Hess's Law Example 4

Worked example: a reaction that cannot be measured directlyCalcium carbonate only decomposes when heated strongly, so its enthalpy change cannot be measured with simple calorimetry. Hess's law lets us calculate it from enthalpy changes of formation.CaCO₃(s) → CaO(s) + CO₂(g)Data: Δ_fH^θ[CaCO₃(s)] = -1206.9, Δ_fH^θ[CaO(s)] = -635.1, Δ_fH^θ[CO₂(g)] = -393.5 kJ mol^-1Step 1. Put the elements Ca(s), C(s) and 1½O₂(g) at the bottom. Draw one arrow up to CaCO₃ and another up to CaO + CO₂.Step 2. The direct route (reactant to products) must equal the indirect route: go down against the CaCO₃ arrow (so change its sign), then up to the products.Δ_rH^θ = -Δ_fH^θ[CaCO₃] + Δ_fH^θ[CaO] + Δ_fH^θ[CO₂]Step 3. Substitute:Δ_rH^θ = +1206.9 + (-635.1) + (-393.5) = +178.3 kJ mol^-1The positive sign shows that the decomposition is endothermic. This is why limestone must be heated continuously in a lime kiln to keep it decomposing.Rule to remember: when you travel along an arrow in the opposite direction to the way it points, reverse the sign of its enthalpy change.