The reaction of 55.8 g sample of iron (Fe) metal with 1.00 mol of oxygen gas is described by the following reaction equation: 4Fe(s) + 3O2(g) → 2Fe2O3(s) Calculate the energy that is released through this reaction based on the quantities of reactants combined. The standard enthalpy of formation, ΔfHϴ, of Fe2O3 is −826 kJ mol–1. (A) 206 kJ (B) 413 kJ (C) 826 kJ (D) 1650 kJ (E) 1101 kJ
Question
The reaction of 55.8 g sample of iron (Fe) metal with 1.00 mol of oxygen gas is described by the following reaction equation: 4Fe(s) + 3O2(g) → 2Fe2O3(s) Calculate the energy that is released through this reaction based on the quantities of reactants combined. The standard enthalpy of formation, ΔfHϴ, of Fe2O3 is −826 kJ mol–1. (A) 206 kJ (B) 413 kJ (C) 826 kJ (D) 1650 kJ (E) 1101 kJ
Solution
To solve this problem, we need to follow these steps:
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First, we need to determine the number of moles of iron (Fe) in the 55.8 g sample. The molar mass of iron is approximately 55.8 g/mol. Therefore, the number of moles of iron in the sample is 55.8 g / 55.8 g/mol = 1 mol.
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The balanced chemical equation tells us that 4 moles of iron react with 3 moles of oxygen to form 2 moles of Fe2O3. Therefore, the 1 mol of iron in our sample can react with 0.75 mol of oxygen to form 0.5 mol of Fe2O3.
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The standard enthalpy of formation of Fe2O3 is -826 kJ/mol. This is the amount of energy released when 1 mol of Fe2O3 is formed. Therefore, the amount of energy released when 0.5 mol of Fe2O3 is formed is -826 kJ/mol * 0.5 mol = -413 kJ.
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The negative sign indicates that energy is released in the reaction. Therefore, the energy released in the reaction is 413 kJ.
So, the correct answer is (B) 413 kJ.
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