Q2(c). Heat of reaction for N₂ + 3H₂ → 2NH₃ at 50°C: Kirchhoff's law
The heat of reaction N₂ + 3H₂ → 2NH₃ at 27°C was found to be -21.97 Kcal. What will be the heat of reaction at 50°C? The molar heat capacities at constant pressure and at 27°C for N₂, H₂ and NH₃ are 6.8, 6.77 and 8.86 cal mol⁻¹ deg⁻¹.
Answer in brief
Δ H₃₂₃=-22.19 kcal (-92.83 kJ)
Key points
- Kirchhoff's law. ((∂Δ H)/(∂ T))_P=Δ Cₚ; with Δ Cₚ constant over 23 K: Δ H_(T₂)=Δ H_(T₁)+Δ Cₚ (T₂-T₁)
- Δ Cₚ=Σ Cₚ(products)-Σ Cₚ(reactants)=2(8.86)-[6.8+3(6.77)]
- Δ Cₚ=17.72-27.11=-9.39 cal K⁻¹
- Δ H₃₂₃=-21 970+(-9.39)(323-300)=-21 970-216 cal
The full model answer
Written out in full, as it should go in the answer booklet. The solution page with its diagrams follows it.
Given: Δ H₃₀₀=-21.97 kcal =-21 970 cal; T₁=27°C=300 K, T₂=50°C=323 K; Cₚ (cal K⁻¹ mol⁻¹): N₂ 6.8, H₂ 6.77, NH₃ 8.86.
- Kirchhoff's law. ((∂Δ H)/(∂ T))_P=Δ Cₚ; with Δ Cₚ constant over 23 K: Δ H_(T₂)=Δ H_(T₁)+Δ Cₚ (T₂-T₁)
- Δ Cₚ=Σ Cₚ(products)-Σ Cₚ(reactants)=2(8.86)-[6.8+3(6.77)]
- Δ Cₚ=17.72-27.11=-9.39 cal K⁻¹
- Δ H₃₂₃=-21 970+(-9.39)(323-300)=-21 970-216 cal
- Δ H₃₂₃=-22 186 cal≈-22.19 kcal (-92.83 kJ)
Reading: Δ Cₚ<0, so the reaction becomes slightly more exothermic as T rises (0.22 kcal over 23 K).
Application. in the Haber process (near 450°C) Kirchhoff's law carries the tabulated Δ H at 298 K to the working temperature.
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All parts of Question 2
- 2(a)(i) MO diagram of NO; NO⁺, CN⁻ and CO; bond order of NO and NO⁺15 marks
- 2(a)(ii) Theory of absolute reaction rates; how a catalyst works10 marks
- 2(b) Integrated Clausius–Clapeyron equation from the Clapeyron equation15 marks
- 2(c) Heat of reaction for N₂ + 3H₂ → 2NH₃ at 50°C: Kirchhoff's law10 marks