Chapter 3, Problem 138AP

One of the reactions that occurs in a blast furnace, where iron ore is converted to cast iron, is

${\text{Fe}}_{\text{2}}{\text{O}}_{\text{3}}\text{ + 3CO }\stackrel{}{\to }{\text{ Fe + 3CO}}_{\text{2}}$

Suppose that $1.64\times {10}^3$ kg of Fe is obtained from a $\text{2}\text{.62 }\times {\text{ 10}}^{\text{3}}$ -kg sample of ${\text{Fe}}_{\text{2}}{\text{O}}_{\text{3}}\text{.}$ Assuming that the reaction goes to completion, what is the percent purity of ${\text{Fe}}_{\text{2}}{\text{O}}_{\text{3}}$ in the original sample?