A commercial hand warmer contains 100 grams of iron and warms according to the thermochemistry equation below. If the oxygen is in excess, how much heat (q) will the hand warmer produce when all of the iron is oxidized (molar mass Fe = 55.8g/mol

Answer: - 736.738 KJ/mol.

Explanation:

The thermochemistrty that represents the reaction of iron with oxygen to produce rust and gives heat is:

4Fe + 3O₂ → 2Fe₂O₃, ΔH°f = - 822.2 KJ/mol.

The stichiometry of this reaction shows that 4 moles of Fe reacts with 3 moles of oxygen to give 2 moles of Fe₂O₃. Also, the formation of 1.0 mole of Fe₂O₃ gives - 822.2 KJ/mol. Now, we need to know the number of moles of iron that will be in the reaction. n = mass / molar mass = 100.0 g / 55.8 g/mol = 1.79 mol. From the stichiometry of the reaction:

4.0 moles of Fe → 2.0 moles of Fe₂O₃

1.79 moles of Fe →? moles of Fe₂O₃

Using cross multiplication:

The number of moles of Fe₂O₃ will produced from the reaction = (1.79 x 2.0) / (4.0) = 0.896 mole.

The production of 1.0 mole of Fe₂O₃ → - 822.2 KJ/mol

The production of 0.896 mole of Fe₂O₃ →? KJ/mol

The 100 g Fe will give = (-822.2 x 0.896) / (1.0) = - 736.738 KJ/mol.