Quick answer: Entropy measures how many ways particles and energy can be arranged; it rises from solid to liquid to gas. This Chemistry 11-12 worksheet on entropy Gibbs energy gives 20 problems from easy to hard: which has more entropy?, predicting the sign of ΔS and entropy of alkanes. The worked answers are on a separate page, and the worksheet is a free printable PDF.
Firstly, these problems train you to predict the sign of an entropy change, calculate ΔS° from tables, use ΔG = ΔH − TΔS to judge feasibility and find changeover temperatures, and link ΔG° to the equilibrium constant. They also progress from qualitative reasoning to multi-step data analysis.
In addition, the level suits A Level, IB Chemistry, CBSE Class 11-12 and senior WAEC and NECO students. Keep ΔH in kJ and ΔS in J until you convert them, and then always use kelvin.
Level: Chemistry grades 11-12 (A Level · IB · Class 11-12) · Curriculum: IB R1.4
Problem 1 Which has more entropy? ★★★
Aarav in Pune compares pairs of substances at the same temperature.1. Ice or liquid water (1 mol each)?
2. One mole of CO₂(g) or one mole of CO₂(s)?
3. NaCl(s) or NaCl dissolved in water (aq)?
4. Two moles of gas or one mole of gas?
Problem 2 Predicting the sign of ΔS ★★★
Predict whether ΔS is positive or negative, with a reason.1. 2H₂O₂(l) → 2H₂O(l) + O₂(g)
2. N₂(g) + 3H₂(g) → 2NH₃(g)
3. CaCO₃(s) → CaO(s) + CO₂(g)
4. H₂O(g) → H₂O(l)
Problem 3 Entropy of alkanes ★★★
The chart shows standard molar entropies of the first three alkanes (gases).1. Firstly, describe the trend.
2. Then calculate the increase in entropy from CH₄ to C₂H₆ and from C₂H₆ to C₃H₈.
3. Finally, suggest why entropy increases along the series.
Problem 4 Gibbs energy of a hand warmer ★★★
Chiamaka in Lagos studies a reaction in a reusable hand warmer: ΔH = −85.0 kJ/mol, ΔS = −120 J K⁻¹ mol⁻¹ at 298 K.1. Firstly, convert ΔS to kJ K⁻¹ mol⁻¹.
2. Then calculate ΔG.
3. Finally, state whether the reaction is spontaneous.
Problem 5 Meaning of the sign of ΔG ★★★
Classify each reaction as spontaneous, non-spontaneous or at equilibrium at the stated temperature.1. ΔG = −12 kJ/mol
2. ΔG = +5 kJ/mol
3. ΔG = 0
4. Finally, state what a positive ΔG tells you about the reverse reaction.
Problem 6 Entropy change for water formation ★★★
Hydrogen–oxygen reactions power a bus in Kisumu: 2H₂(g) + O₂(g) → 2H₂O(l). S° values in J K⁻¹ mol⁻¹: H₂ 130.7, O₂ 205.0, H₂O(l) 69.9.1. Firstly, calculate ΣS°(products) and ΣS°(reactants).
2. Then calculate ΔS°.
3. Finally, explain the sign.
Problem 7 Four sign combinations ★★★
Complete the table by stating when each combination is spontaneous (all temperatures, low T only, high T only or never). Then give the sign of ΔG at low T for the first row.1. ΔH negative, ΔS positive
2. Then ΔH negative, ΔS negative
3. Then ΔH positive, ΔS positive
4. Finally, ΔH positive, ΔS negative
Problem 8 Burning methane ★★★
Wanjiru in Nairobi studies methane in a gas stove: CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(l), ΔH = −890 kJ/mol. S° values in J K⁻¹ mol⁻¹: CH₄ 186.3, O₂ 205.0, CO₂ 213.8, H₂O(l) 69.9.1. Firstly, calculate ΔS°.
2. Then calculate ΔG at 298 K.
3. Finally, state whether the reaction is spontaneous and what else controls its speed.
Problem 9 Melting point of ice ★★★
Kofi in Accra keeps drinks cold with ice. For H₂O(s) → H₂O(l), ΔH = +6.01 kJ/mol and ΔS = +22.0 J K⁻¹ mol⁻¹.1. Firstly, state the value of ΔG at the melting point.
2. Then calculate the melting point in K and °C.
3. Finally, predict whether melting is spontaneous at 290 K.
Problem 10 Boiling point of ethanol ★★★
A distillation lab in Texas uses ethanol: C₂H₅OH(l) → C₂H₅OH(g), ΔH = +38.6 kJ/mol and ΔS = +110 J K⁻¹ mol⁻¹.1. Firstly, calculate the temperature at which ΔG = 0.
