Question

Calculate enthalpy of formation of methane (CH₄) from the following data : 

(i) C (s) + O₂ (g)→ CO₂ (g), Δ_rH° = – 393.5 kJ mol^–1

(ii) H₂ (g) +1/2 O₂ (g) →H₂O(l),Δ_rH° = – 285.8 kJ mol^–1 

(iii) CH₄ (g) + 2O₂ (g) → CO₂ (g) + 2 H₂O (l),Δ_rH° = –890.3 kJ mol^–1 

Answer 1

We aim at : C (s) + 2 H₂ (g)→ CH₄ (g) ; ΔH° = ?

Multiplying eqn. (ii) with 2, adding to eqn. (i) and then subtracting eqn. (iii) from the sum, i.e., operating eqn. (i) + 2 × eqn. (ii) – eqn. (iii), we get

C (s) + 2H₂ (g) – CH₄ (g) → 0; Δ_rH° = – 393.5 + 2 (–285.8) – (–890.3) – 74.8 kJ mol^–1

or C (s) + 2H₂ (g) CH₄ (g); Δ_rH° = – 74.8 kJ mol^–1

Hence, enthalpy of formation of methane is : 

Δ_rH°= – 74.8 kJ mol–1