Chemistry · Year 11 · Module 4 · Lesson 11
HSC Exam Practice
Entropy — Definition, Modelling & Predicting ΔS
Short answer
1.Short answer
Define entropy and state its SI units.
Predict the sign of ΔS for each of the following reactions and justify each prediction using the Δn(gas) rule or relevant phase change reasoning.
(a) N2(g) + 3H2(g) → 2NH3(g)
(b) CaCO3(s) → CaO(s) + CO2(g)
(c) 2H2O2(l) → 2H2O(l) + O2(g)
State the Second Law of Thermodynamics and write the mathematical expression it gives for spontaneous processes.
Distinguish between enthalpy (H) and entropy (S) with reference to: (i) what each quantity measures; (ii) the reference point used for each; and (iii) whether absolute values can be tabulated.
Explain why it is necessary to convert S° from J K−1 mol−1 to kJ K−1 mol−1 before substituting into the Gibbs free energy equation ΔG = ΔH − TΔS. What error results if the conversion is not made?
Outline why dissolving an ionic solid such as NaCl in water generally results in an increase in entropy, using the term microstates in your answer.
Data response
2.Data response — standard entropy bar chart
The bar chart below shows the standard molar entropy S° (J K−1 mol−1) at 298 K for a series of substances. Use the data to answer the sub-questions.
(a) Describe the trend in S° values across the three states of water (solid, liquid, gas) and use the concept of microstates to account for this trend.
(b) Using data from the chart, calculate ΔS for the reaction H2O(l) → H2O(g) and predict whether this process is spontaneous above 100 °C. Account for your answer using the Second Law.
(c) NaCl(s) has a similar S° value to H2O(l) yet NaCl is a solid and H2O is a liquid at 298 K. Suggest one structural reason why NaCl(s) has an unexpectedly high entropy for a solid.
Extended response
3.Source critique
A student writes the following in a homework response:
“The Second Law of Thermodynamics says entropy always increases, so every chemical reaction must have a positive ΔS. This means reactions that form products in a more ordered state — like making solid precipitates from solutions — cannot actually happen. The Second Law also means that refrigerators violate the laws of physics, because they make their contents colder and more ordered.”
Identify the specific scientific errors in this statement and explain the correct chemistry in each case.
4.Extended response — no scaffold
Evaluate the statement: “Entropy is simply a measure of disorder, and endothermic reactions cannot be spontaneous because they take energy from the surroundings.” In your response, analyse the accuracy of each claim and use the Second Law of Thermodynamics to construct a correct account of what determines whether a process is spontaneous. Refer to at least one specific chemical example.
Chemistry · Year 11 · Module 4 · Lesson 11
Answer Key & Marking Guidelines
Section 1 · Short answer · 2 marks · Band 3
Sample response. Entropy (S) is a thermodynamic measure of the dispersal of energy across the available microstates of a system — the more ways energy can be distributed among particles, the higher the entropy. Its SI unit is J K−1 mol−1 (joules per kelvin per mole).
Marking notes. 1 mark for definition referencing microstates or energy dispersal (not just “disorder”). 1 mark for stating units as J K−1 mol−1.
Section 1 · Short answer · 6 marks · Band 3–4
(a) N&sub2;(g) + 3H&sub2;(g) → 2NH&sub3;(g). Δn(gas) = 2 − (1+3) = −2. Moles of gas decrease — ΔS < 0. Fewer gas particles means fewer microstates.
(b) CaCO&sub3;(s) → CaO(s) + CO&sub2;(g). Δn(gas) = 1 − 0 = +1. One mole of gas produced from solid reactants — ΔS > 0. Production of gas creates many more microstates.
(c) 2H&sub2;O&sub2;(l) → 2H&sub2;O(l) + O&sub2;(g). Δn(gas) = 1 − 0 = +1. One mole of O&sub2;(g) produced from liquid reactants — ΔS > 0.
Marking notes. 1 mark per correctly signed ΔS + 1 mark per correct justification referencing Δn(gas) or microstates (6 marks total).
Section 1 · Short answer · 2 marks · Band 3
Sample response. The Second Law of Thermodynamics states that for any spontaneous process, the total entropy of the universe increases: ΔS(universe) = ΔS(system) + ΔS(surroundings) > 0.
