Question

For the reaction, $2{NO}_2\left(g\right)\rightleftharpoons 2NO\left(g\right)+O_2\left(g\right)$,
$K_c=1.8\times {10}^{-6}$ at ${185}^{o}C$. The value of $K_c$ at ${185}^{o}C$ for the reaction:
$NO\left(g\right)+\frac{1}{2}{O}_2\left(g\right)\rightleftharpoons {NO}_2\left(g\right)$ is:

• A. $0.9\times {10}^6$
• B. $7.5\times {10}^2$
• C. $1.95\times {10}^{-3}$
• D. $1.95\times {10}^3$

Answer 1

Answer: (B)

$7.5\times {10}^2$

The equilibrium constant for the reaction
$2{NO}_2\left(g\right)\rightleftharpoons N_2\left(g\right)+2O_2\left(g\right)$

$K_c=\frac{\left[N_2\right][O_2{]}^2}{[N{O}_2{]}^2}=1.8\times {10}^{-6}$
The equilibrium constant for the reaction

$\frac{1}{2}{N}_2\left(g\right)+O_2\left(g\right)\rightleftharpoons {NO}_2\left(g\right)$

$K_2=\frac{\left[N{O}_2\right]}{\sqrt{\left[N_2\right]}\left[O_2\right]}=\frac{1}{\sqrt{K_c}}=\frac{1}{\sqrt{1.8\times {10}^{-6}}}=7.5\times {10}^2$