Explain why the standard entropy change for the formation of sodium chloride from its elements in their standard states is positive, and describe how entropy change and enthalpy change together determine whether a reaction is feasible.

Edexcel A-Level Chemistry (9CH0) — 13.1 Born-Haber cycles and entropy · Explain · 5 marks · View as Markdown

Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).

Sodium chloride is formed from sodium metal and chlorine gas. The overall reaction is highly exothermic. Chemists use both enthalpy change and entropy change to predict whether a reaction will occur spontaneously.

Model answer (5 marks)

The standard entropy change for the formation of NaCl from its elements is positive because the reaction involves the conversion of a gas (Cl₂) into a solid (NaCl). Although the disappearance of a gas reduces the system entropy, the large increase in the number of ways the solid NaCl atoms can be arranged (and the release of lattice energy into the surroundings) more than compensates, giving a net positive ΔS_system. In general, a reaction is feasible when the total entropy change ΔS_total is positive. ΔS_total = ΔS_system + ΔS_surroundings, and ΔS_surroundings = –ΔH/T. Therefore a large negative ΔH (exothermic reaction) increases ΔS_surroundings, which can make ΔS_total positive even if ΔS_system is negative, ensuring the reaction proceeds spontaneously.

Examiner tips

  • Use the definition of entropy and explain the gas‑to‑solid change; mention ΔS_surroundings = –ΔH/T; link ΔS_total > 0 to spontaneity; keep answer concise and use correct symbols.
  • Include the key point that a negative ΔH contributes positively to ΔS_surroundings, which can offset a negative ΔS_system.

Common mistakes

  • Confusing ΔS_system with ΔS_total; writing that the reaction is spontaneous solely because ΔH is negative; omitting the ΔS_surroundings term or the –ΔH/T relationship.

Mark scheme (5 marks)

  1. Entropy is a measure of the disorder (or number of ways of arranging particles) in a system
  2. Chlorine gas has higher entropy than the solid sodium or solid sodium chloride because gas particles are more disordered / have more possible arrangements than solids
  3. The overall entropy change is positive because a mole of gas (chlorine) is consumed but the increase in disorder from other factors / the gaseous reactant disappearing is offset — accept: one mole of gas is used so entropy of the system decreases, therefore the positive entropy change must come from the surroundings
  4. A reaction is feasible when the total entropy change (ΔS_total) is positive / greater than zero
  5. ΔS_total = ΔS_system + ΔS_surroundings, where ΔS_surroundings = −ΔH/T, so a large negative enthalpy change (exothermic) increases ΔS_surroundings and can make the reaction feasible even if ΔS_system is negative

Key terms in this question

entropy

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