MCQ
Consider the reaction

${N_2}(g)\, + 3{H_2}(g)\, \rightleftharpoons \,2N{H_3}(g)$ 

The equilibrium constant of the above reaction is $K_3$. If pure ammonia is left to dissociate, the partial pressure of ammonia at equilibrium is given by (Assume that $P_{NH_3}<\,< P_{total}$ at equilibrium)

  • $\frac{{{3^{3/2}}K_p^{1/2}{P^2}}}{{16}}$
  • B
    $\frac{{K_p^{1/2}{P^2}}}{16}$
  • C
    $\frac{{K_p^{1/2}{P^2}}}{4}$
  • D
    $\frac{{{3^{3/2}}K_p^{1/2}{P^2}}}{4}$

Answer

Correct option: A.
$\frac{{{3^{3/2}}K_p^{1/2}{P^2}}}{{16}}$
a
$\mathop {{N_2}}\limits_x  + \mathop {3{H_2}}\limits_{3x}  \leftrightarrow \mathop {2N{H_3}}\limits_{{P_1}} $

${P_T} = 4x\,{K_P} = \frac{{P_1^2}}{{x \times 27 \times 3}}$

$x = \left( {\frac{P}{4}} \right)$

${P_1} = \sqrt {27{X^4}{K_P}} $

$\sqrt {27} \,{({K_P})^{1/2}}{\left( {\frac{{{P_T}}}{4}} \right)^2} = \frac{{{3^{3/2}}K_P^{1/2}{P^2}}}{{16}}$

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