AP Chemistry · Handsworth Secondary 2026–27
Unit 9 · Thermodynamics & Electrochemistry
Dr. Ras Mulinta
Handsworth Secondary
Notes Package
CED Unit 9, 7–9% of the AP exam, but we have only 5 blocks (the College Board budgets 10–13), so this unit gets no separate unit test. It is still firmly on the AP exam, and last year it was under-covered, so we front-load it well. This unit ties up the redox you met in Unit 4 and connects entropy, free energy, equilibrium (Unit 7), and electrochemistry into one story: which way does a change go, and how far? BC link: extends the redox & cells of BC Chemistry 12 and the energy-change ideas of BC Chemistry 11.
Blocks: 1 → A–B (entropy) · 2 → C–D (Gibbs & control) · 3 → E–F (free energy ↔ K, coupling) · 4 → G–H (cells, E°cell, ΔG=−nFE) · 5 → I–J (Nernst qualitatively, electrolysis)
By the end you can:
- A (9.1) predict the sign of ΔS · B (9.2) calculate ΔS° from absolute entropies · C (9.3) use ΔG° = ΔH° − TΔS° to judge favorability · D (9.4) explain kinetic control of a favored reaction
- E (9.5) relate ΔG°, K, and T · F (9.6–9.7) reason about dissolution & coupled reactions · G (9.8) describe galvanic vs. electrolytic cells & write cell notation · H (9.9) find E°cell & use ΔG° = −nFE° · I (9.10) reason qualitatively with the Nernst equation · J (9.11) use Faraday's law & I = q/t
Name:Block:Date:
A · Introduction to Entropy CED 9.1 · LO 9.1.A
Entropy (S) measures how dispersed matter and energy are. Nature drifts toward more spread-out arrangements, more ways to be. Your first job is just to read the sign of ΔS by inspection.
Sign rules: ΔS > 0 when matter disperses, solid→liquid→gas, dissolving a solid, or more moles of gas on the product side. ΔS also rises with temperature (KMT: kinetic energy spreads over a broader distribution). Fewer gas moles or a gas condensing → ΔS < 0.
Worked example
Predict the sign of ΔS for: 2 SO₂(g) + O₂(g) → 2 SO₃(g).
Count gas moles: reactants 2 + 1 = 3 mol gas → products 2 mol gas. Gas moles drop (3 → 2).
ΔS < 0 (matter becomes less dispersed)
Practice A
- Predict the sign of ΔS for H₂O(l) → H₂O(g).
- Predict the sign of ΔS for N₂(g) + 3 H₂(g) → 2 NH₃(g).
- A gas is warmed from 25 °C to 200 °C at constant volume. Does its entropy rise or fall? Why (use KMT)?
B · Absolute Entropy & Entropy Change CED 9.2 · LO 9.2.A
Unlike enthalpy, every substance has an absolute molar entropy S° (in J·mol⁻¹·K⁻¹), even elements, whose S° is not zero. You combine these the same "products minus reactants" way.
Core: ΔS°rxn = ΣS°(products) − ΣS°(reactants), each term weighted by its coefficient. Watch the units, entropy is in J/K, while ΔH is usually in kJ.
Worked example
For N₂(g) + 3 H₂(g) → 2 NH₃(g), find ΔS°. S°: N₂ = 191.6, H₂ = 130.7, NH₃ = 192.8 J·mol⁻¹·K⁻¹.
Products: 2 × 192.8 = 385.6 · Reactants: 191.6 + 3 × 130.7 = 191.6 + 392.1 = 583.7
ΔS° = 385.6 − 583.7 = −198.1 J·K⁻¹
ΔS° = −198.1 J·K⁻¹ (negative, as the gas-mole count predicted in A)
Practice B
- For 2 H₂(g) + O₂(g) → 2 H₂O(g), find ΔS°. S°: H₂ = 130.7, O₂ = 205.2, H₂O(g) = 188.8 J·mol⁻¹·K⁻¹.
- Your calculated ΔS° in Q1 is negative. Does that match the gas-mole sign rule from section A? Explain.
- Why is the absolute entropy of a perfect crystal at 0 K equal to zero, while at 298 K it is positive?
