The combination of coke and steam produces a mixture called coal gas, which can be used as a fuel or as a starting material for other reactions. If we assume coke can be represented by graphite, the equation for the production of coal gas is:

2C(s)+2H2O(g)--->CH4(g)+CO2(g)
Determine the standard enthalpy change for this reactionf rom the following standard enthalpies of reactions:

C(s)+H2O(g)--->CO(g)+H2(g) ΔH=131.3 kJ
CO(g)+H2O(g)--->CO2(g)+H2(g) ΔH=-41.2 kJ
CH4(g)+H2O(g)--->3H2(g)+CO(g) ΔH=206.1 kJ

ΔH = 15.3kJ

Explanation:

It is possible to obtain standard enthalpy change of a reaction from the sum of half-reactions (Hess's law). Thus:

(1) C(s) + H₂O(g) ⇄ CO(g) + H₂(g) ΔH = 131.3kJ

(2) CO(g) + H₂O(g) ⇄ CO₂(g) + H₂(g) ΔH = -41.2kJ

(3) CH₄(g) + H₂O(g) ⇄ 3H₂(g) + CO(g) ΔH = 206.1kJ

The sum of 2×(1) + (2) gives:

2C(s) + 3H₂O(g) ⇄ CO₂(g) + 3H₂(g) + CO(g) ΔH = 131.3kJ×2 + -41.2kJ  = 221.4kJ

Now, the sum of this reaction with -(3) gives:

2C(s) + 2H₂O(g) ⇄ CH₄(g) + CO₂(g) ΔH = 221.4kJ - 206.1kJ = 15.3kJ

I hope it helps!

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