question_answer

If the equilibrium constant for \[{{N}_{2}}(g)+{{O}_{2}}(g)\rightleftharpoons 2NO(g)\] is K, the equilibrium constant for                                                                                                                                                     [NEET 2015 (Re)] \[\frac{1}{2}{{N}_{2}}(g)+\frac{1}{2}{{O}_{2}}(g)NO(g)\] will the

A)  \[{{K}^{1/2}}\]            

B)                   \[\frac{1}{2}K\]

C)  K                                

D)  \[{{K}_{2}}\]

Correct Answer: B

Solution :

Plan As we can see the reaction for which we have to find out equilibrium constant is different only in stoichiometric coefficient as compared to the given reaction. Hence, we can find equilibrium constant for the required reaction with the help of mentioned equilibrium constant in the problem.

Given, equilibrium constant for the reaction,

is K i.e.

(i)

Let equilibrium constant for the reaction,

is i.e.

On squaring both sides

(ii)

On comparing Eqs. (i) and (ii), we get

or