The equilibrium constant at 298 K for the reaction $\mathrm{A}+\mathrm{B} \rightleftharpoons \mathrm{C}+\mathrm{D}$ is 100 . If the initial concentrations of all the four species were 1 M each, then equilibrium concentration of $D$ (in $\mathrm{mol} \mathrm{L}^{-1}$ ) will be

• A

  $0.182$
• Correct answer
  B

  $1.818$
• C

  $1.182$
• D

  $0.818$

Solution

$\begin{aligned} & 100=\frac{(1+x)(1+x)}{(1-x)(1-x)} \\ & \Rightarrow \quad \frac{1+x}{1-x}=10 \\ & \Rightarrow \quad 1+x=10-10 x \\ & \Rightarrow \quad 11 x=9 \\ & x=\frac{9}{11}=0.818 \end{aligned}$ (D) $1+x=1+0.818=1.818$

Hence, the correct answer is option: 'B'.