Question

$F{e}_2{O}_3\left(s\right)$ may be converted to Fe by the reaction, $F{e}_2{O}_3+3H_2\left(g\right)\rightleftharpoons 2Fe\left(s\right)+3H_{2}O\left(g\right)$ ; for which $K_p=8$ at temperature $720C$. What % of $H_2$ remains unreacted after the reaction has come to equilibrium?

• A. $\approx 22$%
• B. $\approx 34$%
• C. $\approx 66$%
• D. $\approx 78$%

Answer 1

The correct option is B $\approx 34$%

$K_p=8=\frac{P_{H_{2}O}^3}{P_{H_2}^3}$
$F{e}_2{O}_3+3H_2\left(g\right)\rightleftharpoons 2Fe\left(s\right)+3H_{2}O\left(g\right)$
$K_p=8=\frac{(3x{)}^3}{(P-3x{)}^3}$
$\frac{3x}{P-3x}=2\Rightarrow 3x=2P-6x$
$x=\frac{2P}{9}$
Remained $H_2=\frac{P-\frac{2P}{9}\times 3}{P}\times 100\simeq 34$%.