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

Solution :
\[\begin{align} & \text{Given,} \\ & \begin{matrix} {} & A & + \\ \text{No}\text{. of moles initially} & 1 & {} \\ \text{At equilibrium} & 1-a & {} \\ \end{matrix}\,\,\,\begin{matrix} B & \rightleftharpoons & C \\ 1 & {} & 1 \\ 1-a & {} & 1+a \\ \end{matrix}\,\,\,\,\,\,\begin{matrix} + \\ {} \\ {} \\ \end{matrix}\,\,\,\,\,\,\begin{matrix} D \\ 1 \\ 1+a \\ \end{matrix} \\ \end{align}\]
$$\eqalign{ & \therefore \,\,{K_c} = {\left( {\frac{{1 + a}}{{1 - a}}} \right)^2} = 100 \cr & \therefore \,\,\frac{{1 + a}}{{1 - a}} = 10 \cr & {\text{On solving}} \cr & a = 0.81 \cr & {\left[ D \right]_{{\text{At}}\,{\text{eq}}}} = 1 + a = 1 + 0.81 = 1.81 \cr} $$