MCQ
For a reaction; $A + B \rightleftharpoons C + D$ , the initial concentration of $A$ and $B$ are equal but the equilibrium concentration of $C$ is twice that of equilibrium concentration of $A$. The $K_c$ is
  • $4$
  • B
    $9$
  • C
    $0.25$
  • D
    $1/9$

Answer

Correct option: A.
$4$
a
$\mathop {\mathop A\limits_a }\limits_{(a - x)}  + \mathop {\mathop B\limits_a }\limits_{(a - x)}  \rightleftharpoons \mathop {\mathop C\limits_0 }\limits_x  + \mathop {\mathop D\limits_0 }\limits_x $

$x=2(a-x)$

$\therefore \mathrm{x}=\frac{2 \mathrm{a}}{3}$

$\therefore[\mathrm{A}]=\frac{\mathrm{a}}{3}=[\mathrm{B}]$ and $[\mathrm{C}]=[\mathrm{D}]=\frac{2 \mathrm{a}}{3}$

$\therefore K_{c}=\frac{\frac{2 a}{3} \times \frac{2 a}{3}}{\frac{a}{3} \times \frac{a}{3}}=4$

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