C · Gibbs Free Energy & Thermodynamic Favorability CED 9.3 · LO 9.3.A
Enthalpy and entropy compete. Gibbs free energy combines them into one number that tells you whether a process is thermodynamically favored. (We say "favored," not "spontaneous", spontaneous wrongly suggests "instant.")
Core: ΔG° = ΔH° − TΔS°. Favored when ΔG° < 0. Also ΔG°rxn = ΣΔG°f(products) − ΣΔG°f(reactants).
Sign table: ΔH° < 0, ΔS° > 0 → favored at all T. ΔH° > 0, ΔS° < 0 → favored at no T. ΔH° > 0, ΔS° > 0 → favored at high T. ΔH° < 0, ΔS° < 0 → favored at low T. (Same / opposite signs are read by inspection, no calculation needed.)
Worked example
A reaction has ΔH° = +178 kJ and ΔS° = +161 J·K⁻¹. Is it favored at 298 K? At what temperature does it become favored?
Convert ΔS° to kJ: 161 J·K⁻¹ = 0.161 kJ·K⁻¹. At 298 K: ΔG° = 178 − (298)(0.161) = 178 − 47.98 = +130 kJ → not favored.
Crossover where ΔG° = 0: T = ΔH°/ΔS° = 178 / 0.161 = 1106 K.
Not favored at 298 K (ΔG° ≈ +130 kJ); becomes favored above ≈ 1.11 × 10³ K (high-T case).
Practice C
- ΔH° = −92.2 kJ, ΔS° = −198.1 J·K⁻¹. Calculate ΔG° at 298 K. Is it favored?
- Using only signs: ΔH° < 0 and ΔS° > 0. Favored at which temperatures? Why no calculation needed?
- Find the temperature at which ΔG° = 0 for ΔH° = +44.0 kJ, ΔS° = +118.8 J·K⁻¹.
D · Thermodynamic vs. Kinetic Control CED 9.4 · LO 9.4.A
"Favored" (ΔG° < 0) tells you a reaction can go, not that it will go fast. A reaction can be thermodynamically favored yet effectively frozen by a high activation energy.
Key distinction: thermodynamics (ΔG°) sets the destination; kinetics (Eₐ) sets the speed. A favored reaction stuck at an unmeasurable rate is under kinetic control: and a system that isn't reacting is not necessarily at equilibrium.
Worked example
Diamond → graphite has ΔG° < 0 at room conditions, yet diamonds last forever. Explain.
ΔG° < 0 means the conversion is thermodynamically favored, graphite is the lower-free-energy form.
But breaking the rigid carbon network has a huge activation energy, so the rate is essentially zero at 25 °C.
The reaction is favored but under kinetic control (high Eₐ); the unreacted diamond is not at equilibrium.
Practice D
- A gasoline–air mixture has ΔG° ≪ 0 for combustion but sits unburned in a tank. What controls it, and what removes the block?
- True or false: if a favored reaction shows no measurable change, the system must be at equilibrium. Explain.
- Does a catalyst change ΔG° for a reaction? Does it change the rate? Explain the difference.
E · Free Energy & Equilibrium CED 9.5 · LO 9.5.A
ΔG° is the bridge to the equilibrium constant K you learned in Unit 7. The sign of ΔG° tells you which side equilibrium favors; its size tells you how lopsided.
Standard state: ΔG° = −RT ln K, so K = e^(−ΔG°/RT). ΔG° < 0 → K > 1 (products favored); ΔG° > 0 → K < 1; ΔG° ≈ 0 → K ≈ 1.
Any state: ΔG = ΔG° + RT ln Q. Compare Q to K: the reaction runs toward equilibrium and stops where ΔG = 0 (Q = K). Use R = 8.314 J·mol⁻¹·K⁻¹.
Worked example
At 298 K, a reaction has ΔG° = −16.0 kJ·mol⁻¹. Find K.
ln K = −ΔG°/(RT) = −(−16000 J·mol⁻¹) / [(8.314)(298)] = 16000 / 2477.6 = 6.458
K = e^6.458 = 6.4 × 10²
K ≈ 6.4 × 10² (> 1, so products are favored, consistent with ΔG° < 0)
Not tested: equilibrium arguments like Le Châtelier's principle are not applied to operating electrochemical cells (section I), those systems are not at equilibrium.
Practice E
- At 298 K, K = 1.0 × 10⁻⁵. Find ΔG°. Is it positive or negative? (R = 8.314 J·mol⁻¹·K⁻¹.)
