Hess's Law Example 5

Worked example: hydrogenation of ethene from combustion dataCalculate the enthalpy change for:C₂H₄(g) + H₂(g) → C₂H₆(g)Data: Δ_cH^θ[C₂H₄(g)] = -1411.0, Δ_cH^θ[H₂(g)] = -285.8, Δ_cH^θ[C₂H₆(g)] = -1559.7 kJ mol^-1Here the reactants are compounds, not elements, but the method is the same. Every substance in the equation can burn, so the combustion products go at the bottom of the cycle.Step 1. Check that both routes end in the same place. Burning C₂H₄ + H₂ gives 2CO₂ + 3H₂O(l). Burning C₂H₆ also gives 2CO₂ + 3H₂O(l), as Hess's law requires.Step 2. Use reactants minus products:Δ_rH^θ = [Δ_cH^θ(C₂H₄) + Δ_cH^θ(H₂)] - Δ_cH^θ(C₂H₆)Step 3. Substitute:Δ_rH^θ = (-1411.0 + -285.8) - (-1559.7)
= -1696.8 + 1559.7 = -137.1 kJ mol^-1The reaction is exothermic.A quick sense check: the answer is much smaller than any of the combustion values. That is expected, because most of the energy released on burning is the same on both routes and cancels out.