Equilibrium Question 656
Question: The equilibrium constant for the reaction $ {N_{2(g)}}+{O_{2(g)}} $ ⇌ $ 2N{O_{(g)}} $ at temperature T is $ 4\times {10^{-4}} $ . The value of $ K_{c} $ for the reaction $ N{O_{(g)}} $ ⇌ $ \frac{1}{2}{N_{2(g)}}+\frac{1}{2}{O_{2(g)}} $ at the same temperature is [AIEEE 2004]
Options:
A) $ 4\times {10^{-4}} $
B) $ 50 $
C) $ 2.5\times 10^{2} $
D) 0.02
Show Answer
Answer:
Correct Answer: B
Solution:
$ N_2(g)+O_2(g) $ ⇌ $ 2NO(g) $
$ Kc=\frac{{{[NO]}^{2}}}{[N_2][O_2]}=4\times {10^{-4}} $
$ NO_2 $ ⇌ $ \frac{1}{2}N_2(g)+\frac{1}{2}O_2(g) $
$ {{{K}’}_{c}}=\frac{{{[N_2]}^{1/2}}{{[O_2]}^{1/2}}}{[NO]}=\frac{1}{\sqrt{Kc}}=\frac{1}{\sqrt{4\times {10^{-4}}}} $
$ =\frac{1}{2\times {10^{-2}}}=\frac{100}{2}=50 $
