Question

For a reaction

$\mathrm{X}+\mathrm{Y}\rightleftharpoons 2\mathrm{Z}$

$1.0$ mol of $\mathrm{X}$, $1.5$mol of $\mathrm{Y}$ and $0.5$ mol of Z were taken in a $1$ $\mathrm{L}$ vessel and allowed to react. At equilibrium, the concentration of $\mathrm{Z}$ was$1.0$ $\mathrm{mol}{\mathrm{L}}^{-1}$. The equilibrium constant of reaction is $\frac{\mathrm{x}}{15}$. The value of $\mathrm{x}$ is _________.

Answer 1

Step1: The concentration Z is $1.0$molL^-1

In this reaction, X contains $1$moles, Y contains ,$1.5$ moles and Z contains $0.5$moles when the time is $0$.

At equilibrium, Let the moles be x. The reaction is in forward direction so Z has $0.5+2xmoles$, X has $1-x$and Y has $1.5-xmoles$.

$$\begin{gathered} \mathrm{X}+\mathrm{Y}\rightleftharpoons 2\mathrm{Z} \\ \mathrm{t}=011.50.5 \\ \mathrm{at}\mathrm{equillibrium}1-\mathrm{x}1.5-\mathrm{x}0.5+2\mathrm{x} \end{gathered}$$

Step 2: Formula used ${\mathrm{K}}_{\mathrm{eq}}=\mathrm{Concentration}\mathrm{of}\mathrm{product}/\mathrm{Concentration}\mathrm{of}\mathrm{reactant}={\left[\mathrm{Z}\right]}^2/\left[\mathrm{X}\right]\left[\mathrm{Y}\right]$

Step 3: $$\begin{gathered} \mathrm{The}\mathrm{concentration}\mathrm{of}\mathrm{Z}=0.5+2\mathrm{x} \\ 1=0.5+2\mathrm{x} \\ \mathrm{x}=0.25 \end{gathered}$$

$$\begin{gathered} \mathrm{X}+\mathrm{Y}\rightleftharpoons 2\mathrm{Z} \\ \mathrm{at}\mathrm{equillibrium}1-\mathrm{x}1.5-\mathrm{x}0.5+2\mathrm{x} \\ 0.751.251 \end{gathered}$$

$$\begin{gathered} {\mathrm{K}}_{\mathrm{eq}}={\left[\mathrm{Z}\right]}^2/\left[\mathrm{X}\right]\left[\mathrm{Y}\right] \\ {\mathrm{K}}_{\mathrm{eq}}={\left[1\right]}^2/[3/4][5/4] \\ {\mathrm{K}}_{\mathrm{eq}}=\left[1\right]/[15/16] \\ {\mathrm{K}}_{\mathrm{eq}}=\left[16\right]/\left[15\right] \\ \mathrm{as}\mathrm{x}/15.\mathrm{So}\mathrm{according}\mathrm{to}\mathrm{the}\mathrm{given}\mathrm{statement}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{x}\mathrm{is}16 \\ 1.0\mathrm{mol}\mathrm{of}\mathrm{X},1.5\mathrm{mol}\mathrm{of}\mathrm{Y}\mathrm{and}0.5\mathrm{mol}\mathrm{of}\mathrm{Z}\mathrm{were}\mathrm{taken}\mathrm{in}\mathrm{a}1\mathrm{L}\mathrm{vessel}\mathrm{and}\mathrm{allowed}\mathrm{to}\mathrm{react}. \\ \mathrm{At}\mathrm{equilibrium},\mathrm{the}\mathrm{concentration}\mathrm{of}\mathrm{Z}\mathrm{was}1.0{\mathrm{mol}}^{-1}\mathrm{L}.\mathrm{The}\mathrm{equilibrium}\mathrm{constant}\mathrm{of}\mathrm{reaction}\mathrm{is}\mathrm{x}/15.\mathbf{The}\mathbf{}\mathbf{value}\mathbf{}\mathbf{of}\mathbf{}\mathbf{x}\mathbf{}\mathbf{is}\mathbf{16}\mathbf{}. \end{gathered}$$