R1.1.5 Hess's Law — IB Chemistry

Hess's Law states that the total enthalpy change for a reaction is independent of the route taken, provided the initial and final conditions are the same.

Why Hess's Law Works

Enthalpy is a state function — it only depends on the initial and final states, not the path. This means we can calculate ΔH for reactions that are difficult or impossible to measure directly.

Using Enthalpies of Formation

Hess's Law Formula (Formation Data)

\(
                    \Delta H_{rxn}^{\ominus} = \sum \Delta H_f^{\ominus}(\text{products}) - \sum \Delta
                    H_f^{\ominus}(\text{reactants}) \)

Worked Example

Example: Calculate ΔH for the reaction

C₂H₄(g) + H₂(g) → C₂H₆(g)

Given:

ΔH_f⊖ [C₂H₄] = +52.3 kJ mol⁻¹
ΔH_f⊖ [C₂H₆] = −84.7 kJ mol⁻¹
ΔH_f⊖ [H₂] = 0 kJ mol⁻¹ (element in standard state)

\( \Delta H = \Delta H_f(\text{products}) - \Delta H_f(\text{reactants}) \)
\( \Delta H = (-84.7) - (52.3 + 0) \)
\( \Delta H = -137.0 \text{ kJ mol}^{-1} \)

Using Enthalpies of Combustion

Hess's Law Formula (Combustion Data)

\(
                    \Delta H_{rxn}^{\ominus} = \sum \Delta H_c^{\ominus}(\text{reactants}) - \sum \Delta
                    H_c^{\ominus}(\text{products}) \)

Note: reactants minus products (opposite to the formation formula).

Think About It

Why are the formation and combustion versions of Hess's Law "opposite" in their sign arrangement?

In a formation cycle, elements → compound is the forward direction. In a combustion cycle, compound → combustion products goes forward. The arrows in the energy cycle face different directions relative to the target reaction, which reverses the subtraction order.