Marking notes. 1 mark for qualitative statement (universe entropy increases for spontaneous processes). 1 mark for the mathematical expression ΔS(universe) > 0 (with system + surroundings identified).
Section 1 · Short answer · 4 marks · Band 4
Sample response. Enthalpy (H) measures the heat content at constant pressure, essentially the energy stored in chemical bonds. Its reference is conventional: ΔH°f = 0 for elements in their standard state; only changes in enthalpy (ΔH) can be measured, so absolute H values cannot be tabulated. Units: kJ mol−1. Entropy (S) measures the dispersal of energy across available microstates. Its reference is absolute: S = 0 for a perfect crystal at 0 K (Third Law), so absolute S° values can be tabulated for all substances — unlike enthalpy, S° of elements is not zero at 298 K. Units: J K−1 mol−1.
Marking notes. 1 mark for what enthalpy measures (heat content / bond energy) and its conventional zero; 1 mark for stating absolute H cannot be tabulated. 1 mark for what entropy measures (microstates / energy dispersal) and its absolute zero (Third Law); 1 mark for stating absolute S° can be tabulated.
Section 1 · Short answer · 2 marks · Band 3–4
Sample response. ΔH is in kJ mol−1 and TΔS must also be in kJ mol−1 for the equation ΔG = ΔH − TΔS to be dimensionally consistent. If S° is used in J K−1 mol−1 without dividing by 1000, the TΔS term is 1000 times larger than it should be, giving a wildly incorrect value for ΔG.
Marking notes. 1 mark for explaining the dimensional mismatch (kJ vs J). 1 mark for identifying the specific error: TΔS is inflated by a factor of 1000.
Section 1 · Short answer · 2 marks · Band 3
Sample response. When NaCl dissolves, the ordered crystal lattice breaks apart and Na&sup+; and Cl− ions become dispersed throughout the solution. In the lattice, particles are fixed in position (few microstates); in solution, ions can occupy many possible positions and move freely, creating a vastly larger number of microstates. This increase in microstates corresponds to an increase in entropy (ΔS > 0).
Marking notes. 1 mark for identifying that lattice breakdown frees ions to move throughout solution. 1 mark for linking this freedom to an increase in microstates and therefore ΔS > 0.
Section 2 · Data response · 8 marks · Band 4–5
Part (a) — 3 marks. S° increases from solid (41.3) to liquid (69.9) to gas (188.7) J K−1 mol−1 — a consistent increase across the three states [1]. In the solid state, water molecules are locked in a lattice with only vibrational freedom; in the liquid state molecules can translate and rotate but are still close together; in the gas state molecules can move freely in all directions across a large volume, with the greatest number of possible positions and speeds [1]. More microstates at each successive state corresponds to higher entropy [1].
Part (b) — 3 marks. ΔS = S°(g) − S°(l) = 188.7 − 69.9 = +118.8 J K−1 mol−1 [1]. The positive value means the system gains entropy. Above 100 °C, evaporation is spontaneous. By the Second Law, a process is spontaneous when ΔS(universe) > 0 [1]. ΔS(system) = +118.8 J K−1 mol−1; although evaporation is endothermic (making ΔS(surroundings) slightly negative), the large positive ΔS(system) ensures ΔS(universe) > 0 above the boiling point, so the process is spontaneous [1].
Part (c) — 2 marks. NaCl consists of alternating Na&sup+; and Cl− ions in a cubic lattice; the two different ion types introduce positional and vibrational variety that increases the number of accessible microstates compared to a simpler monatomic solid [1]. Accept also: the ionic interactions are relatively weak compared to covalent solids like diamond, allowing more vibrational motion and therefore more microstates at 298 K [1].
