Chemical equilibrium

Exercise 9

    

A mixture of $NO_2(g)$ and $N_2O_4(g)$ is introduced at a given temperature into a container. Equilibrium is established at a total pressure of $1$ atm: $N_2O_4(g)$ $2NO_2(g)$ At equilibrium, the two gases have equal partial pressures. Calculate the value of the equilibrium constant $K_p$.

$K_p=\frac{p_{N_2O_4}}{p_{NO_2}^2}$ Let $x$ be the partial pressure of $NO_2$ and $N_2O_4$. It follows that: $p_{N_2O_4}$ $+$ $p_{NO_2}$ $=P_{total}$ $x$ $+$ $x$ $=$ $1$ $x$ $=$ $\frac{1}{2}$ $K_p$ $=$ $\frac{\frac{1}{2}}{(\frac{1}{2})^2}$ $=$ $2\; atm$