Consider the steps in coal gasification: C (coal) + H2O (g) → CO (g) + H2 (g) ΔH°rxn = 129.7 kJ CO (g) + H2O (g) → CO2 (g) + H2 (g) ΔH°rxn = - 41 kJ CO (g) + 3H2 (g) → CH4 (g) + H2O (g) ΔH°rxn = - 206 kJ Calculate the heat of reaction, ΔH°rxn, for overall reaction for the production of methane, CH4.

The answer to your question is ΔHrxn = 0 kJ

Explanation:

Process

1. - Multiply Equation 1 by 2

2C (coal) + 2H₂O ⇒ 2CO (g) + 2H₂ ΔH rxn = 259.4 kJ

2. - Sum equation 2

CO (g) + H₂O ⇒ CO₂ (g) + H₂ (g) ΔHrxn = - 41 kJ

Result

2C + 3H₂O + CO ⇒ 2CO + 3H₂ + CO₂ ΔHrxn = 218.4 kJ

Simplification

2C + 3H₂O ⇒ CO + 3H₂ + CO₂

3. - Sum equation 3

CO (g) + 3H₂ (g) ⇒ CH₄ (g) + H₂O (g) ΔHrxn = - 218.4 kJ

Result

2C + 3H₂O + 3H₂ + CO ⇒ CO + 3H₂ + CO₂ + CH₄ + H₂O

Simplification

2C + 2H₂O ⇒ CO₂ + CH₄ ΔHrxn = 0 kJ