question_answer

The following equilibria are given:                                                 [AIPMT 2003]

\[\begin{matrix}    {{N}_{2}}+3{{H}_{2}}2N{{H}_{3}} & {{K}_{1}}  \\ \end{matrix}\]

\[\begin{matrix}    {{N}_{2}}+{{O}_{2}}2NO & {{K}_{2}}  \\ \end{matrix}\]

\[\begin{matrix}    {{H}_{2}}+\frac{1}{2}{{O}_{2}}{{H}_{2}}O & {{K}_{3}}  \\ \end{matrix}\]

The equilibrium constant of the reaction \[2N{{H}_{3}}+\frac{5}{2}{{O}_{2}}\rightleftharpoons 2NO+3{{H}_{2}}O\] in terms of \[{{K}_{1}},\text{ }{{K}_{2}}\] and \[{{K}_{3}}\] is:

A)  \[\frac{{{K}_{1}}K_{3}^{2}}{{{K}_{2}}}\]

B)                   \[\frac{{{K}_{2}}\,K_{3}^{3}}{{{K}_{1}}}\]

C)  \[{{K}_{1}}\,{{K}_{2}}\,{{K}_{3}}\]              

D)  \[\frac{{{K}_{1}}\,{{K}_{2}}}{{{K}_{3}}}\]

Correct Answer: B

Solution :

For equilibrium

(i)

(ii)

(iii)

For reaction,

(iv)

From equations number (i), (ii) and (ii)