MCQ
The equilibrium constant for the reaction ${N_{2(g)}} + {O_{2(g)}}$ $\rightleftharpoons$ $2N{O_{(g)}}$ at temperature $T$ is $4 \times {10^{ - 4}}$. The value of ${K_c}$ for the reaction $N{O_{(g)}}$ $\rightleftharpoons$ $\frac{1}{2}{N_{2(g)}} + \frac{1}{2}{O_{2(g)}}$ at the same temperature is
  • A
    $4 \times {10^{ - 4}}$
  • $50$
  • C
    $2.5 \times {10^2}$
  • D
    $0.02$

Answer

Correct option: B.
$50$
b
${N_2}_{(g)} + {O_2}_{(g)}$ $ \rightleftharpoons $ $2NO_{(g)}$

$Kc = \frac{{{{[NO]}^2}}}{{[{N_2}][{O_2}]}} = 4 \times {10^{ - 4}}$

$N{O_2}$ $ \rightleftharpoons $ $\frac{1}{2}{N_2}_{(g)} + \frac{1}{2}{O_2}_{(g)}$

${K'_c} = \frac{{{{[{N_2}]}^{1/2}}{{[{O_2}]}^{1/2}}}}{{[NO]}} = \frac{1}{{\sqrt {Kc} }} = \frac{1}{{\sqrt {4 \times {{10}^{ - 4}}} }}$

$ = \frac{1}{{2 \times {{10}^{ - 2}}}} = \frac{{100}}{2} = 50$

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