- Without calculating, what is K (roughly) if ΔG° = 0? Justify with the equation.
- A reaction has ΔG° = +25 kJ·mol⁻¹. Are reactants or products favored at equilibrium? Explain.
F · Free Energy of Dissolution & Coupled Reactions CED 9.6–9.7 · LO 9.6.A, 9.7.A
Two qualitative ideas. First, why some salts dissolve and others don't is a tug-of-war of enthalpy and entropy terms. Second, an unfavorable reaction can be driven by an outside energy source or by coupling to a favorable one.
Dissolution: ΔG° for dissolving reflects breaking lattice forces, reorganizing solvent, and solvating ions. The competing enthalpy/entropy pieces nearly cancel, so the overall sign is hard to predict, reason about it qualitatively, don't expect a clean number.
Coupling: an unfavorable step (ΔG° > 0) can be pushed by an external source (electricity in electrolysis; light in photosynthesis) or by adding a favorable step that shares an intermediate so the summed ΔG° < 0 (e.g. ATP → ADP driving biosynthesis).
Worked example
Step 1: A → B, ΔG° = +20 kJ (unfavorable). Step 2: B → C, ΔG° = −35 kJ. Can the overall A → C proceed?
B is the shared intermediate; add the steps: ΔG°total = (+20) + (−35) = −15 kJ.
Yes, coupled, A → C has ΔG° = −15 kJ < 0, so the favorable step drags the unfavorable one along.
Practice F
- Step 1 has ΔG° = +30 kJ; step 2 has ΔG° = −18 kJ. Is the coupled overall reaction favored? Show the sum.
- Name the external energy source that drives (a) an electrolytic cell and (b) photosynthesis.
- Why is predicting the overall sign of ΔG° for dissolving a salt harder than for a gas-phase reaction?
G · Galvanic (Voltaic) & Electrolytic Cells CED 9.8 · LO 9.8.A
An electrochemical cell separates a redox reaction into two half-cells so the electrons must travel through a wire, that flow is electricity. This is the Unit 4 redox you already balanced, now put to work.
Anatomy: oxidation at the anode, reduction at the cathode (mnemonic: An Ox, Red Cat). Electrons flow anode → cathode through the wire; the salt bridge carries ions to keep each half-cell neutral. Galvanic = favored reaction makes current (E°cell > 0); electrolytic = an external supply forces an unfavored reaction (E°cell < 0).
Cell notation: anode | anode soln ‖ cathode soln | cathodeoxidation on the left, reduction on the right, ‖ is the salt bridge. Example: Zn | Zn²⁺ ‖ Cu²⁺ | Cu.
Worked example
In a Zn/Cu galvanic cell, Zn is oxidized and Cu²⁺ is reduced. Write the half-reactions, identify anode/cathode, and give the cell notation.
Oxidation (anode): Zn → Zn²⁺ + 2e⁻ · Reduction (cathode): Cu²⁺ + 2e⁻ → Cu
Electrons leave the Zn anode, flow through the wire to the Cu cathode.
Cell notation: Zn | Zn²⁺ ‖ Cu²⁺ | Cu (anode left, cathode right)
Not tested: labeling an electrode as "positive" or "negative" is not assessed (it flips between galvanic and electrolytic cells). Identify electrodes by oxidation/reduction instead.
Practice G
- In a cell, Fe → Fe²⁺ + 2e⁻ occurs in one half-cell and Ag⁺ + e⁻ → Ag in the other. Which is the anode? Write the cell notation.
- State the direction of electron flow (through the wire) in any galvanic cell, in terms of anode and cathode.
- How does an electrolytic cell differ from a galvanic cell in (a) sign of E°cell and (b) energy source?
H · Cell Potential & Free Energy CED 9.9 · LO 9.9.A
Each half-reaction has a standard reduction potential E°. Combine the two to get the cell's voltage E°cell, which is directly linked to ΔG°.
Core: E°cell = E°cathode − E°anode (both taken as reduction potentials; do NOT multiply E° by coefficients). A positive E°cell means a favored (galvanic) reaction.
Link to free energy: ΔG° = −nFE°, where n = moles of electrons transferred and F = 96485 C·mol⁻¹. E°cell > 0 ⇔ ΔG° < 0 ⇔ favored.
