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Chemical Equation Rendering Tests

This page verifies that MathJax and the mhchem package are rendering correctly. Each equation is shown with its inline form and, where appropriate, a display (block) form. All equations use $...$ and $$...$$ delimiters — never backslash notation.

1. Photosynthesis (Overall)

The most fundamental equation in plant biology.

Inline: \(\ce{6CO2 + 6H2O ->[\text{light}] C6H12O6 + 6O2}\)

Block:

\[\ce{6CO2 + 6H2O ->[\text{light}][\text{chlorophyll}] C6H12O6 + 6O2}\]

2. Cellular Respiration (Overall)

The reverse of photosynthesis; releases stored chemical energy as ATP.

Inline: \(\ce{C6H12O6 + 6O2 -> 6CO2 + 6H2O + \text{ATP}}\)

Block:

\[\ce{C6H12O6 + 6O2 -> 6CO2 + 6H2O + \text{ATP (36-38 mol)}}\]

3. ATP Hydrolysis

The universal energy-releasing reaction that powers cellular work.

Inline: \(\ce{ATP + H2O -> ADP + P_i + \text{energy}}\)

Block:

\[\ce{ATP + H2O -> ADP + P_i} \quad \Delta G = -30.5 \ \text{kJ/mol}\]

4. Water Autoionization and pH

The basis of acid-base chemistry and biological buffering.

Inline: \(\ce{H2O <=> H+ + OH-}\)

The ion product of water: \(K_w = [\ce{H+}][\ce{OH-}] = 1 \times 10^{-14}\)

Definition of pH:

\[\text{pH} = -\log[\ce{H+}]\]

5. Carbonic Acid Buffer System

Critical for maintaining blood pH and CO₂ transport.

\[\ce{CO2 + H2O <=> H2CO3 <=> H+ + HCO3-}\]

The Henderson-Hasselbalch equation for this buffer:

\[\text{pH} = \text{p}K_a + \log\frac{[\ce{HCO3-}]}{[\ce{H2CO3}]}\]

6. NAD⁺ / NADH Redox Half-Reaction

The central electron carrier in glycolysis and cellular respiration.

Reduction (gains electrons):

\[\ce{NAD+ + H+ + 2e- -> NADH}\]

Oxidation (loses electrons):

\[\ce{NADH -> NAD+ + H+ + 2e-}\]

7. Glycolysis Net Equation

The anaerobic first stage of cellular respiration.

\[\ce{C6H12O6 + 2NAD+ + 2ADP + 2P_i -> 2C3H4O3 + 2NADH + 2H+ + 2ATP + 2H2O}\]

Simplified: glucose yields 2 pyruvate, 2 NADH, and a net gain of 2 ATP.

8. Lactic Acid Fermentation

Regenerates NAD⁺ under anaerobic conditions in muscle cells.

\[\ce{C3H4O3 + NADH + H+ -> C3H6O3 + NAD+}\]

Or written with names: pyruvate + NADH \(\ce{->}\) lactate + \(\ce{NAD+}\)

9. Nitrogen Fixation

Converts atmospheric nitrogen to ammonia; performed by nitrogen-fixing bacteria.

\[\ce{N2 + 8H+ + 8e- + 16ATP -> 2NH3 + H2 + 16ADP + 16P_i}\]

Simplified net:

\[\ce{N2 + 3H2 -> 2NH3}\]

10. Enzyme-Substrate Reaction (Michaelis-Menten)

The two-step model of enzyme catalysis with the Michaelis-Menten rate law.

\[\ce{E + S <=>[$k_1$][$k_{-1}$] ES ->[$k_2$] E + P}\]

Reaction rate:

\[v = \frac{V_{\max}[S]}{K_m + [S]}\]

Where \(K_m = \dfrac{k_{-1} + k_2}{k_1}\) is the Michaelis constant.

Rendering Checklist

If all equations above display correctly, the following are confirmed working:

  • [ ] \ce{} chemical formula rendering (subscripts, superscripts)
  • [ ] Forward arrows -> in chemical equations
  • [ ] Equilibrium arrows <=> in chemical equations
  • [ ] Conditions above/below arrows ->[\text{light}]
  • [ ] Inline $...$ math
  • [ ] Block $$...$$ math
  • [ ] Greek letters: \(\Delta G\), \(\Delta H\), \(\Delta S\)
  • [ ] Fractions: \(\frac{V_{\max}[S]}{K_m + [S]}\)
  • [ ] Superscripts and subscripts in math mode: \(K_m\), \(k_{-1}\), \(10^{-14}\)
  • [ ] Ion charges: \(\ce{H+}\), \(\ce{OH-}\), \(\ce{HCO3-}\), \(\ce{NAD+}\)