cell}}\) = standard cell potential (volts)

Since 1 V = 1 J/C, the units work out to joules per mole of reaction.

Example: For the Zn-Cu cell, \(n = 2\) electrons, \(E°_{\text{cell}} = +1.10\) V:

\[\Delta G° = -(2)(96,485)(1.10) = -2.12 \times 10^5 \text{ J/mol} = -212 \text{ kJ/mol}\]

The large negative \(\Delta G°\) confirms this is a highly spontaneous reaction.

Connecting E° to the Equilibrium Constant

Combining \(\Delta G° = -nFE°\) with \(\Delta G° = -RT \ln K\):

\[-nFE° = -RT \ln K\]
\[E° = \frac{RT}{nF} \ln K = \frac{0.02569 \text{ V}}{n} \ln K\]

At 25°C, this simplifies to:

\[E° = \frac{0.0592}{n} \log K\]

This equation connects all three major thermodynamic quantities:

\(E°_{\text{cell}}\) \(\Delta G°\) \(K\) Reaction
\(> 0\) \(< 0\) \(> 1\) Spontaneous forward
\(= 0\) \(= 0\) \(= 1\) At equilibrium
\(< 0\) \(> 0\) \(< 1\) Non-spontaneous forward

The Nernst Equation

Non-Standard Conditions

The standard cell potential \(E°\) applies only when all concentrations are 1 M and pressures are 1 atm. For any other conditions, use the Nernst equation:

\[E = E° - \frac{RT}{nF} \ln Q\]

At 25°C (substituting \(RT/F = 0.02569\) V):

\[E = E° - \frac{0.0592}{n} \log Q\]

where \(Q\) is the reaction quotient (same form as \(K\), but with actual concentrations).

Example: Calculate \(E\) for the Zn-Cu cell when \([\ce{Zn^{2+}}] = 0.100\) M and \([\ce{Cu^{2+}}] = 2.00\) M.

The reaction is: \(\ce{Zn + Cu^{2+} -> Zn^{2+} + Cu}\), \(n = 2\), \(E° = 1.10\) V

\[Q = \frac{[\ce{Zn^{2+}}]}{[\ce{Cu^{2+}}]} = \frac{0.100}{2.00} = 0.0500\]
\[E = 1.10 - \frac{0.0592}{2} \log(0.0500) = 1.10 - (0.0296)(-1.301) = 1.10 + 0.0385 = 1.14 \text{ V}\]

The cell potential is higher than standard because the low \([\ce{Zn^{2+}}]\) and high \([\ce{Cu^{2+}}]\) favor the forward reaction.

Concentration Cells

A concentration cell is a galvanic cell in which both electrodes are made of the same metal, but the two half-cells have different ion concentrations. The cell potential arises entirely from the concentration difference.

Example: two copper half-cells with \([\ce{Cu^{2+}}] = 0.010\) M (anode) and \([\ce{Cu^{2+}}] = 1.00\) M (cathode).

\[E° = 0 \text{ V (same electrode material)}\]
\[Q = \frac{[\ce{Cu^{2+}}]_{\text{anode}}}{[\ce{Cu^{2+}}]_{\text{cathode}}} = \frac{0.010}{1.00} = 0.010\]
\[E = 0 - \frac{0.0592}{2} \log(0.010) = -\frac{0.0592}{2}(-2) = +0.0592 \text{ V}\]

Electrons flow from the dilute side (anode — oxidation reduces \([\ce{Cu^{2+}}]\)) to the concentrated side (cathode — reduction increases \([\ce{Cu^{2+}}]\)). The cell runs until both concentrations are equal and \(E = 0\).

Watch Out!

Catalyst warns you In the Nernst equation, \(Q\) uses the same expression as the equilibrium constant \(K\) for the balanced overall cell reaction — not the individual half-reactions. Students often write \(Q\) incorrectly by using only one half-cell's concentrations. Always write the full balanced equation first, then construct \(Q\).

Diagram: Nernst Equation MicroSim

Interactive Nernst Equation Cell Potential Calculator

Type: microsim sim-id: nernst-equation-explorer
Library: p5.js
Status: Specified

Learning objective: Students will be able to (Applying) use the Nernst equation to calculate cell potential at non-standard conditions and predict how concentration changes affect cell voltage.

Canvas: 840 × 580 px, responsive to window resize.

