A laboratory handbook lists the following enthalpy changes (all at 298K):
• Step A NH4Cl(s) → NH4⁺(aq) + Cl⁻(aq) ΔH∘=+14.8kJ mol−1
• Step B NH3(g) + H⁺(aq) → NH4⁺(aq) ΔH∘=−51.7kJ mol−1
• Step C HCl(g) → H⁺(aq) + Cl⁻(aq) ΔH∘=−75.1kJ mol−1
A student is asked to determine the enthalpy change for the vaporization of water,
H2O(l) → H2O(g) ΔH∘=ykJ mol−1,
using the incomplete energy cycle described below.
Cycle description (verbal):
1. Solid NH4Cl is dissolved directly in liquid water to form aqueous ions (overall enthalpy change = Step A + an unknown contribution from the vaporization of some of the water).
2. Alternatively, NH4Cl is first decomposed to NH3(g) and HCl(g), each of which is separately dissolved in liquid water (Steps B and C), again requiring the vaporization of the same amount of water.
The student notices that the ion–formation steps (A, B, and C) can be arranged so that the only difference between the two routes in the cycle is the direction in which water changes phase.
(a) Translate the verbal description into a balanced chemical equation for each of the two alternative routes, clearly indicating the phase of water involved.
(b) Write an algebraic relationship among y and the numerical enthalpy values for Steps A–C that follows from the energy cycle.
(c) Calculate y and include appropriate units.
(d) State one assumption inherent in using this cycle that could introduce systematic error into the calculated y value, and briefly explain its effect.