Question

The density of an equilibrium mixture of $N_2{O}_4$ and $N{O}_2$ at 1 atm and 346 K is 1.8 g/L. Calculate $K_C$ for the reaction:

$N_2{O}_4\left(g\right)\rightleftharpoons 2N{O}_2\left(g\right)$

• A. $12.8$
• B. $24$
• C. $0.36$
• D. $7.2$

Answer 1

The correct option is D $7.2$

The average molar mass of the gaseous mixture is $M=\frac{\rho RT}{P}$
$M=\frac{1.8\times 0.0821\times 346}{1}$
$M=51.13$
Let x be the mole fraction of $N_2{O}_4$
The mole fraction of $N{O}_2$ is $1-x$
Th average molar mass of the mixture is $\frac{92x+46(1-x)}{1}=51.13$
$46x=5.13$
$x=0.11$
$K_C=\frac{[N{O}_2{]}^2}{\left[N_2{O}_4\right]}=\frac{(0.89{)}^2}{0.11}=7.2$