Question

One of the reactions that occurs in a blast furnace, where iron ore is converted to cast iron is as follows:
$F{e}_2{O}_3+3CO⟶2Fe+3C{O}_2$
Suppose that $1.64\times {10}^3$ kg of Fe are obtained from $2.62\times {10}^3$ kg sample $F{e}_2{O}_3$. Assuming that the reaction goes to completion, what is the percent purity of $F{e}_2{O}_3$ in the original sample (rounded to the nearest integer)?

Answer 1

$1$ mole of $F{e}_2{O}_3$ gives $2$ moles of $Fe$.
Hence, $159.69$ kg of $F{e}_2{O}_3$ will give $2\times 55.854$ kg of $Fe$.
Hence, theoretical yield $=2.62\times {10}^3\times \frac{2\times 55.85}{159.69}=1.833\times {10}^3$.
Percentage yield $=\frac{1.64\times {10}^3}{1.833\times 1063}\times 100=89$.
Hence, the percentage purity of $F{e}_2{O}_3$ is $89\%$.