Hess's Law Example 2

Worked example: enthalpy change of formation from combustion dataMethane cannot be made directly from carbon and hydrogen in a calorimeter, so its standard enthalpy change of formation is found with a Hess cycle using enthalpy changes of combustion.C(s) + 2H₂(g) → CH₄(g)Data: Δ_cH^θ[C(s)] = -393.5, Δ_cH^θ[H₂(g)] = -285.8, Δ_cH^θ[CH₄(g)] = -890.3 kJ mol^-1Step 1. Write the target equation at the top. Below it, write the combustion products that both sides form: CO₂(g) + 2H₂O(l).Step 2. Route 1 goes straight from the elements to the combustion products: burn 1 mol of C and 2 mol of H₂.Step 3. Route 2 goes from the elements to methane (Δ_fH^θ), then burns the methane. Both routes have the same total, so:Δ_fH^θ = ΣΔ_cH^θ(reactants) - ΣΔ_cH^θ(products)Step 4. Substitute, remembering to multiply by the balancing numbers:Δ_fH^θ = (-393.5) + 2(-285.8) - (-890.3)
= -965.1 + 890.3 = -74.8 kJ mol^-1In a combustion cycle the arrows point down, towards the combustion products. Take care with the double negative: subtracting -890.3 means adding 890.3.