Equilibrium Question 546
Question: Equilibrium constants $ K_1 $ and $ K_2 $ for the following equilibria $ NO(g)+\frac{1}{2}O_2 $ $ \overset{K_1}{\leftrightharpoons} $ $ NO_2(g) $ and $ 2NO_2(g) $ $ \overset{K_2}{\leftrightharpoons} $ $ 2NO(g)+O_2(g) $ are related as [CBSE PMT 2005]
Options:
A) $ K_2=\frac{1}{K_1} $
B) $ K_2=K_1^{2} $
C) $ K_2=\frac{K_1}{2} $
D) $ K_2=\frac{1}{K_1^{2}} $
Show Answer
Answer:
Correct Answer: D
Solution:
$ K_1=\frac{[NO_2]}{[NO]{{[O_2]}^{1/2}}} $ ; $ K_2=\frac{{{[NO]}^{2}}[O_2]}{{{[NO_2]}^{2}}} $
$ \Rightarrow $ $\frac{{{[NO_2]}^{2}}}{{{[NO]}^{2}}[O_2]}=\frac{1}{K_2} $
$ \Rightarrow $ $\frac{[NO_2]}{[NO]\ {{[O_2]}^{1/2}}}=\frac{1}{\sqrt{K_2}} $
$ \Rightarrow $ $K_1=\frac{1}{\sqrt{K_2}} $ ; $ K_2=\frac{1}{K_1^{2}} $ .
