The dissociative chemisorption of x_2(g) on a metal surface follows langmuir adsorption isotherm. The ratio of the rate constants of the adsorption and desorption process is 4atm^-1. The fraction surface coverage of x (adsorbed) at 1atm pressure is

According to Langmuir adsorption isotherm. In case of a diatomic molecule,

$$\begin{gathered} {\mathrm{\theta }}^2=\frac{{\mathrm{K}}_{\mathrm{a}}.{(1-\mathrm{\theta })}^2.{\mathrm{P}}_{\mathrm{x}}}{{\mathrm{K}}_{\mathrm{d}}} \\ \frac{{\mathrm{\theta }}^2}{{(1-\mathrm{\theta })}^2}=\frac{{\mathrm{K}}_{\mathrm{a}}}{{\mathrm{K}}_{\mathrm{d}}}\times {\mathrm{P}}_{\mathrm{x}} \end{gathered}$$

where, $\theta =$The fraction of surface coverage of x =?

K_a=rate constants of the adsorption

K_b=rate constants of the desorption

P_x= Pressure of a gas'x' =1atm.

$$\begin{gathered} \mathrm{Now}, \frac{{\mathrm{\theta }}^2}{{(1-\mathrm{\theta })}^2}=4\times 1=2^2 \\ \frac{\mathrm{\theta }}{(1-\mathrm{\theta })}=2 \\ \mathrm{\theta }=0.67 \end{gathered}$$