2. Then convert it to °C.
3. Finally, explain what happens to the sign of ΔG above this temperature.
Problem 11 Dissolving sodium chloride ★★★
Mei in Singapore dissolves salt: NaCl(s) → Na⁺(aq) + Cl⁻(aq), ΔH = +3.9 kJ/mol. S° values in J K⁻¹ mol⁻¹: NaCl(s) 72.1, Na⁺(aq) 59.0, Cl⁻(aq) 56.5.1. Firstly, calculate ΔS°.
2. Then calculate ΔG at 298 K.
3. Finally, explain why the endothermic process is spontaneous.
Problem 12 From ΔG to the equilibrium constant ★★★
Use R = 8.31 J K⁻¹ mol⁻¹ and T = 298 K.1. Firstly, a reaction has K = 4.0 × 10³. Calculate ΔG° in kJ/mol.
2. another reaction has ΔG° = +15.0 kJ/mol. Calculate K.
3. Finally, state which reaction favours products.
Problem 13 Reading a ΔG–T graph ★★★
The graph shows ΔG against temperature for a reaction.1. Firstly, read the value of ΔH from the intercept at T = 0.
2. Then calculate ΔS from the gradient.
3. Finally, read the temperature where ΔG = 0 and state when the reaction is spontaneous.
Problem 14 Entropy of the surroundings ★★★
Diego in Texas burns ethanol: C₂H₅OH(l) + 3O₂(g) → 2CO₂(g) + 3H₂O(l), ΔH = −1367 kJ/mol at 298 K, ΔS(system) = −138.4 J K⁻¹ mol⁻¹.1. Firstly, calculate ΔS(surroundings).
2. Then calculate ΔS(total).
3. Finally, show that −TΔS(total) equals ΔG.
Problem 15 Decomposition of hydrogen peroxide ★★★
A first-aid kit in Leeds contains hydrogen peroxide: 2H₂O₂(l) → 2H₂O(l) + O₂(g), ΔH = −196 kJ/mol. S° values in J K⁻¹ mol⁻¹: H₂O₂(l) 109.6, H₂O(l) 69.9, O₂(g) 205.0.1. Firstly, calculate ΔS° and ΔG at 298 K.
2. Then explain why the bottle can be stored for months although ΔG is very negative.
Problem 16 Baking soda decomposition ★★★
Bilal in Lahore heats baking soda: 2NaHCO₃(s) → Na₂CO₃(s) + H₂O(g) + CO₂(g), ΔH = +135.6 kJ/mol. S° values in J K⁻¹ mol⁻¹: NaHCO₃ 101.7, Na₂CO₃ 135.0, H₂O(g) 188.8, CO₂ 213.8.1. Firstly, calculate ΔS°.
2. Then calculate ΔG at 298 K and state whether baking soda decomposes at room temperature.
3. Finally, calculate the minimum temperature for decomposition in K and °C.
Problem 17 The contact process ★★★
A sulfuric acid plant in Kampala makes SO₃: 2SO₂(g) + O₂(g) → 2SO₃(g), ΔH = −198 kJ/mol. S° values in J K⁻¹ mol⁻¹: SO₂ 248.2, O₂ 205.0, SO₃ 256.8.1. Firstly, calculate ΔS°.
2. Then calculate ΔG at 298 K and at 1200 K.
3. Then calculate the temperature above which the forward reaction stops being spontaneous.
4. Finally, explain why the plant uses about 700 K even though low T favours products.
Problem 18 Dinitrogen tetroxide equilibrium ★★★
Colourless N₂O₄(g) ⇌ 2NO₂(g) (brown). ΔH = +57.2 kJ/mol and ΔS = +175.8 J K⁻¹ mol⁻¹. Use R = 8.31 J K⁻¹ mol⁻¹.1. Firstly, calculate ΔG at 298 K.
2. Then calculate K at 298 K.
3. Finally, calculate the temperature at which K = 1 and predict the colour change on heating.
Problem 19 Three reactions on one graph ★★★
The graph shows ΔG against T for reactions A, B and C. Their data are: A ΔH = −120 kJ/mol, ΔS = +0.080 kJ K⁻¹ mol⁻¹; B ΔH = +50 kJ/mol, ΔS = −0.110 kJ K⁻¹ mol⁻¹; C ΔH = +90 kJ/mol, ΔS = +0.200 kJ K⁻¹ mol⁻¹.1. Firstly, match each line on the graph to A, B or C by its starting point and gradient.
2. Then state which reaction is spontaneous at all temperatures and which at none.
3. Finally, calculate the crossover temperature for C and its ΔG at 298 K.
Problem 20 Spot the errors ★★★
A student calculates ΔG for a reaction with ΔH = −50.0 kJ/mol and ΔS = −100 J K⁻¹ mol⁻¹ at 298 K and writes: ΔG = −50.0 − 298 × (−100) = +29 750 kJ/mol, so the reaction does not happen.1. Firstly, identify the error.
2. Then calculate the correct ΔG.
3. Finally, calculate the temperature above which the reaction stops being spontaneous.
