Question

State Hess’s Law. Explain how it can be applied to find the enthalpy change of a reaction.

Answer 1

Hess’s law
- Statement: The enthalpy change for a chemical reaction is the same whether the reaction occurs in one step or several steps; i.e. the enthalpy change depends only on the initial and final states, not on the path between them.
- Rationale: Enthalpy H is a state function, so ΔH is path-independent.

How to apply Hess’s law to find ΔH for a reaction
1. Identify the target reaction whose ΔH you need.
2. List available reactions with known enthalpy changes (ΔH values).
3. Manipulate the known reactions to algebraically sum to the target reaction:
- Reverse a reaction → change sign of its ΔH.
- Multiply a reaction by a factor → multiply its ΔH by the same factor.
4. Add the algebraically adjusted equations; cancel species that appear on both sides.
5. Sum the adjusted ΔH values to obtain the ΔH for the target reaction.

Useful short formulas
- Using standard enthalpies of formation: ΔH°rxn = Σ(ν ΔH°f, products) − Σ(ν ΔH°f, reactants).
- Keep track of states (g, l, s, aq) and of units (usually kJ mol−1) and note that tabulated values are normally for standard conditions (298 K, 1 bar).

Quick example
Given:
C (s) + O2 (g) → CO2 (g) ΔH = −393.5 kJ
CO (g) + 1/2 O2 (g) → CO2 (g) ΔH = −283.0 kJ
Find ΔH for: C (s) + 1/2 O2 (g) → CO (g)

Reverse the second reaction (change sign):
CO2 → CO + 1/2 O2 ΔH = +283.0 kJ

Add to the first:
C + O2 → CO2 ΔH = −393.5 kJ
CO2 → CO + 1/2 O2 ΔH = +283.0 kJ
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C + 1/2 O2 → CO ΔH = −393.5 + 283.0 = −110.5 kJ

So ΔH for C + 1/2 O2 → CO is −110.5 kJ by Hess’s law.