Question

The equilibrium constant $\left(K_c\right)$ for the reaction, $N_2\left(g\right)+O_2\left(g\right)\rightleftharpoons 2NO\left(g\right)$ at room temperature $T$ is $4\times {10}^{-4}$. The value of $K_c$ for $NO\left(g\right)\rightleftharpoons \frac{1}{2}{N}_2\left(g\right)+\frac{1}{2}{O}_2\left(g\right)$ at the same $T$ is:

• A. $0.02$
• B. $50$
• C. $4\times {10}^{-4}$
• D. $2.5\times {10}^{-2}$

Answer 1

The correct option is B $50$

$N_2\left(g\right)+O_2\left(g\right)\to 2NO\left(g\right)$

$K_c=\frac{[NO{]}^2}{\left[N_2\right]\left[O_2\right]}$

Therefore,

$2NO\left(g\right)\to N_2\left(g\right)+O_2\left(g\right)$

$K{c}^{\prime }=\frac{1}{K_c}$

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

$K_c^{\prime \prime }=\frac{\left[N_2{]}^{\frac{1}{2}}\right[O_2]}{\left[N{O}_2\right]}$

$\sqrt{K_c^{\prime }}=\frac{\sqrt{{10}^4}}{4}$

$=\frac{100}{2}$

$50$