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GATE 2021 CH – Question 20

Chemical Reaction Engineering · Heterogeneous catalysis, diffusion effects and catalyst deactivation · 1 mark · Multiple choice

Ethylene adsorbs on the vacant active sites V of a transition metal catalyst according to the mechanism $\mathrm{C_2H_4+2V\rightleftharpoons C_2H_4\text{ adsorbed on two sites}}$. If $N_T,N_V$ and $N_{C_2H_4}$ denote the total number of active sites, number of vacant active sites and number of adsorbed $\mathrm{C_2H_4}$ molecules, respectively, the balance on the total number of active sites is given by

  1. $N_T=N_V+N_{C_2H_4}$
  2. $N_T=N_V+2N_{C_2H_4}$
  3. $N_T=2N_V+N_{C_2H_4}$
  4. $N_T=N_V+0.5N_{C_2H_4}$

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Correct answer: (B) $N_T=N_V+2N_{C_2H_4}$

Explanation

Count **sites**, rather than adsorbed molecules. Every vacant site contributes one site, while the adsorption mechanism consumes **two vacant sites for each ethylene molecule**.

The occupied-site count is therefore $2N_{C_2H_4}$ and the site balance is $\mathbf{N_T=N_V+2N_{C_2H_4}}$. Options A and D undercount occupied sites; C incorrectly doubles the vacant sites. **Answer: B.**