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GATE 2023 CH – Question 43

Chemical Reaction Engineering · Heterogeneous catalysis, diffusion effects and catalyst deactivation · 2 marks · Multiple choice

CO and H$_2$ participate in a catalytic reaction. The partial pressures (in atm) of the reacting species CO and H$_2$ in the feed stream are $p_{CO}$ and $p_{H_2}$, respectively. While CO undergoes molecular adsorption, H$_2$ adsorbs via dissociative adsorption, that is, as hydrogen atoms. The equilibrium constants (in atm$^{-1}$) corresponding to adsorption of CO and H$_2$ to the catalyst sites are $K_{CO}$ and $K_{H_2}$, 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 CORRECT ratio of the concentration of catalyst sites occupied by CO to that by hydrogen atoms?

the four options are: (A) $\frac{K_{CO}p_{CO}}{\sqrt{K_{H_2}p_{H_2}}}$, (B) $\frac{K_{CO}}{\sqrt{K_{H_2}}}$, (C) $\frac{p_{CO}}{\sqrt{p_{H_2}}}$, (D) $\frac{K_{CO}p_{CO}}{K_{H_2}p_{H_2}}$.
  1. Option A in the figure
  2. Option B in the figure
  3. Option C in the figure
  4. Option D in the figure

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Show answer and explanation

Correct answer: (A) Option A in the figure

Explanation

For molecular adsorption of CO, $C_{CO\cdot S} = K_{CO}p_{CO}C_v$. For dissociative adsorption $H_2 + 2S \rightleftharpoons 2H\cdot S$, $K_{H_2}p_{H_2} = \frac{C_{H\cdot S}^2}{C_v^2}$, so $C_{H\cdot S} = \sqrt{K_{H_2}p_{H_2}}\,C_v$. The ratio is $\frac{K_{CO}p_{CO}}{\sqrt{K_{H_2}p_{H_2}}}$.