Applications of Thermodynamics & Electrochemistry — AP Chemistry Study Guide

For: AP Chemistry candidates sitting AP Chemistry.

Covers: Gibbs free energy and spontaneity, equilibrium constant from $\Delta G$, galvanic vs electrolytic cells, standard reduction potentials, Nernst equation, electrolysis stoichiometry — AP Chemistry Unit 9.

You should already know: Thermodynamics enthalpy/entropy (Unit 6), equilibrium $K$ (Unit 7), redox identification (Unit 4).

A note on the practice questions: All worked questions in the "Practice Questions" section below are original problems written by us in the AP Chemistry style for educational use. They are not reproductions of past College Board papers and may differ in wording, numerical values, or context. Use them to practise the technique; cross-check with official College Board mark schemes for grading conventions.

1. Why Apps of Thermodynamics Matters

Unit 9 ties Unit 6 (thermodynamics) and Unit 7 (equilibrium) into the practical questions: will this reaction happen, how far will it go, and how much electrical work can it deliver. About 7–9% of AP Chemistry comes from this unit, but Unit 9 + redox is a perennial FRQ pairing.

Two big ideas:

1. Gibbs free energy $\Delta G=\Delta H-T\Delta S$ — sign of $\Delta G$ predicts spontaneity, magnitude relates to the equilibrium constant $K$.
2. Electrochemistry — coupling spontaneous redox to do electrical work (galvanic cell) or using electrical work to drive non-spontaneous redox (electrolytic cell).

2. Gibbs free energy

$$\Delta G=\Delta H-T\Delta S$$

Sign convention:

• $\Delta G<0$ → spontaneous (forward direction).
• $\Delta G>0$ → non-spontaneous (reverse is spontaneous).
• $\Delta G=0$ → at equilibrium.

Whether $\Delta G$ is negative depends on temperature:

• $\Delta H<0$, $\Delta S>0$ → spontaneous at all $T$.
• $\Delta H>0$, $\Delta S<0$ → never spontaneous.
• $\Delta H<0$, $\Delta S<0$ → spontaneous at low $T$.
• $\Delta H>0$, $\Delta S>0$ → spontaneous at high $T$.

$\Delta G$ at non-standard conditions: $\Delta G=\Delta G^{\circ }+RT\ln Q$. At equilibrium $Q=K$, $\Delta G=0$, so $\Delta G^{\circ }=-RT\ln K$.

3. Galvanic (voltaic) cells

A galvanic cell uses a spontaneous redox reaction to produce electricity. Two compartments (half-cells) connected by:

1. an external wire (electron flow from anode to cathode),
2. a salt bridge (ion flow to balance charge).

Anode = oxidation (electrons released). Cathode = reduction (electrons consumed). Mnemonic: An Ox, Red Cat.

Cell potential: $$E_{\text{cell}}^{\circ }=E_{\text{cathode}}^{\circ }-E_{\text{anode}}^{\circ }$$

Both are looked up as standard reduction potentials. A positive $E_{\text{cell}}^{\circ }$ means the reaction is spontaneous as written.

Connecting to thermodynamics: $\Delta G^{\circ }=-nF{E}_{\text{cell}}^{\circ }$, where $n$ is moles of electrons transferred and $F=96485$ C/mol (Faraday's constant). Spontaneous reaction → $E^{\circ }>0$ → $\Delta G^{\circ }<0$.

4. Electrolytic cells

Reverse of galvanic. An external power source pushes current through, driving a non-spontaneous redox.

Sign of cathode/anode flips relative to galvanic:

• Galvanic cell: cathode = +, anode = −.
• Electrolytic cell: cathode = −, anode = +.

But the chemistry is unchanged — anode is still oxidation, cathode is still reduction.

Applications: electrolysis of water (produces H₂ and O₂), electroplating, refining of metals, charging a rechargeable battery.

5. Faraday's law of electrolysis

Charge passed = current × time: $Q=I\cdot t$ (coulombs).

Moles of electrons: $n_e=Q/F$.

Moles of substance produced/consumed at an electrode: $$n_{\text{substance}}=\frac{n_e}{\text{electrons per ion}}$$

For example, 1 mole of Cu²⁺ → Cu requires 2 mol electrons. So passing 2F (192 970 C) deposits 1 mol Cu (= 63.55 g).

6. Nernst equation

For non-standard concentrations: $$E_{\text{cell}}=E_{\text{cell}}^{\circ }-\frac{RT}{nF}\ln Q$$

At 25 °C this simplifies to $E_{\text{cell}}=E_{\text{cell}}^{\circ }-(0.0592/n)\log Q$.

When $Q=K$, $E_{\text{cell}}=0$, the cell is dead (at equilibrium).

When ion concentrations on either side of a concentration cell differ, even a single metal in solutions of different M⁺ concentrations produces a small EMF — driven by entropy of mixing.

