Hess's Law Example 6

Worked example: formation of ethanol from combustion dataCalculate Δ_fH^θ for ethanol:2C(s) + 3H₂(g) + ½O₂(g) → C₂H₅OH(l)Data: Δ_cH^θ[C(s)] = -393.5, Δ_cH^θ[H₂(g)] = -285.8, Δ_cH^θ[C₂H₅OH(l)] = -1367.3 kJ mol^-1This example has two traps.Trap 1: oxygen. Oxygen is one of the elements in ethanol, but oxygen does not burn, so it has no enthalpy change of combustion. It contributes nothing to the sum.Trap 2: balancing numbers. There are 2 mol of carbon and 3 mol of hydrogen, so their combustion values are multiplied by 2 and 3.Step 1. Both routes end at 2CO₂(g) + 3H₂O(l).Step 2. Write the expression:Δ_fH^θ = 2Δ_cH^θ[C] + 3Δ_cH^θ[H₂] - Δ_cH^θ[C₂H₅OH]Step 3. Substitute:2(-393.5) + 3(-285.8) = -787.0 + (-857.4) = -1644.4
Δ_fH^θ = -1644.4 - (-1367.3) = -277.1 kJ mol^-1Forgetting the balancing numbers gives -393.5 - 285.8 + 1367.3 = +688.0 kJ mol^-1, which is wrong even in sign. Always multiply by the balancing numbers before adding.