Chapter 10: Catalysis and Catalytic Reactors

Finding the Mechanism

\( 2 \text{CO} + \text{O}_2 \rightleftharpoons 2 \text{CO}_2 \quad \text{(cat)} \)

The following data were obtained for the oxidation of CO over a catalyst. All rates are initial rates

The initial rate was found to be independent of CO₂.  

a)   Suggest a rate law consistent with the data

Hint 1  Sketch \( -r_{\text{CO}} \) versus C_O2.

Hint 2  Sketch \( -r_{\text{CO}} \) versus C_COat low concentration.

Hint 3  Sketch \( -r_{\text{CO}} \) versus C_CO at high concentration.

Full Solution What is the rate law?

b)   Suggest mechanisms consistent with the rate law

Hint 1 What do the trends suggest?

Hint 2 What is the mechanism?

Full Solution

Hint 1

Use only the data points for which the concentration of CO is the same.

at \( C_{\text{O}_2} = 1 \), \( -r_{\text{CO}} = 0.02 \, \text{mol}/\text{dm}^3 \cdot \text{s} \)

at \( C_{\text{O}_2} = 9 \), \( -r_{\text{CO}} = 0.06 \, \text{mol}/\text{dm}^3 \cdot \text{s} \)

\( \left( \frac{0.06}{0.02} \right) = \left( \frac{9}{1} \right)^n \)

\( n = \frac{1}{2} \)

\( -r_{\text{CO}} \sim C_{\text{O}_2}^{1/2} \)

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Hint 2: Low concentration

For constant CO₂

We see at low concentration the rate is linear in CO and \( -r'_{\text{CO}} \sim C_{\text{CO}} \)

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Hint 3: High concentration

At high concentrations the rate decreases with increasing concentration

\( -r'_{\text{CO}} \sim \frac{1}{C_{\text{CO}}} \)

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Full Solution: Part A

Combining

\( -r_{\text{CO}}' = \frac{k C_{\text{CO}} C_{\text{O}_2}^{1/2}}{(1 + K_{\text{CO}} C_{\text{CO}})^2} \)

For fixed concentration of O₂ and low concentration of CO and

\( K_{\text{CO}} C_{\text{CO}} \ll 1 \)

Rate increases linearly with CO: agrees with data

\( -r_{\text{CO}}' \sim C_{\text{CO}} \)

High concentration

\( -r_{\text{CO}}' \sim \frac{k C_{\text{CO}}}{(K_{\text{CO}} C_{\text{CO}})^2} \sim \frac{1}{C_{\text{CO}}} \)

\( K_{\text{CO}} C_{\text{CO}} \gg 1 \)

Rate decreases with increasing CO: agrees with data

Consequently the rate law

\( -r'_{\text{CO}} = \frac{k C_{\text{CO}} C_{\text{O}_2}^{1/2}}{(1 + K_{\text{CO}} C_{\text{CO}})^2} \)

Satisfies the data

Back to Part b

Hint 1

From the denominator of the rate law, we see that CO is adsorbed and that O₂ is either weakly adsorbed (K_O2P_O2^1/2 << 1) or not adsorbed at all.  

The 1/2 order with respect to oxygen suggests dissociative adsorption.  

Because the initial rate is independent of CO2, it is either not adsorbed on the surface or weakly adsorbed.  

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Hint 2

The following mechanism is consistent with the rate law

Molecular Adsorption

\( \text{CO} + S \rightleftharpoons \text{CO} \cdot S \quad -r_{\text{ADCO}} = k_{\text{ACO}} \left[ C_{\text{CO}} C_{\nu} - \frac{C_{\text{CO}S}}{K_{\text{CO}}} \right] \)

Dissociative Adsorption

\( \text{O}_2 + 2S \rightleftharpoons 2O \cdot S \quad -r_{\text{ADO}} = k_{\text{AO}} \left[ C_{\text{O}_2} C_{\nu}^2 - \frac{C_{\text{CO}S}^2}{K_{\text{O}_2}} \right] \)

Surface Reaction

\( \text{CO} \cdot S + O \cdot S \rightarrow \text{CO}_2 + 2S \)

\( r_S = k C_{\text{CO}} \cdot S C_{\text{CO}_S} \)

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Full Solution: Part B

The following mechanism is consistent with the rate law

Molecular Adsorption

\( \text{CO} + S \rightleftharpoons \text{CO} \cdot S \quad -r_{\text{ADCO}} = k_{\text{ACO}} \left[ C_{\text{CO}} C_{\nu} - \frac{C_{\text{CO}S}}{K_{\text{CO}}} \right] \)

Dissociative Adsorption

\( \text{O}_2 + 2S \rightleftharpoons 2O \cdot S \quad -r_{\text{ADO}} = k_{\text{AO}} \left[ C_{\text{O}_2} C_{\nu}^2 - \frac{C_{\text{CO}S}^2}{K_{\text{O}_2}} \right] \)

Surface Reaction

\( \text{CO} \cdot S + O \cdot S \rightarrow \text{CO}_2 + 2S \)

\( r_S = k C_{\text{CO}} \cdot S C_{\text{CO}_S} \)

Assume surface reaction limits

\( -r'_{\text{CO}} = r_S = k_S C_{\text{CO}} \cdot S C_{\text{CO}} \)

\( r_{\text{AdCO}} \sim 0 = C_{\text{CO}} C_{\nu} - \frac{C_{\text{CO}S}}{K_{\text{CO}}} \)

\( C_{\text{CO}S} = K_{\text{CO}} C_{\text{CO}} C_{\nu} \)

\( r_{\text{AdO}_2} \sim 0 = C_{\text{O}_2} C_{\nu}^2 - \frac{C_{\text{CO}S}^2}{K_{\text{O}_2}} \)

\( C_{\text{OS}} = C_{\nu} \sqrt{K_{\text{O}_2} C_{\text{O}_2}} \)

\( r_{\text{CO}_2} = -r_{\text{CO}} = k_{\text{CO}} \cdot S C_{\text{CO}} = k K_{\text{CO}} K_{\text{O}_2} C_{\text{CO}}^{1/2} C_{\text{O}_2}^{1/2} C_{\nu}^2 \)

\( C_T = C_{\nu} + C_{\text{CO}_S} + C_{\text{CO}S} \)

\( = C_{\nu} + K_{\text{CO}} C_{\text{CO}} C_{\nu} + K_{\text{O}_2} C_{\text{O}_2}^{1/2} C_{\text{O}_2}^{1/2} C_{\nu} \)

\( C_{\nu} = \frac{C_T}{1 + K_{\text{CO}} C_{\text{CO}} + K_{\text{O}_2} C_{\text{O}_2}^{1/2} C_{\text{O}_2}} \)

\( r_{\text{CO}_2} = -r_{\text{CO}} = \frac{k}{1 + K_{\text{CO}} C_{\text{CO}} + K_{\text{O}_2} C_{\text{O}_2}^{1/2}} \)

We see that oxygen is weakly adsorbed (very small \( K_{\text{O}_2} \)) such that \( K_{\text{O}_2}^{1/2} C_{\text{O}_2}^{1/2} \ll 1 \)

\( -r_{\text{CO}} = \frac{k C_{\text{CO}} C_{\text{O}_2}^{1/2}}{(1 + K_{\text{CO}} C_{\text{CO}})^2} \)

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