The rate-controlling step for the solid-catalyzed irreversible reaction

$A + B \longrightarrow C$

is known to be the reaction of adsorbed $A$ with adsorbed $B$ to give adsorbed $C$. If $P_i$ is the partial pressure of components $i$ and $K_i$ the adsorption equilibrium constant of components $i$, then the form of the Langmuir-Hinshelwood rate expression will be

1. $\text{rate} \:{\displaystyle \propto }\frac{P{_A}P{_B}}{1 + K{_A}P{_A} + K{_B}P{_B} + K{_C}P{_C} }$
2. $\text{rate} \: {\displaystyle \propto }\frac{P{_A}P{_B}}{(1 + K{_A}P{_A} + K{_B}P{_B} + K{_C}P{_C})^2 }$
3. $\text{rate} \: {\displaystyle \propto }\frac{P{_A}P{_B}}{(1 + K{_A}P{_A} + K{_B}P{_B} + K{_C}P{_C})^0.5 }$
4. $\text{rate} \: {\displaystyle \propto }\frac{P{_A}P{_B}}{P{_C}}$