7. Worked Example

A galvanic cell uses Zn|Zn²⁺ (1.0 M) and Cu|Cu²⁺ (1.0 M) half-cells. Standard reduction potentials: $E^{\circ }({\text{Cu}}^{2+}/\text{Cu})=+0.34$ V, $E^{\circ }({\text{Zn}}^{2+}/\text{Zn})=-0.76$ V.

(a) Write the spontaneous overall reaction and identify the cathode. (b) Calculate $E_{\text{cell}}^{\circ }$. (c) Calculate $\Delta G^{\circ }$ and $K$ at 25 °C. (d) If the cell runs for 30.0 minutes at 0.50 A, how much Zn (g) is consumed?

Solution.

(a) Cu²⁺ has higher reduction potential → Cu²⁺/Cu is the cathode (reduction). Zn|Zn²⁺ is the anode (oxidation). Net: $\text{Zn}(s)+{\text{Cu}}^{2+}(aq)\to {\text{Zn}}^{2+}(aq)+\text{Cu}(s)$.

(b) $E_{\text{cell}}^{\circ }=E_{\text{cathode}}^{\circ }-E_{\text{anode}}^{\circ }=0.34-(-0.76)=1.10$ V.

(c) $\Delta G^{\circ }=-nF{E}^{\circ }=-2\cdot 96485\cdot 1.10=-212267$ J/mol ≈ −212 kJ/mol. $\ln K=-\Delta G^{\circ }/RT=212267/(8.314\cdot 298)=85.7$, so $K\approx e^{85.7}\approx 1.6\times 10^{37}$.

(d) Charge $Q=It=0.50\cdot (30\cdot 60)=900$ C. Electrons: $n_e=900/96485=9.33\times 10^{-3}$ mol. Each Zn → Zn²⁺ gives 2 electrons, so $n_{\text{Zn}}=9.33\times 10^{-3}/2=4.66\times 10^{-3}$ mol. Mass: $4.66\times 10^{-3}\cdot 65.38=$ 0.305 g Zn consumed.

8. Common Pitfalls

• Confusing anode signs: in galvanic cells, anode is negative. In electrolytic cells, anode is positive. The chemistry (oxidation at anode) is unchanged; only the polarity flips.
• Forgetting $n$ in $\Delta G=-nFE$: $n$ is the number of electrons in the balanced cell reaction, which may differ from coefficients of either half-reaction.
• Misreading reduction potentials table: all values are reductions. To get the oxidation potential, flip the sign.
• Applying Nernst at standard conditions: when all concentrations are 1 M and gases are 1 atm, $Q=1$, $\ln Q=0$, and $E=E^{\circ }$. Don't bother with Nernst; just use $E^{\circ }$.

9. Practice Questions (CED Style)

1. Calculate $\Delta G^{\circ }$ for the reaction ${\text{Sn}}^{2+}+2{\text{Ag}}^{+}\to {\text{Sn}}^{4+}+2\text{Ag}$ given $E^{\circ }({\text{Ag}}^{+}/\text{Ag})=+0.80$ V and $E^{\circ }({\text{Sn}}^{4+}/{\text{Sn}}^{2+})=+0.15$ V.
2. How long must a current of 1.50 A pass through molten NaCl to deposit 5.00 g of Na metal?
3. A concentration cell has Cu electrodes in 0.0010 M Cu²⁺ and 1.00 M Cu²⁺ solutions. Determine which electrode is the anode and calculate $E_{\text{cell}}$ at 25 °C.

10. Quick Reference Cheatsheet

• Gibbs: $\Delta G=\Delta H-T\Delta S$. $\Delta G<0$ spontaneous.
• Connection: $\Delta G^{\circ }=-RT\ln K=-nF{E}^{\circ }$.
• Galvanic cell: spontaneous, $E^{\circ }>0$, $\Delta G^{\circ }<0$. Cathode (+), anode (−).
• Electrolytic cell: external power drives non-spontaneous redox. Cathode (−), anode (+).
• Faraday: $Q=It$; mol electrons $=Q/F$; $F=96485$ C/mol.
• Nernst (25 °C): $E=E^{\circ }-(0.0592/n)\log Q$.
• An Ox, Red Cat: ANode = OXidation; REDuction at CAThode.

11. What's Next

Apps of Thermodynamics is the final unit of AP Chemistry. It builds on every prior unit: redox (Unit 4), thermodynamics (Unit 6), equilibrium (Unit 7). For exam preparation, drill the FRQ pattern of "given a galvanic cell, calculate $E^{\circ }$, $\Delta G^{\circ }$, $K$, and how much mass is deposited at one electrode" — this is a 6-7 point question that appears almost every year. Use Ollie to step through complex Nernst-equation problems or to verify your sign convention on $E^{\circ }$.