Question

Mining companies use this reaction to obtain iron from iron ore:

Fe2O3(s)+3 CO(g)--->2 Fe(s)+3 CO2(g)
The reaction of 167 g Fe2O3 with 81.1 gCO produces 75.5 gFe.
Determine the theoretical yield.

Answer 1

The theoretical yield of Fe can be determined by calculating the moles of Fe produced from the given masses of Fe2O3 and CO, using the stoichiometry of the balanced equation. In this case, the theoretical yield of Fe is 29.2 g.

Step-by-step explanation:

The theoretical yield can be determined by calculating the moles of Fe produced from the given masses of Fe2O3 and CO, using the stoichiometry of the balanced equation as a conversion factor. First, we convert the given masses to moles using the molar masses of Fe2O3 and CO. Then, we compare the ratios of moles of Fe and moles of Fe2O3 to find the theoretical yield of Fe.

In this case, we have 167 g of Fe2O3 and 81.1 g of CO. The molar masses of Fe2O3 and CO are 159.69 g/mol and 28.01 g/mol, respectively. Converting the masses to moles, we have:

Fe2O3:

167 g × (1 mol/159.69 g) = 1.046 mol

CO:

81.1 g × (1 mol/28.01 g) = 2.895 mol

According to the balanced equation, the stoichiometric ratio of Fe to Fe2O3 is 2:1. Therefore, the moles of Fe produced is half the moles of Fe2O3:

Fe:

1.046 mol/2 = 0.523 mol

To find the mass of Fe produced, we multiply the moles of Fe by its molar mass:

Fe:

0.523 mol × 55.85 g/mol = 29.2 g

Therefore, the theoretical yield of Fe from the given masses of Fe2O3 and CO is 29.2 g.