Question

A vessel at $1000K$ contains carbon dioxide with a pressure of $0.5atm$. Some of the carbon dioxide is converted to carbon monoxide on addition of graphite. Calculate the value of $K_p$ if total pressure at equilibrium is $0.8atm$.

Answer 1

${CO}_2\left(g\right)+C\left(s\right)\rightleftharpoons 2CO\left(g\right)$
Initial pressure $0.5atm$ $0atm$
Equilibrium pressure, $(0.5-x)atm$ $2xatm$
At equilibrium, the total pressure is $0.8atm$
$p_{total}=p_{{CO}_2}+p_{CO}$
$0.8=(0.5-x)+2x=0.5+x$
or $x=0.3atm$
Applying law of mass action,
$K_p=\frac{{\left(p_{CO}\right)}^2}{p_{{CO}_2}}=\frac{{(2\times x)}^2}{0.5-x}=\frac{{(2\times 0.3)}^2}{0.5-0.3}=1.8atm$