Quick answer: Entropy S measures the dispersal of energy and matter, and the Gibbs free energy change ΔG = ΔH − TΔS predicts spontaneity: a reaction is spontaneous when ΔG is negative. This AP Chemistry worksheet on Gibbs free energy gives 20 problems from easy to hard: predict the sign of ΔS, rank by entropy and entropy of water formation. The worked answers are on a separate page, and the worksheet is a free printable PDF.
These problems train Unit 9 of AP Chemistry: predicting the sign of entropy change, calculating ΔS°, ΔH and ΔG, finding crossover temperatures, and linking ΔG° to the equilibrium constant. They also suit A Level and first-year university chemistry.
Level 1 problems work on signs and one-step substitution. Level 2 problems combine several quantities and interpret graphs. The last five problems are level 3: multi-step reactions, coupled processes and the entropy of the universe.
Level: AP Chemistry · Curriculum: AP Chem Unit 9
Problem 1 Predict the sign of ΔS ★★★
Predict whether ΔS is positive or negative for (a) NaCl(s) → Na⁺(aq) + Cl⁻(aq), (b) 2NO₂(g) → N₂O₄(g), (c) CaCO₃(s) → CaO(s) + CO₂(g), (d) H₂O(g) → H₂O(l).Problem 2 Rank by entropy ★★★
Rank from lowest to highest standard molar entropy: He(g), Fe(s), H₂O(l).Problem 3 Entropy of water formation ★★★
Calculate ΔS° for 2H₂(g) + O₂(g) → 2H₂O(l) using S° = 130.7, 205.1 and 69.9 J/(mol·K).Problem 4 A simple ΔG calculation ★★★
Aarav in Pune is given ΔH = −40.0 kJ and ΔS = −100 J/K for a reaction at 298 K. Calculate ΔG and state whether the reaction is spontaneous.Problem 5 Endothermic but spontaneous ★★★
A process has ΔH = +50.0 kJ and ΔS = +150 J/K. Calculate ΔG at 400 K and decide whether it is spontaneous.Problem 6 Four cases ★★★
The diagram shows four regions A to D for the possible signs of ΔH and ΔS.2. State the region where it is spontaneous only at high temperature.
3. State the region where it is spontaneous only at low temperature.
Problem 7 Entropy of methane combustion ★★★
Chiamaka in Lagos studies CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(g). S° values (J/(mol·K)): CH₄ 186.3, O₂ 205.1, CO₂ 213.8, H₂O(g) 188.8.1. Calculate ΔS°.
2. Explain why the value is so small although the reaction releases so much heat.
Problem 8 Decomposition of limestone ★★★
CaCO₃(s) → CaO(s) + CO₂(g) has ΔH° = +178.3 kJ. S° (J/(mol·K)): CaCO₃ 92.9, CaO 39.8, CO₂ 213.8.1. Calculate ΔS°.
2. Calculate ΔG° at 298 K.
3. Calculate the temperature above which the decomposition is spontaneous.
Problem 9 Free energy of formation ★★★
Use ΔG°f values (kJ/mol): CaCO₃(s) −1128.8, CaO(s) −603.3, CO₂(g) −394.4. Calculate ΔG° for CaCO₃(s) → CaO(s) + CO₂(g) and compare it with the value from ΔH° − TΔS°.Problem 10 Melting of ice ★★★
For melting, ΔH = +6.01 kJ/mol and ΔS = +22.0 J/(mol·K).1. Calculate the melting temperature.
2. Calculate ΔG at 263 K and at 283 K.
3. State which temperature favours melting.
Problem 11 Boiling of ethanol ★★★
Ethanol boils at 351 K (78 °C) with ΔH(vap) = 38.6 kJ/mol. At the boiling point ΔG = 0 for the phase change.1. Calculate ΔS(vap) in J/(mol·K).
2. Explain why ΔS(vap) is positive.
Problem 12 K from ΔG° ★★★
A reaction has ΔG° = −20.0 kJ at 298 K. Calculate K.Problem 13 ΔG° from K ★★★
Wanjiru in Nairobi measures K = 1.0 × 10⁻⁵ at 298 K for a reaction. Calculate ΔG° and comment on the sign.Problem 14 Free energy away from standard state ★★★
A reaction has ΔG° = +10.0 kJ at 298 K. Bilal in Lahore sets up a mixture with Q = 1.0 × 10⁻³.1. Calculate ΔG.
2. State the direction in which the reaction proceeds.
Problem 15 Reading a ΔG against T line ★★★
Mei in Singapore measures ΔG = −20 kJ at 300 K and ΔG = +20 kJ at 500 K.2. Calculate ΔH.
3. Calculate the temperature at which ΔG = 0.
Problem 16 Making sulfur trioxide ★★★
Consider 2SO₂(g) + O₂(g) → 2SO₃(g). ΔHf° (kJ/mol): SO₂ −296.8, SO₃ −395.7. S° (J/(mol·K)): SO₂ 248.2, O₂ 205.1, SO₃ 256.8.1. Calculate ΔH° and ΔS°.
2. Calculate ΔG° at 298 K.
3. Calculate the temperature above which the reaction is not spontaneous under standard conditions.
Problem 17 Temperature and the equilibrium constant ★★★
Using the data of “Making sulfur trioxide”, Kofi in Accra considers the industrial temperature 800 K.1. Calculate ΔG° at 800 K.
2. Calculate K at 800 K.
3. Explain why plants nevertheless use about 700 to 800 K.
Problem 18 Coupled reactions ★★★
In a cell, glucose + Pi → glucose-6-phosphate has ΔG° = +13.8 kJ, and ATP → ADP + Pi has ΔG° = −30.5 kJ at 298 K.1. Add the two reactions and calculate ΔG° for the coupled reaction.
2. Calculate K for the coupled reaction.
3. Explain why coupling lets the first reaction proceed.
Problem 19 Instant cold pack ★★★
Diego in Texas notices that dissolving NH₄NO₃(s) in water makes the pack cold. ΔH = +25.7 kJ/mol and ΔS = +108.7 J/(mol·K).1. Calculate ΔG at 298 K.
2. Explain why the process is spontaneous although it absorbs heat.
3. Calculate the temperature below which dissolving would not be spontaneous.
Problem 20 Entropy of the universe ★★★
The ammonia reaction N₂ + 3H₂ → 2NH₃ has ΔH° = −92.2 kJ and ΔS°(system) = −198.7 J/(mol·K) at 298 K.1. Calculate ΔS(surroundings) = −ΔH/T.
2. Calculate ΔS(universe).
3. Show that ΔS(universe) = −ΔG/T and explain what its sign means.
