Q. The equilibrium constant for the reaction, $N_{2}(g) + O_{2}(g) \rightleftharpoons 2NO(g)$ At temperature $T\ is\ 4 \times 10^{- 4}$. The value of $K_{c}$ for the reaction $NO(g) \rightleftharpoons \frac{1}{2}N_{2}(g) + \frac{1}{2}O_{2}(g)$ at the same temperature is
A) $2.5 \times 10^{2}$
B) 50
C) $4 \times 10^{- 4}$
D) 0.02
Explanation
(b)
$N_{2}(g) + O_{2}(g) \rightleftharpoons 2NO(g)$
$K_{c} = \frac{\lbrack NO\rbrack^{2}}{\left\lbrack N_{2} \right\rbrack\left\lbrack O_{2} \right\rbrack} = 4 \times 10^{- 4}$
$NO \rightleftharpoons \frac{1}{2}N_{2}(g) + \frac{1}{2}O_{2}(g)$
$K_{c}^{'} = \frac{\left\lbrack N_{2} \right\rbrack^{\frac{1}{2}}\left\lbrack O_{2} \right\rbrack^{\frac{1}{2}}}{\lbrack NO\rbrack}$
$= \sqrt{\frac{1}{K_{c}}} = \sqrt{\frac{1}{4 \times 10^{- 4}}} = 50$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.