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Given C(graphite) + O2(g) → CO2(g) ; ΔrH° = −393.5 kJ mol−1 H2(g) + 1/2 O2(g) → H2O(l) ; ΔrH° = −285.8 kJ mol−1 CO2(g) + 2H2O(l) → CH4(g) + 2O2(g) ; ΔrH° = +890.3 kJ mol−1 Based on the above thermochemical equations, the value of ΔfH° at 298 K for the reaction C(graphite) + 2H2(g) → CH4(g) will be :

1. +74.8 kJ mol−1
2. +144.0 kJ mol−1
3. −74.8 kJ mol−1
4. −144.0 kJ mol−1

Correct answer: +74.8 kJ mol−1

Solution

The enthalpy change for the formation of methane from graphite and hydrogen can be calculated using Hess's law by combining the given reactions. By rearranging and adding the enthalpy changes of the relevant reactions, we find that the overall reaction results in a positive enthalpy change of +74.8 kJ mol−1.

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