MCQ
The following equilibria are given :
$N_2 + 3H_2  \rightleftharpoons  2NH_3 ; K_1$
$N_2 + O_2  \rightleftharpoons  2NO ; K_2$
$H_2 + \frac{1}{2}O_2  \rightleftharpoons  H_2O; K_3$

The equilibrium constant of the reaction $2N{H_3} + \frac{5}{2}{O_2} \rightleftharpoons 2NO + 3{H_2}O$ in terms of $K_1, K_2$ and $K_3$ is

  • A
    $\frac{{{K_1}{K_2}}}{{{K_3}}}$
  • B
    $\frac{{{K_1}K_3^2}}{{{K_2}}}$
  • $\frac{{{K_2}K_3^3}}{{{K_1}}}$
  • D
    $K_1K_2K_3$

Answer

Correct option: C.
$\frac{{{K_2}K_3^3}}{{{K_1}}}$
c
$(I)\,{N_2} + 3{H_2} \leftrightarrow 2N{H_3};$

               ${K_1} = \frac{{{{[N{H_3}]}^2}}}{{[{N_2}]{{[{H_2}]}^3}}}$

$(II)\,{N_2} + {O_2} \leftrightarrow 2NO;$

               ${K_2} = \frac{{{{[NO]}^2}}}{{[{N_2}][{O_2}]}}$

$(III)\,{H_2} + \frac{1}{2}{O_2} \leftrightarrow {H_2}O;$

               ${K_3} = \frac{{[{H_2}O]}}{{[{H_2}]{{[{O_2}]}^{1/2}}}}$

$(IV)\,2N{H_3} + \frac{5}{2}{O_2} \leftrightarrow 2NO + 3{H_2}O$

               ${K_c} = \frac{{{{[NO]}^2}{{[{H_2}O]}^3}}}{{{{[N{H_3}]}^2}{{[{O_2}]}^{5/2}}}} = \frac{{{K_2}K_3^3}}{{{K_1}}}$

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