JEE Main · 2021 · 25 Jul 2021 · Shift 1 · Equilibrium

Let $\alpha$ be the amount of $A$ and $B$ that reacts. Starting from $1$ M of each species, at equilibrium $[A]=[B]=1-\alpha$ and $[C]=1+\alpha$; since the initial reaction quotient $Q=1$ lies below $K=100$, the reaction moves forward and $0<\alpha <1$. The equilibrium condition $\frac{1+\alpha }{(1-\alpha {)}^2}=100$ rearranges to $100{\alpha }^2-201\alpha +99=0$, whose root in the physical range is $\alpha =\frac{201-\sqrt{801}}{200}\approx 0.863$. Hence $[C]=1+\alpha \approx 1.863$ M, which written as $x\times 10^{-1}$ M gives $x\approx 19$.