Section 3 · Source critique · 4 marks · Band 4–5
Error 1 — “every reaction must have positive ΔS.” Incorrect. The Second Law says ΔS(universe) > 0, not ΔS(system) > 0. A reaction can have negative ΔS for the system (e.g. N&sub2; + 3H&sub2; → 2NH&sub3; has ΔS < 0) and still be consistent with the Second Law if it is sufficiently exothermic to raise ΔS(surroundings) enough. [1 mark]
Error 2 — “precipitate formation cannot happen.” Incorrect. The formation of a solid precipitate from aqueous solution does decrease the entropy of the system (solid < aqueous ions). However, many precipitation reactions are exothermic, releasing heat to the surroundings and increasing ΔS(surroundings) sufficiently to ensure ΔS(universe) > 0. Precipitation reactions therefore can and do occur spontaneously. [1 mark]
Error 3 — “refrigerators violate the laws of physics.” Incorrect. Refrigerators decrease the entropy inside the cabinet (the system) but do so by doing work (consuming electrical energy) and expelling heat to the kitchen via the coils at the back. The entropy increase in the surroundings (room + power station waste heat) exceeds the entropy decrease inside the fridge. ΔS(universe) > 0, fully consistent with the Second Law. [1 mark]
Underlying principle: The Second Law does not forbid local entropy decreases; it requires only that the total entropy of the universe (system + surroundings) increases for any spontaneous process. [1 mark]
Section 3 · Extended response · 8 marks · Band 5–6
Marking criteria.
- 1 mark — Identifies that “entropy = disorder” is a useful intuition but not the formal definition; entropy is the number of available microstates / dispersal of energy among particles.
- 1 mark — Explains why the microstate definition is more precise (quantifiable; avoids ambiguity; accounts for cases like stretched rubber band or gases).
- 1 mark — Identifies the specific error in the claim about endothermic reactions: confuses ΔS(system) with ΔS(universe); spontaneity is governed by the universe, not the system alone.
- 1 mark — States the Second Law correctly: ΔS(universe) = ΔS(system) + ΔS(surroundings) > 0 for spontaneous processes.
- 1 mark — Applies the Second Law to show how an endothermic process can be spontaneous: if ΔS(system) is sufficiently large and positive, ΔS(universe) can still exceed zero even though ΔS(surroundings) < 0 (because surroundings lose heat).
- 1 mark — Uses a valid specific chemical example (e.g. NH&sub4;NO&sub3; dissolving in water: endothermic, instant cold pack, spontaneous because large positive ΔS(system) from ionic lattice → free aqueous ions; or NH&sub4;Cl dissolving; or dry ice sublimation).
- 1 mark — Addresses the interaction between ΔH, ΔS, and temperature as drivers of spontaneity (e.g. some endothermic reactions are only spontaneous at high temperature, where TΔS outweighs ΔH; previews Gibbs free energy reasoning).
- 1 mark — Response is logically structured, uses precise thermodynamic terminology throughout (microstates, system, surroundings, spontaneous, Second Law), and reaches an explicit evaluative conclusion.
Sample Band 6 response. The claim contains two distinct errors that must be addressed separately. First, defining entropy as “disorder” is imprecise. While disorder correlates with entropy in many everyday cases, the formal definition is that entropy (S) measures the number of available microstates — the different ways energy can be distributed among all particles in a system. This definition is quantifiable and avoids misleading cases (a stretched rubber band has more entropy than a coiled one, despite appearing more “ordered”; similarly, a gas expanding into a vacuum increases entropy without any change in visual “disorder”). Second, the claim that endothermic reactions cannot be spontaneous conflates the entropy of the system with the entropy of the universe. The Second Law of Thermodynamics states that for any spontaneous process, ΔS(universe) = ΔS(system) + ΔS(surroundings) > 0. For an endothermic reaction, heat flows from the surroundings into the system, so ΔS(surroundings) < 0. However, if ΔS(system) is sufficiently large and positive, ΔS(universe) can still be positive and the process is spontaneous. A clear example is the dissolving of ammonium nitrate (NH&sub4;NO&sub3;) in water, the basis of instant cold packs. This reaction is endothermic (ΔH ≈ +25.7 kJ mol−1), yet it is spontaneous at room temperature because the ionic crystal lattice breaks apart into freely moving NH&sub4;&sup+; and NO&sub3;− ions dispersed throughout solution — a large increase in microstates means ΔS(system) is large and positive, sufficient to outweigh the negative ΔS(surroundings). ΔS(universe) > 0, consistent with the Second Law. In summary: entropy is not disorder but microstates, and endothermic reactions can be spontaneous when the system entropy gain is large enough to ensure the universe’s entropy still increases overall.