Hess's Law Example 8

Worked example: combining equationsSometimes you are given whole equations with their enthalpy changes instead of a table of data. Hess's law means you can add and subtract equations like algebra, as long as you do the same to their ΔH values.Find Δ_fH^θ of carbon monoxide:C(s) + ½O₂(g) → CO(g)This cannot be measured directly, because burning carbon in a limited supply of oxygen gives a mixture of CO and CO₂.Given:
(1) C(s) + O₂(g) → CO₂(g) ΔH = -393.5 kJ mol^-1
(2) CO(g) + ½O₂(g) → CO₂(g) ΔH = -283.0 kJ mol^-1Step 1. The target has C(s) on the left, so keep equation (1) as it is.Step 2. The target has CO(g) on the right, so reverse equation (2) and change the sign of its ΔH:
CO₂(g) → CO(g) + ½O₂(g) ΔH = +283.0 kJ mol^-1Step 3. Add them. CO₂ cancels, and O₂ on the left minus ½O₂ on the right leaves ½O₂:C(s) + ½O₂(g) → CO(g)
ΔH = -393.5 + 283.0 = -110.5 kJ mol^-1Rules: reversing an equation changes the sign of ΔH; multiplying an equation by a number multiplies ΔH by the same number. Always check that the combined equations cancel down to exactly the target equation.