Worked example
For Zn | Zn²⁺ ‖ Cu²⁺ | Cu: E°(Cu²⁺/Cu) = +0.34 V, E°(Zn²⁺/Zn) = −0.76 V. Find E°cell, then ΔG°.
Cathode = Cu (reduction), anode = Zn (oxidation): E°cell = E°cathode − E°anode = 0.34 − (−0.76) = +1.10 V.
n = 2 electrons. ΔG° = −nFE° = −(2)(96485 C·mol⁻¹)(1.10 V) = −212267 J·mol⁻¹.
E°cell = +1.10 V (favored); ΔG° = −2.12 × 10⁵ J·mol⁻¹ = −212 kJ·mol⁻¹.
Practice H
- Given E°(Ag⁺/Ag) = +0.80 V and E°(Cu²⁺/Cu) = +0.34 V, find E°cell for a Cu/Ag galvanic cell. Which metal is the anode?
- A cell has E°cell = +0.46 V with n = 2. Calculate ΔG° (F = 96485 C·mol⁻¹).
- A proposed cell gives E°cell = −0.25 V. Is the reaction galvanic or electrolytic? What is the sign of ΔG°?
I · Cell Potential Under Nonstandard Conditions (Nernst, Qualitative) CED 9.10 · LO 9.10.A
Real cells rarely sit at 1 M / 1 atm. As a cell runs, concentrations change and the voltage drifts, toward zero, reaching exactly zero at equilibrium (a dead battery). Reason about this with the Nernst equation qualitatively.
Nernst (qualitative): E = E° − (RT/nF) ln Q. At standard conditions Q = 1 and E = E°. As the reaction proceeds, Q rises toward K and E falls; at equilibrium Q = K and E = 0. Pushing the cell farther from equilibrium than Q = 1 raises |E|; moving it closer lowers |E|.
Worked example
A Zn/Cu cell (E° = +1.10 V) runs until [Cu²⁺] has dropped well below [Zn²⁺]. Does E rise or fall from +1.10 V? Reason with Nernst, no number needed.
Q = [Zn²⁺]/[Cu²⁺]. Lower [Cu²⁺] and higher [Zn²⁺] make Q > 1, so ln Q > 0.
In E = E° − (RT/nF) ln Q, subtracting a positive term lowers E.
E falls below +1.10 V, the cell drifts toward equilibrium (E → 0), consistent with a battery running down.
Not tested: plug-and-chug algorithmic Nernst calculations are insufficientand Le Châtelier reasoning does not apply to a running cell (it is not at equilibrium). You need the qualitative direction of the voltage change.
Practice I
- For a cell at Q = 1, what is E in terms of E°? Justify from the Nernst equation.
- As any galvanic cell discharges, Q moves toward K. What happens to E, and what is E at equilibrium?
- A concentration cell has the same metal/ion in both half-cells but different concentrations. Is E° zero? Why can E still be nonzero?
J · Electrolysis & Faraday's Law CED 9.11 · LO 9.11.A
In electrolysis we push current through a cell to force a reaction (e.g. electroplating). Faraday's law is a stoichiometry chain: charge → moles of electrons → moles of substance → mass.
The chain: q = I·t (charge in C) → mol e⁻ = q / F (F = 96485 C·mol⁻¹) → mol substance via the half-reaction's electron ratio → mass via molar mass. Also I = q/t.
Worked example
A current of 2.00 A flows for 30.0 min through molten/aqueous Cu²⁺. What mass of copper plates out? Cu²⁺ + 2e⁻ → Cu, M(Cu) = 63.55 g/mol.
t = 30.0 min × 60 = 1800 s. q = I·t = 2.00 × 1800 = 3600 C.
mol e⁻ = 3600 / 96485 = 0.03731 mol. mol Cu = 0.03731 / 2 = 0.018655 mol (2 e⁻ per Cu).
mass Cu = 0.018655 × 63.55 = 1.19 g
Practice J
- How long (s) must 1.50 A flow to deposit 0.500 g of silver? Ag⁺ + e⁻ → Ag, M = 107.87 g/mol.
- A current of 3.00 A runs for 1.00 h. How many moles of electrons pass? (F = 96485 C·mol⁻¹.)
- Why does plating one mole of Al from Al³⁺ require more charge than plating one mole of Ag from Ag⁺?