Q30 / 90 · JEE Main 2021 (26 Aug Shift 2) · Chemistry

The equilibrium constant $K_{c}$ at $298 K$ for the reaction
$A + B ⇌ C + D$ is $100 .$ Starting with an equimolar solution with concentrations of $A, B, C$ and $D$ all equal to $1 M$ , the equilibrium concentration of $D$ is _____ $\times 10^{- 2} M$ . (Nearest integer)

Correct answer: 182

Solution

$K_{C} = {[\frac{1 + x}{1 - x}]}^{2} = 100$

$= \frac{1 + x}{1 - x} = 10$

$= 1 + x = 10 - 10 x$

$11 x = 9$

$x = [\frac{9}{11}]$

$[D]= [1 + \frac{9}{11}] = [\frac{20}{11}] = 1.818 = 1.82 M (approx) \Rightarrow 182 \times 10^{- 2} M$

Hence, the correct answer is 182.