Given that
(i) CH4 (g) + 2O2 (g) → CO2 (g) + CH2O(g);∆CHΘ = −890.3 kJ mol−1
(ii) C(s) + O2 (g) → CO2 (g);∆CHΘ = −393.5 kJ mol−1
(iii) H2 (g) + \(\frac{1}{2}\)O2 (g) → H2O(g); ∆CHΘ = −285.8 kJ mol−1
We have to calculate ∆fHΘ of the equation:
C(s) + 2H2 (g) → CH4 (g); ∆fHΘ = ?
Appling inspection method,
−eq. (i) + eq. (ii) + 2 × eq. (iii)
−CH4(g) − 2O2(g) + C(s) + O2(g) + 2H2(g) + O2 (g) → −CO2 (g) − 2H2O(g) + CO2(g)
Or C(s) + 2H2(g)
\(\therefore\) ∆fHΘ = −(−890.3) + (−393.5) + 2 × (−285.8)
= 890.3 − 393.5 − 571.6
= 890.3 − 965.1
= −75.8 kJ mol−1