Hess's Law: Enthalpy of Formation of Methane

Hard

Problem

Calculate the standard enthalpy change (delta H degree) for the formation of methane from its elements: C(s, graphite) + 2H2(g) -> CH4(g). Use delta H degree f values: C(s) = 0 kJ/mol, H2(g) = 0 kJ/mol, CH4(g) = -74.8 kJ/mol.

Given

Formation reaction: C(s, graphite) + 2H2(g) -> CH4(g)
Standard enthalpies of formation: C(s) = 0, H2(g) = 0, CH4(g) = -74.8 kJ/mol
Elements in their standard state have delta H degree f = 0 by definition

Find

The standard enthalpy of reaction delta H degree for C(s) + 2H2(g) -> CH4(g).

Principle

Hess's law says enthalpy is a state function: the total enthalpy change depends only on the start and end states, not the path. So the enthalpy of any reaction equals the formation enthalpies of the products (each multiplied by its coefficient) minus those of the reactants. A formation enthalpy is defined as zero for elements in their most stable standard state.

Formula

\Delta H^{\circ}_{\mathrm{rxn}} = \sum n\Delta H^{\circ}_f(\mathrm{prod}) - \sum n\Delta H^{\circ}_f(\mathrm{react})

delta H rxn = sum(n x delta Hf products) - sum(n x delta Hf reactants)

Solution

List the formation enthalpies with stoichiometric weights. Products: 1 mol CH4 x (-74.8 kJ/mol) = -74.8 kJ.
Reactants: 1 mol C(s) x 0 kJ/mol = 0 kJ; 2 mol H2(g) x 0 kJ/mol = 0 kJ. Total = 0 kJ.
Subtract reactants from products: delta H degree rxn = (-74.8 kJ) - (0 kJ) = -74.8 kJ per mole of reaction.
Interpretation of sign: negative means exothermic — 74.8 kJ of heat is released when 1 mol of CH4 forms.

Delta H degree rxn = -74.8 kJ/mol.

Unit check

Each term is (mol of substance x kJ/mol), so every term carries kJ, and the difference is in kJ per mole of reaction as written. The elements' zero values carry the same kJ units, so the subtraction is dimensionally consistent.

What this means physically

Forming methane from its elements releases 74.8 kJ per mole — the reaction is exothermic. Equivalently, it costs 74.8 kJ/mol to tear methane apart into graphite and hydrogen, a number that feeds directly into combustion and bond-energy calculations.

Common mistake

Students subtract in the wrong order (reactants minus products) and report +74.8 kJ/mol, or forget that elements in their standard state (like C and H2) have formation enthalpies of exactly zero.