A vessel contains A(g) and B(g) at 2 atm and 4 atm respectively at TK, the mixture is allowed to attain equilibrium at TK, according to the reaction

$8\mathrm{B}\left(\mathrm{g}\right)\rightleftharpoons 8\mathrm{A}\left(\mathrm{g}\right)+\mathrm{C}\left(\mathrm{s}\right)$

At equilibrium ${\left(\frac{n_A}{n_B}\right)}_{\text{eq. }}={\left(\frac{n_B}{n_A}\right)}_{\text{initial }}$

Find the value of y if K_c = 2^y

$$\begin{gathered} 8\mathrm{B}\left(\mathrm{g}\right) \rightleftharpoons 8\mathrm{A}\left(\mathrm{g}\right) + \mathrm{C}\left(\mathrm{s}\right) \\ \mathrm{Initial} \mathrm{no}. \mathrm{of} \mathrm{moles} \frac{4\mathrm{V}}{\mathrm{RT}} \frac{2\mathrm{V}}{\mathrm{RT}} \\ \mathrm{No}. \mathrm{of} \mathrm{moles} \mathrm{at} \mathrm{eq}. \frac{4\mathrm{V}}{\mathrm{RT}}-\mathrm{x} \frac{2\mathrm{V}}{\mathrm{RT}}+\mathrm{x} \mathrm{x} \end{gathered}$$

Given that

$\frac{\frac{2\mathrm{V}}{\mathrm{RT}}+\mathrm{x}}{\frac{4\mathrm{V}}{\mathrm{RT}}-\mathrm{x}}=\frac{\frac{4\mathrm{V}}{\mathrm{RT}}}{\frac{2\mathrm{V}}{\mathrm{RT}}}$

$\therefore \mathrm{x}=\frac{2\mathrm{V}}{\mathrm{RT}}$

$\therefore {\mathrm{K}}_{\mathrm{c}}=\frac{{\left(\frac{4\mathrm{V}}{\mathrm{RT}}\right)}^8}{{\left(\frac{2\mathrm{V}}{\mathrm{RT}}\right)}^8}=2^8$

$\therefore \mathrm{y}=8$