Chemistry

Chemistry

Problem

Given the following reactions and their enthalpy changes: (i) N2(g)+3H2(g)→2NH3(g)ΔHa=−92.4 kJ\text{N}_2(g)+3\text{H}_2(g)\rightarrow 2\text{NH}_3(g)\quad \Delta H_a = -92.4\,\text{kJ} (ii) NH3(g)+HCl(g)→NH4Cl(s)ΔHb=−176 kJ\text{NH}_3(g)+\text{HCl}(g)\rightarrow \text{NH}_4\text{Cl}(s)\quad \Delta H_b = -176\,\text{kJ} (iii) 12H2(g)+12Cl2(g)→HCl(g)ΔHc=−92.3 kJ\tfrac{1}{2}\text{H}_2(g)+\tfrac{1}{2}\text{Cl}_2(g)\rightarrow \text{HCl}(g)\quad \Delta H_c = -92.3\,\text{kJ} Determine the enthalpy change, in kJ, for the formation of NH4Cl(s)\text{NH}_4\text{Cl}(s) from its elements as represented by 12N2(g)+2H2(g)+12Cl2(g)→NH4Cl(s)\tfrac{1}{2}\text{N}_2(g) + 2\text{H}_2(g) + \tfrac{1}{2}\text{Cl}_2(g) \rightarrow \text{NH}_4\text{Cl}(s).
Intuitive explanation

This problem asks you to use Hess's Law—the principle that enthalpy is a state function, so you can add and scale given reactions to construct any target reaction. The key insight is to treat the given equations like algebraic equations: multiply or divide them by factors, then add them together so that unwanted species cancel and you're left with your target equation. Keep careful track of signs: reversing a reaction flips the sign of ΔH\Delta H, and multiplying a reaction by a factor multiplies its ΔH\Delta H by that same factor.

Intuitive explanation

This problem asks you to use Hess's Law—the principle that enthalpy is a state function, so you can add and scale given reactions to construct any target reaction. The key insight is to treat the given equations like algebraic equations: multiply or divide them by factors, then add them together so that unwanted species cancel and you're left with your target equation. Keep careful track of signs: reversing a reaction flips the sign of ΔH\Delta H, and multiplying a reaction by a factor multiplies its ΔH\Delta H by that same factor.

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