Consider three chemical species X, Y

CHEMISTRY · Multi-part · A Level · Chemistry · Energetics · Energetics

Problem

Consider three chemical species X, Y, and Z that are related by the following hypothetical steps carried out under identical conditions: • Step 1: X→Y\mathrm{X \to Y} enthalpy change ΔH1\Delta H_1 • Step 2: Y→Z\mathrm{Y \to Z} enthalpy change ΔH2\Delta H_2 • Direct Step: X→Z\mathrm{X \to Z} enthalpy change ΔH3\Delta H_3 The three steps form a closed thermochemical cycle. (a) Derive an algebraic relationship among ΔH1\Delta H_1, ΔH2\Delta H_2, and ΔH3\Delta H_3 that must be satisfied by any closed thermochemical cycle. Show each logical step in your derivation. (b) If Step 1 is written in the reverse direction (i.e., Y→X\mathrm{Y \to X}), express the new enthalpy change ΔH1′\Delta H_1' in terms of ΔH1\Delta H_1, and rewrite the relationship from part (a) to reflect this reversal. (c) Discuss one circumstance under which algebraic addition of enthalpy changes for individual steps would NOT correctly predict the enthalpy change for the overall process. In your answer, reference the underlying thermodynamic assumption that is violated.

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