Top half — cell diagram (300 px tall): - Stylized diagram showing anode and cathode compartments with ion concentrations labeled - Voltmeter display showing computed E in large digits (green if positive, red if negative) - Electron flow direction arrows on wire

Bottom half — controls and computation display: - Dropdown: Select reaction (Zn-Cu | Fe-Cu | Concentration cell | Custom) - Input/Slider: \(E°_{\text{cell}}\) (auto-filled for selected reactions, editable for custom) - Input/Slider: \(n\) — moles of electrons transferred - Slider: log scale for \([\text{oxidized species}]\) at anode (0.001–2.0 M) - Slider: log scale for \([\text{reduced species}]\) at cathode (0.001–2.0 M) - Computed: \(Q\) value (scientific notation), \(\log Q\), \(E\) value - Show Nernst equation with values substituted in: \(E = X.XX - (0.0592/n) \times \log(Q)\) - Below: \(\Delta G = -nFE\) computed in kJ/mol - A simple graph: x-axis = \(\log Q\) from −4 to 4, y-axis = \(E\) (V), showing the linear Nernst relationship with a moveable point at current conditions

Color coding: \(E > 0\) shown in green, \(E < 0\) in red, \(E = 0\) highlighted with a yellow band.

Implementation: p5.js with createSlider() and createSelect() DOM elements. All computations update live.

Electrolytic Cells

Non-Spontaneous Reactions Driven by Electricity

While galvanic cells convert chemical energy to electrical energy, electrolytic cells do the opposite — they use electrical energy to drive non-spontaneous redox reactions. Examples include electroplating, rechargeable batteries (charging cycle), industrial chlorine production, and the Hall-Héroult process for aluminum production.

In an electrolytic cell:

  • An external power source (battery) drives the current
  • The electrode connected to the positive terminal is the anode (still oxidation)
  • The electrode connected to the negative terminal is the cathode (still reduction)
  • The minimum voltage required equals the magnitude of the negative \(E°_{\text{cell}}\) for the reaction

Electrolysis of Water

A classic electrolytic reaction is the decomposition of water:

\[\ce{2 H2O (l) -> 2 H2 (g) + O2 (g)}\]

The two half-reactions are:

  • Cathode (reduction): \(\ce{2 H2O (l) + 2 e- -> H2 (g) + 2 OH- (aq)}\) (\(E° = -0.83\) V)
  • Anode (oxidation): \(\ce{2 H2O (l) -> O2 (g) + 4 H+ (aq) + 4 e-}\) (\(E° = -1.23\) V for reduction, so \(+1.23\) V drives the reverse)

The minimum voltage required: \(E°_{\text{cell, required}} = 0.83 + 1.23 = 1.23\) V (ignoring overpotential losses).

In practice, a voltage of about 1.8–2.0 V is needed due to overpotential — extra voltage required to overcome activation energy barriers at the electrodes.

Electroplating

Electroplating deposits a thin layer of one metal onto another object using electrolysis. The object to be plated is the cathode; the plating metal (often \(\ce{Ag}\), \(\ce{Au}\), \(\ce{Cr}\), or \(\ce{Ni}\)) is the anode dissolving into solution to replenish ions.

Example — silver plating:

  • Cathode: \(\ce{Ag+ (aq) + e- -> Ag (s)}\) (silver deposits on object)
  • Anode: \(\ce{Ag (s) -> Ag+ (aq) + e-}\) (silver anode dissolves)

The thickness of the plating is controlled by the total charge passed (time × current), calculated using Faraday's laws.

Faraday's Laws of Electrolysis

Faraday's Constant

Faraday's constant (\(F\)) is the charge carried by one mole of electrons:

\[F = 96,485 \text{ C/mol e}^- \approx 96,500 \text{ C/mol e}^-\]

The total charge passed through an electrolytic cell is:

\[q = I \times t\]

where \(I\) = current in amperes (A) and \(t\) = time in seconds (s). Since 1 A = 1 C/s, \(q\) is in coulombs.

Faraday's Laws and Electrolysis Stoichiometry

Faraday's first law: the mass of substance deposited or dissolved is proportional to the charge passed.

Faraday's second law: for the same charge, the mass deposited is inversely proportional to the number of electrons required per ion.

