Hard

Calculating Enthalpy Changes Using Hess's Law

Simple Explanation

To find an unknown reaction's ΔH using Hess's law, arrange known reactions (with known ΔH values) so that, when added together, their reactants and products cancel out to leave exactly the target reaction — reversing a reaction flips the sign of its ΔH, and scaling a reaction's coefficients scales its ΔH by the same factor.

Why Do We Need It?

This is the practical, step-by-step skill version of Hess's law — the technique used to actually solve real enthalpy problems, not just state the law.

Formula

Hess's Law

ΔH(overall) = ΔH₁ + ΔH₂ + ΔH₃ + …

The overall enthalpy change for a reaction equals the sum of the enthalpy changes for any set of steps that add up to the same overall reaction.

ΔH(overall): — enthalpy change for the reaction as a whole, in kJ/mol
ΔH₁, ΔH₂, …: — enthalpy changes of each individual step in an alternative pathway between the same starting reactants and final products

When to use it: Whenever a reaction's enthalpy change cannot be measured directly, but can be built from other reactions whose enthalpy changes are already known.

Worked Example

Find ΔH for the formation of methane using two known reactions

Given: (1) C(s) + O₂(g) → CO₂(g), ΔH₁ = −393.5 kJ/mol, and (2) H₂(g) + ½O₂(g) → H₂O(l), ΔH₂ = −285.8 kJ/mol, and (3) CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(l), ΔH₃ = −890.3 kJ/mol, find ΔH for C(s) + 2H₂(g) → CH₄(g).

Why Does This Work?

Adding chemical equations together is valid because it represents a real, physically possible multi-step pathway between the same overall reactants and products — and Hess's law guarantees that pathway's total ΔH must equal the direct reaction's ΔH, since enthalpy only depends on the start and end points.

Real-Life Example

Determining methane's formation enthalpy

Methane's enthalpy of formation cannot be measured directly, because carbon and hydrogen gas do not react cleanly to form pure methane in a lab.

Chemists instead combine the well-known, easily measured combustion enthalpies of carbon, hydrogen, and methane itself using Hess's law — exactly as shown in the worked example — to calculate methane's formation enthalpy indirectly.

Practice

Given S(s) + O₂(g) → SO₂(g), ΔH₁ = −296.8 kJ/mol, and SO₂(g) + ½O₂(g) → SO₃(g), ΔH₂ = −98.9 kJ/mol, find ΔH for S(s) + 3/2 O₂(g) → SO₃(g).

Hard

kJ/mol

Common mistake

Forgetting to flip the sign of ΔH when reversing a reaction, or forgetting to scale ΔH when multiplying a reaction's coefficients — both the reaction equation and its ΔH must be adjusted together, consistently.

Quick Review

Arrange known reactions so their sum equals the target reaction.
Reversing a reaction flips the sign of its ΔH.
Scaling a reaction's coefficients scales its ΔH by the same factor.