$\mathrm{CO}$ and $\mathrm{H}_2$ participate in a catalytic reaction. The partial pressures (in atm) of the reacting species $\mathrm{CO}$ and $\mathrm{H}_2$ in the feed stream are $p_{\mathrm{Co}}$ and $p_{\mathrm{H}_2}$, respectively. While $\mathrm{CO}$ undergoes molecular adsorption, $\mathrm{H}_2$ adsorbs via dissociative adsorption, that is, as hydrogen atoms. The equilibrium constants (in atm ${ }^{-1}$ ) corresponding to adsorption of $\mathrm{CO}$ and $\mathrm{H}_2$ to the catalyst sites are $K_{\mathrm{CO}}$ and $K_{\mathrm{H}_2}$, respectively. Total molar concentration of active sites per unit mass of the catalyst is $C_t$ (in mol. (g cat $)^{-1}$ ). Both the adsorption steps are at equilibrium. Which one of the following expressions is the $\text{CORRECT}$ ratio of the concentration of catalyst sites occupied by $\mathrm{CO}$ to that by hydrogen atoms?
- $\frac{K_{\mathrm{CO}} p_{\mathrm{CO}}}{\sqrt{K_{\mathrm{H}_2} p_{\mathrm{H}_2}}}$
- $\frac{K_{\mathrm{CO}}}{\sqrt{K_{\mathrm{H}_2}}}$
- $\frac{p_{\mathrm{CO}}}{\sqrt{p_{\mathrm{H}_2}}}$
- $\frac{K_{\mathrm{CO}} p_{\mathrm{CO}}}{K_{\mathrm{H}_2} p_{\mathrm{H}_2}}$