The stoichiometry calculation chain:

\[q \text{ (coulombs)} \xrightarrow{\div F} \text{mol } e^- \xrightarrow{\text{mole ratio}} \text{mol metal} \xrightarrow{\times M} \text{mass (g)}\]

Example: How many grams of copper are deposited when a current of 2.50 A flows for 30.0 min through a \(\ce{CuSO4}\) solution? (\(M_{\ce{Cu}} = 63.55\) g/mol; \(\ce{Cu^{2+}} + 2e^- \to \ce{Cu}\))

Step 1 — Total charge:

\[q = I \times t = 2.50 \text{ A} \times (30.0 \times 60 \text{ s}) = 2.50 \times 1800 = 4500 \text{ C}\]

Step 2 — Moles of electrons:

\[n_{e^-} = \frac{4500 \text{ C}}{96,485 \text{ C/mol}} = 0.04664 \text{ mol } e^-\]

Step 3 — Moles of copper (2 electrons per copper):

\[n_{\ce{Cu}} = \frac{0.04664}{2} = 0.02332 \text{ mol}\]

Step 4 — Mass of copper:

\[m = 0.02332 \times 63.55 = 1.48 \text{ g}\]

You've Got This!

Catalyst encourages you Faraday's law calculations follow the same pattern every time: convert current × time to coulombs, divide by 96,485 to get moles of electrons, use stoichiometry from the half-reaction, then convert to grams with molar mass. Once you do two or three of these, the pattern becomes automatic!

Example 2: What current (in amperes) must flow for 45.0 min to deposit exactly 1.00 g of silver from \(\ce{AgNO3}\) solution? (\(M_{\ce{Ag}} = 107.87\) g/mol; \(\ce{Ag+ + e- -> Ag}\))

Working backwards:

\[n_{\ce{Ag}} = \frac{1.00}{107.87} = 9.27 \times 10^{-3} \text{ mol}\]

Since 1 electron per Ag: \(n_{e^-} = 9.27 \times 10^{-3}\) mol

\[q = (9.27 \times 10^{-3})(96,485) = 894 \text{ C}\]
\[I = \frac{q}{t} = \frac{894 \text{ C}}{45.0 \times 60 \text{ s}} = \frac{894}{2700} = 0.331 \text{ A}\]

Diagram: Electrolysis Stoichiometry Calculator MicroSim

Interactive Faraday's Law Calculator

Type: microsim sim-id: faraday-law-calculator
Library: p5.js
Status: Specified

Learning objective: Students will be able to (Applying) calculate the mass of substance deposited or dissolved in an electrolytic cell using Faraday's laws, given current, time, and the number of electrons transferred.

Canvas: 820 × 560 px, responsive to window resize.

Solve-for mode (radio buttons at top): - "Find mass deposited" (default) - "Find time needed" - "Find current needed"

Input panel: - Dropdown: Select metal (Cu 2e⁻ | Ag 1e⁻ | Au 3e⁻ | Al 3e⁻ | Fe 2e⁻ | Custom) - If Custom: input molar mass and electrons per ion - Input: Current I (A) — if solving for time or mass - Input: Time t (minutes) — if solving for mass or current - Input: Target mass m (g) — if solving for time or current

Step-by-step solution display (right side): Show the full calculation chain with boxes for each step:

Box 1: \(q = I \times t = \_ \text{ C}\) Box 2: \(n_{e^-} = q / F = \_ \text{ mol } e^-\) Box 3: \(n_{\text{metal}} = n_{e^-} / z = \_ \text{ mol}\) (where z = electrons per ion) Box 4: \(m = n_{\text{metal}} \times M = \_ \text{ g}\)

Each box highlights with a green fill as "Calculate" is clicked, stepping through the solution.

Visual: A small animated electrolytic cell diagram showing current flowing, ions migrating, and metal depositing (particle count scales with calculated mass, capped at 50 particles for visual clarity).

Reset button to clear all fields.

Implementation: p5.js with createInput(), createSelect(), createRadio(), createButton() DOM elements.

Batteries, Fuel Cells, and Corrosion

Primary and Secondary Batteries

A battery is a collection of galvanic cells connected in series. Batteries are classified as:

Primary batteries (non-rechargeable): the reaction is irreversible — once the reactants are consumed, the battery is dead.

  • Alkaline cell: \(\ce{Zn}\) anode / \(\ce{MnO2}\) cathode in \(\ce{KOH}\) electrolyte. ~1.5 V. Used in flashlights, remotes.
  • Mercury cell: \(\ce{Zn}\) anode / \(\ce{HgO}\) cathode. ~1.35 V stable voltage. Used in hearing aids (being phased out due to toxicity).

