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Question 4.20: Heat of Reaction The combustion of 1 mol of methane gas, CH4...

Heat of Reaction

The combustion of 1 mol of methane gas, CH4\text{CH}_{4}, to carbon dioxide and water is an exothermic reaction that liberates 191.7 kcal.

CH4(g)+O2(g)⟶CO2(g)+2H2O(g)+191.7 kcal\text{CH}_{4}\text{(g)} + \text{O}_{2}\text{(g)} \longrightarrow \text{CO}_{2}\text{(g)} + 2\text{H}_{2}\text{O(g)} + 191.7\ \text{kcal}

How much heat is liberated when 4.52 g of CH4\text{CH}_{4} undergoes combustion?

Strategy
According to the balanced chemical equation, we know that 1 mol CH4\text{CH}_{4} = 191.7 kcal. Therefore, we convert the grams of CH4\text{CH}_{4} to moles and then apply the heat conversion factor.

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4.52 g CH4×1 mol CH416 g CH4×191.7 kcal1 mol CH4=54.2 kcal4.52\ \text{g CH}_{4}\times \frac{1\ \text{mol CH}_{4}}{16\ \text{g CH}_{4}} \times \frac{191.7\ \text{kcal}}{1\ \text{mol CH}_{4}} = 54.2\ \text{kcal}

Therefore, we conclude that when 4.52 g of CH4\text{CH}_{4} undergoes combustion, 54.2 kcal of heat is liberated.

■ Quick Check 4.20
Solid iron and oxygen gas react to form solid iron(III) oxide, liberating 406.3 kcal of heat according to the following balanced chemical equation. 4Fe(s)+3O2(g)⟶2Fe2O3(s)+406.3 kcal4\text{Fe(s)} + 3\text{O}_{2}\text{(g)} \longrightarrow 2\text{Fe}_{2}\text{O}_{3}\text{(s)} + 406.3\ \text{kcal}. How many kcal of heat are liberated when 2.50 g of Fe reacts?

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