Chapter 14, Problem 93RQ

To study the following reaction at $\text{20 °C}$,

$\text{NO}\left(g\right){\text{+ NO}}_{\text{2}}\left(g\right){\text{ + H}}_{\text{2}}\text{O}\left(g\right)\stackrel{}{\rightleftharpoons }{\text{2HNO}}_{\text{2}}\left(g\right)$

a mixture of $\text{NO}\left(g\right){\text{, NO}}_{\text{2}}\left(g\right){\text{, and H}}_{\text{2}}\text{O}\left(g\right)$ was prepared in a 10.0 L glass bulb. For ${\text{NO, NO}}_{\text{2}}{\text{, and HNO}}_{\text{2}}$, the initial concentrations were as follows: $\left[\text{NO}\right]\text{ = }\left[{\text{NO}}_{\text{2}}\right]\text{ = 2}{\text{.59 × 10}}^{\text{-3}}M\text{ and }\left[{\text{HNO}}_{\text{2}}\right]\text{ = 0 }M$. The initial partial pressure of ${\text{H}}_{\text{2}}\text{O}\left(g\right)$ was 17.5 torr. When equilibrium was reached, the ${\text{HNO}}_{\text{2}}$ concentration was $4.0\times {10}^{-4}M$. Calculate the equilibrium constant, $K_c$ for this reaction.