Secondary batteries (rechargeable): the reaction is reversible — passing current in the reverse direction restores the original reactants.

  • Lead-acid battery: Used in cars. 6 cells, each producing ~2 V (total ~12 V).
  • Discharge: \(\ce{Pb (s) + PbO2 (s) + 2 H2SO4 (aq) -> 2 PbSO4 (s) + 2 H2O (l)}\)
  • Recharge: reverse the reaction using the alternator.
  • Lithium-ion battery: Powers laptops and phones. \(\ce{LiCoO2}\) cathode, graphite anode. ~3.6 V per cell.
  • Nickel-metal hydride (NiMH): Used in hybrid vehicles.

Fuel Cells

A fuel cell is a galvanic cell that converts the chemical energy of a fuel (continuously supplied) into electricity without combustion. The hydrogen-oxygen fuel cell:

  • Anode: \(\ce{H2 (g) -> 2 H+ (aq) + 2 e-}\)
  • Cathode: \(\ce{O2 (g) + 4 H+ (aq) + 4 e- -> 2 H2O (l)}\)
  • Overall: \(\ce{2 H2 (g) + O2 (g) -> 2 H2O (l)}\) \(\quad \Delta G° = -474\) kJ

Fuel cells are more efficient than combustion engines (up to ~60% efficiency vs. ~25% for internal combustion) and produce only water as a byproduct.

Corrosion

Corrosion is the spontaneous oxidation of a metal. Iron rusting is the most economically important example. Rust forms through an electrochemical process requiring both oxygen and water:

\[\ce{4 Fe (s) + 3 O2 (g) + 6 H2O (l) -> 2 Fe2O3 * 3H2O (s)}\]

The process is galvanic: one region of the iron surface acts as an anode (iron oxidizes), another region acts as a cathode (oxygen is reduced). Salt water accelerates corrosion by increasing the conductivity of the electrolyte.

Corrosion prevention strategies:

  • Galvanizing: Coat iron with zinc (\(\ce{Zn}\)). Zinc is a more active metal — it oxidizes preferentially (sacrificial anode), protecting the iron even if the coating is scratched.
  • Cathodic protection: Attach a block of magnesium or zinc (active metal) to iron structures (pipelines, ship hulls). The active metal oxidizes sacrificially.
  • Barrier coatings: Paint, oil, or plastic prevent water and oxygen from reaching the metal surface.
  • Alloying: Stainless steel (iron + chromium) resists corrosion because a thin, protective \(\ce{Cr2O3}\) layer forms spontaneously.

Catalyst's Key Insight

Catalyst is thinking Galvanizing and cathodic protection both exploit the same principle from the reduction potential table: a more active metal (more negative \(E°\)) will oxidize preferentially, protecting the less active metal. Zinc (\(E° = -0.76\) V) protects iron (\(E° = -0.44\) V) because zinc is oxidized first. Once all the zinc is gone, the iron starts corroding.

Summary

Electrochemistry connects the spontaneity of redox reactions to electrical energy through two central equations:

\[\Delta G° = -nFE°_{\text{cell}} \quad \text{and} \quad E° = \frac{0.0592}{n} \log K\]

Galvanic (voltaic) cells:

  • Anode: oxidation (negative terminal, electrons flow out)
  • Cathode: reduction (positive terminal, electrons flow in)
  • \(E°_{\text{cell}} = E°_{\text{cathode}} - E°_{\text{anode}}\)
  • Spontaneous when \(E°_{\text{cell}} > 0\) (equivalent to \(\Delta G° < 0\), \(K > 1\))

Nernst equation (non-standard conditions):

\[E = E° - \frac{0.0592}{n} \log Q\]

Electrolytic cells:

  • Require external power; drive non-spontaneous reactions
  • Faraday's law: \(q = It\); \(n_{e^-} = q/F\); stoichiometry gives moles of product

Faraday's constant: \(F = 96,485\) C/mol e⁻

Applications:

  • Batteries (galvanic cells stored in a package)
  • Fuel cells (continuous galvanic conversion)
  • Corrosion (spontaneous galvanic oxidation)
  • Electroplating and electrolysis (electrolytic applications)

Great Work, Chemists!

Catalyst celebrates Congratulations — you've completed all 18 chapters of AP Chemistry! From atoms and bonding all the way to electrochemical cells and batteries, you now have a complete toolkit for understanding the molecular world. Every charge on your phone, every reaction in your body, every material around you — all of it is chemistry. You've got this!