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 heat of reaction,  ΔH°rxn, for overall reaction in coal gasification for the production of methane, CH₄ is 12.4 kJ

From the question,

We are to determine the heat of reaction for overall reaction for the production of methane in coal gasification

The equation for the reaction of coal gasification is

2C(coal) + 2H₂O → CO₂ + CH₄  

From the question,

We have the following equations of reactions

(1)        C(coal) + H₂O(g) → CO(g) + H₂(g)               ΔH°rxn = 129.7 kJ

(2)       CO(g) + H₂O(g) → CO₂(g) + H₂(g)               ΔH°rxn = -41 kJ

(3)       CO(g) + 3H₂(g) → CH₄(g) + H₂O(g)              ΔH°rxn = -206 kJ

Multiply (1) by 2 to get

(4)       2C(coal) + 2H₂O(g) → 2CO(g) + 2H₂(g)       ΔH°rxn = 259.4 kJ

Now, adding equations (2), (3), and (4), we get

(2)       CO(g) + H₂O(g) → CO₂(g) + H₂(g)               ΔH°rxn = -41 kJ

(3)       CO(g) + 3H₂(g) → CH₄(g) + H₂O(g)              ΔH°rxn = -206 kJ

(4)       2C(coal) + 2H₂O(g) → 2CO(g) + 2H₂(g)       ΔH°rxn = 259.4 kJ

          2C(coal) + 2H₂O(g) → CH₄(g) + CO₂(g)        ΔH°rxn = 12.4 kJ

Hence, the heat of reaction,  ΔH°rxn, for overall reaction in coal gasification for the production of methane, CH₄ is 12.4 kJ

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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