Question

Calculate the energy required to decompose 57.0 kg of Fe₃O₄ according to the following reaction? The molar mass of Fe₃O₄ is 231.55 g/mol.

Fe₃O₄(s) → 3 Fe(s) + 2 O₂(g) ΔΗ°rχη = +1118 kJ
a. 8.26 × 10⁵ kJ
b. 1.09 × 10⁴ kJ
c. 5.50 × 10⁵ kJ
d. 1.38 × 10⁵ kJ
e. 2.75 × 10⁵ kJ

Answer 1

The energy required to decompose 57.0 kg of Fe₃O₄ is approximately 2.75 × 10⁵ kJ. The correct answer is e. 2.75 × 10⁵ kJ.

Step-by-step explanation:

To calculate the energy required to decompose Fe₃O₄, we use the equation:

Fe₃O₄(s) → 3 Fe(s) + 2 O₂(g)

The molar mass of Fe₃O₄ is 231.55 g/mol.

The energy change, ΔH°rxn, for the reaction is +1118 kJ.

We can calculate the energy required to decompose 57.0 kg of Fe₃O₄ by converting the mass to moles:

57.0 kg x (1000 g/kg) ÷ (231.55 g/mol) = 246.20 mol

Then, we can use the molar ratio from the balanced chemical equation to determine the energy required:

246.20 mol Fe₃O₄ x (1118 kJ) ÷ (1 mol Fe₃O₄) = 275,045.60 kJ

Therefore, the energy required to decompose 57.0 kg of Fe₃O₄ is approximately 2.75 × 10⁵ kJ.