Entropy and the direction of change

What entropy is (spec 12.1 to 12.4)

Entropy, S, is a measure of disorder: the number of ways particles and their energy can be arranged. Units J mol^-1 K^-1.

• S increases from solid to liquid to gas, and increases with temperature.
• A perfect crystal at 0 K has zero entropy, so every substance above 0 K has a positive standard entropy.
• Natural changes go in the direction of increasing total entropy: a gas spreads through a room, heat flows from hot to cold.

Endothermic changes such as dissolving ammonium nitrate or the reaction of solid hydrated barium hydroxide with ammonium chloride happen spontaneously because entropy increases.

Predicting the sign of ΔSsystem (spec 12.5)

ΔS is positive when:

• a substance melts, boils or sublimes
• an ionic lattice dissolves (ions become free to move, although ordering of water around small, highly charged ions works against this)
• a reaction makes more moles of gas, for example CaCO3(s) -> CaO(s) + CO2(g)

ΔS is negative when gas moles decrease, as in N2(g) + 3H2(g) -> 2NH3(g).

Calculating ΔSsystem (spec 12.7)

ΔS°system = ΣS°(products) - ΣS°(reactants), multiplying each S° by the number of moles in the equation. Elements in their standard states have non-zero entropies, unlike their enthalpies of formation.

Worked example

Calculate ΔS°system for 2H2(g) + O2(g) -> 2H2O(l). S° / J mol^-1 K^-1: H2(g) 130.6, O2(g) 205.0, H2O(l) 69.9.

1. Products: 2 x 69.9 = 139.8
2. Reactants: 2 x 130.6 + 205.0 = 466.2
3. ΔS = 139.8 - 466.2

Answer: ΔS°system = -326.4 J mol^-1 K^-1 (three moles of gas become liquid)

Check yourself

1. Which has the highest standard molar entropy?
   • H2O(l)
   • H2O(s)
   • H2O(g)
   • NaCl(s)
   Show answer

   H2O(g). Gas particles are the most disordered.

2. What is the sign of ΔSsystem for N2(g) + 3H2(g) -> 2NH3(g)?
   • Negative, because 4 moles of gas become 2
   • Positive, because a new substance forms
   • Zero, because the reaction is reversible
   • Positive, because the reaction is exothermic
   Show answer

   Negative, because 4 moles of gas become 2. Fewer moles of gas means less disorder.

3. Calculate ΔS°system, in J mol^-1 K^-1, for N2(g) + 3H2(g) -> 2NH3(g). S° / J mol^-1 K^-1: N2 191.6, H2 130.6, NH3 192.3.
   Show answer

   -198.8 J mol^-1 K^-1. 2(192.3) - [191.6 + 3(130.6)] = 384.6 - 583.4 = -198.8 J mol^-1 K^-1.

4. Which statement about entropy is correct?
   • Elements in their standard states have zero entropy
   • A perfect crystal at 0 K has zero entropy
   • Entropy decreases as temperature rises
   • Gases have lower entropy than solids
   Show answer

   A perfect crystal at 0 K has zero entropy. Only a perfect crystal at absolute zero has S = 0; elements at 298 K have positive entropy.

5. Ammonium nitrate dissolves in water spontaneously although the process is endothermic. What explains this?
   • The process is really exothermic
   • Ammonium nitrate is covalent
   • Entropy is not involved in dissolving
   • The entropy increase as the lattice breaks up outweighs the unfavourable enthalpy change
   Show answer

   The entropy increase as the lattice breaks up outweighs the unfavourable enthalpy change. Dissolving frees the ions, increasing entropy enough to make the total entropy change positive.

6. Which reaction has the largest increase in entropy of the system?
   • H2O(g) -> H2O(l)
   • CaCO3(s) -> CaO(s) + CO2(g)
   • 2SO2(g) + O2(g) -> 2SO3(g)
   • Mg(s) + Cl2(g) -> MgCl2(s)
   Show answer

   CaCO3(s) -> CaO(s) + CO2(g). Only this one makes gas from solids; the others reduce the moles of gas.

7. What is the sign of ΔSsystem when ice melts?
   • Negative
   • Zero
   • It depends on the pressure only
   • Positive
   Show answer

   Positive. Liquid water is more disordered than ice.

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Sources

• Pearson Edexcel IAL Chemistry (2018) specification
• Pearson Edexcel IAL Chemistry (2018) scheme of work

Last updated 7 November 2026. Spotted a mistake? Tell us.