Question

The homogeneous reaction is carried out in a 2-litre container at a particular temperature by taking 1 mole each of A, B, C and D respectively. If $K_C$ for the reaction is $\frac{1}{4}$ then the equilibrium concentration of C is :

$A\left(g\right)+B\left(g\right)\rightleftharpoons C\left(g\right)+D\left(g\right)$

• A. $\frac{1}{3}M$
• B. $\frac{2}{3}M$
• C. $\frac{4}{3}M$
• D. $\frac{1}{2}M$

Answer 1

The correct option is B $\frac{2}{3}M$

The equilibrium reaction is $A\left(g\right)+B\left(g\right)\rightleftharpoons C\left(g\right)+D\left(g\right).$

The expression for the equilibrium constant is $K_c=\frac{\left[C\right]\left[D\right]}{\left[A\right]\left[B\right]}.$

$\left[A\right]=\frac{(1-x)}{2};\left[B\right]=\frac{(1-x)}{2}$

$\left[C\right]=\frac{(1+x)}{2};\left[D\right]=\frac{(1+x)}{2}$

Substitute values in the above expression:

$\frac{1}{4}=\frac{[0.5+0.5x][0.5+0.5x]}{[0.5-0.5x][0.5-0.5x]}.$

$x=\mathrm{0.33.}$

$\left[C\right]=\frac{2}{3}M.$