Using ΔH_f^⦵ and ΔH_c^⦵ to Calculate Enthalpy Changes HL Only

Specification Reference R1.2.4

Quick Notes

Hess’s Law allows enthalpy changes to be calculated using standard data:
- ΔH^⦵ = ΣΔH_f^⦵(products) − ΣΔH_f^⦵(reactants)
- ΔH^⦵ = ΣΔH_c^⦵(reactants) − ΣΔH_c^⦵(products)
Enthalpy values are found in the data booklet, units are kJ mol⁻¹.
Remember:
- ΔH_f^⦵ values describe making 1 mole of compound from its elements.
- ΔH_c^⦵ values describe complete combustion in oxygen.

Full Notes

Instead of drawing out full energy cycles, we can use two standard equations to determine enthalpy change using enthalpies of formation or enthalpies of combustion.

Enthalpy from Formation Data (ΔH_f^⦵)

Use this equation:
ΔH^⦵ = ΣΔH_f^⦵(products) − ΣΔH_f^⦵(reactants)

Steps:

Write a balanced equation for the reaction.
Look up ΔH_f^⦵ values for each compound.
Apply the formula using mole ratios from the equation.

Worked Example

Calculate ΔH^⦵ for the reaction C₂H₄(g) + H₂(g) → C₂H₆(g).

Given: ΔH_f^⦵[C₂H₄(g)] = +52.3, ΔH_f^⦵[H₂(g)] = 0, ΔH_f^⦵[C₂H₆(g)] = −84.7
ΔH^⦵ = (−84.7) − (52.3 + 0)
ΔH^⦵ = −137.0 kJ mol⁻¹

Enthalpy from Combustion Data (ΔH_c^⦵)

Use this equation:
ΔH^⦵ = ΣΔH_c^⦵(reactants) − ΣΔH_c^⦵(products)

This method uses combustion values to “bypass” the target reaction, forming a Hess cycle.

Worked Example

Calculate ΔH^⦵ for the reaction C₂H₆(g) + Cl₂(g) → C₂H₅Cl(g) + HCl(g).

Given: ΔH_c^⦵[C₂H₆(g)] = −1560, ΔH_c^⦵[C₂H₅Cl(g)] = −1735, ΔH_c^⦵[HCl(g)] = −92.3, ΔH_c^⦵[Cl₂(g)] = 0
ΔH^⦵ = [−1560 + 0] − [−1735 + (−92.3)]
ΔH^⦵ = −1560 − (−1827.3) = +267.3 kJ mol⁻¹

Summary of When to Use Each Equation

Enthalpy Data Used	Equation to Use	Typical Use Case
Formation (ΔH_f^⦵)	ΔH^⦵ = ΣΔH_f^⦵(products) − ΣΔH_f^⦵(reactants)	Most direct, used in standard tables
Combustion (ΔH_c^⦵)	ΔH^⦵ = ΣΔH_c^⦵(reactants) − ΣΔH_c^⦵(products)	Often used when formation data isn’t available

Matt’s exam tip

Important Reminders

Use balanced equations and correct molar ratios.
Ensure all substances are in their standard states.
Values must match the physical states of substances in the reaction.
ΔH_f^⦵ of elements in standard states = 0.
ΔH_c^⦵ of elements = often 0 for O₂(g), H₂(g), etc.

Summary

Enthalpy changes can be calculated using ΔH_f^⦵ or ΔH_c^⦵ data with Hess’s Law.
Formation data is direct and standard, while combustion data is useful when formation data is unavailable.
Always apply balanced equations, correct states, and molar ratios.

Using ΔHf⦵ and ΔHc⦵ to Calculate Enthalpy Changes HL Only