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