Chapter 10: Catalysis and Catalytic Reactors

CO/NO Problem

1)

\( \text{CO} + \text{NO} \rightleftharpoons \text{CO}_2 + \tfrac{1}{2} \text{N}_2 \)

Mechanism

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

\(\text{NO} + \text{S} \rightleftharpoons \text{NO} \cdot \text{S} \quad \quad r_{\text{ADNO}} = k_{\text{ANO}} \left[P_{\text{NO}} C_V - \frac{C_{\text{NO} \cdot \text{S}}}{K_{\text{NO}}} \right]\)

\(\text{NO} \cdot \text{S} + \text{CO} \cdot \text{S} \rightleftharpoons \text{CO}_2 \cdot \text{S} + \text{N} \cdot \text{S} \quad \quad r_S = k_{S1} \left[ \frac{C_{\text{CO} \cdot \text{S}} C_{\text{NO} \cdot \text{S}} - C_{\text{CO}_2 \cdot \text{S}} C_{\text{N} \cdot \text{S}}}{K_{S1}} \right]\)

\(\text{N} \cdot \text{S} + \text{N} \cdot \text{S} \rightleftharpoons \text{N}_2 + 2\text{S} \quad \quad r_{\text{SN}_2} = k_{S2} \left[C_{\text{N} \cdot \text{S}}^2 - K_{\text{N}_2} P_{\text{N}_2} C_V^2 \right]\)

\(\text{CO}_2 \cdot \text{S} \rightleftharpoons \text{CO}_2 + \text{S} \quad \quad r_D = k_{\text{CO}_2} \left[ C_{\text{CO}_2 \cdot \text{S}} - K_{\text{CO}_2} P_{\text{CO}_2} C_V \right]\)

Surface Reaction Limits

\( r_S = k_{S1} \left[ C_{\text{CO} \cdot \text{S}} C_{\text{NO} \cdot \text{S}} - \frac{C_{\text{CO}_2 \cdot \text{S}} C_{\text{N} \cdot \text{S}}}{K_{S1}} \right] \)

 

Which of the following is false:

A: \( C_{\text{CO} \cdot \text{S}} = K_{\text{CO}} P_{\text{CO}} C_V \)

B: \( C_{\text{NO} \cdot \text{S}} = K_{\text{NO}} P_{\text{NO}} C_V \)

C: \( C_{\text{N} \cdot \text{S}} = K_{\text{N}_2} P_{\text{N}_2} C_V \)

D: \( C_{\text{CO}_2 \cdot \text{S}} = K_{\text{CO}_2} P_{\text{CO}_2} C_V \)

E: \( C_{\text{N} \cdot \text{S}} = K_{\text{N}_2}^{1/2} P_{\text{N}_2}^{1/2} C_V \)

Go To Solution #1

 
































































2)

\( \text{CO} + \text{NO} \rightleftharpoons \text{CO}_2 + \tfrac{1}{2} \text{N}_2 \)

Which of the following rate laws is correct

A

\( -r'_{\text{CO}} = \frac{ k \left( P_{\text{CO}} P_{\text{NO}} - \frac{P_{\text{CO}_2} P_{\text{N}_2}^{1/2}}{K_P} \right) }{ 1 + K_{\text{NO}} P_{\text{NO}} + K_{\text{CO}} P_{\text{CO}} + K_{\text{CO}_2} P_{\text{CO}_2} + K_{\text{N}_2} P_{\text{N}_2} } \)

B

\( -r'_{\text{CO}} = \frac{ k \left( P_{\text{CO}} P_{\text{NO}} - \frac{P_{\text{CO}_2} P_{\text{N}_2}^{1/2}}{K_P} \right) }{ 1 + K_{\text{NO}} P_{\text{NO}} + K_{\text{CO}} P_{\text{CO}} + K_{\text{CO}_2} P_{\text{CO}_2} + K_{\text{N}_2}^{1/2} P_{\text{N}_2}^{1/2} } \)

C

\( -r'_{\text{CO}} = \frac{ k \left( P_{\text{CO}} P_{\text{NO}} - \frac{P_{\text{CO}_2} P_{\text{N}_2}^{1/2}}{K_P} \right) }{ \left( 1 + K_{\text{NO}} P_{\text{NO}} + K_{\text{CO}} P_{\text{CO}} + K_{\text{CO}_2} P_{\text{CO}_2} + K_{\text{N}_2} P_{\text{N}_2} \right)^2 } \)

D

\( -r'_{\text{CO}} = \frac{ k \left( P_{\text{CO}} P_{\text{NO}} - \frac{P_{\text{CO}_2} P_{\text{N}_2}^{1/2}}{K_P} \right) }{ \left( 1 + K_{\text{NO}} P_{\text{NO}} + K_{\text{CO}} P_{\text{CO}} + K_{\text{CO}_2} P_{\text{CO}_2} + K_{\text{N}_2}^{1/2} P_{\text{N}_2}^{1/2} \right)^2 } \)

Go To Solution #2






























































  

3) 

\( CO \cdot S + NO \cdot S \quad \text{and} \quad CO + NO \rightleftharpoons CO_2 + \frac{1}{2} N_2 \)

\(-r'_{\text{CO}} = \frac{k \left[ P_{\text{CO}} P_{\text{NO}} - \frac{P_{\text{CO}_2} P_{\text{N}_2}^{1/2}}{K_P} \right]}{\left( 1 + K_{\text{NO}} P_{\text{NO}} + K_{\text{CO}} P_{\text{CO}} + K_{\text{CO}_2} P_{\text{CO}_2} + \sqrt{K_{\text{N}_2} P_{\text{N}_2}} \right)^2} \)

Diagram of a differential reactor with CO, N₂, and NO flowing in and out.
Rate vs P_N₂ at low P_CO and P_NO with P_CO₂ = 0.

What can you tell from the above figure?

  1. Reaction is irreversible.

  2. N2 is weakly adsorbed.

  3. NO is weakly adsorbed.

  4. Reaction is at equilibrium.

  5. None of the above.

Go To Solution #3






























































 

4) 

\( \text{CO} \cdot S + \text{NO} \cdot S \rightleftharpoons \text{CO} + \text{NO} \rightarrow \text{CO}_2 + \frac{1}{2} \text{N}_2 \)

\( -r'_{\text{CO}} = \frac{k P_{\text{CO}} P_{\text{NO}} - \frac{P_{\text{CO}_2}^{1/2} P_{\text{N}_2}}{K_P}}{\left( 1 + K_{\text{NO}} P_{\text{NO}} + K_{\text{CO}} P_{\text{CO}} + K_{\text{CO}_2} P_{\text{CO}_2} + \sqrt{K_{\text{N}_2} P_{\text{N}_2}} \right)^2} \)

                                        

Differential reactor with CO, CO₂, N₂, NO inputs.

Constant -r'CO vs PCO₂ at PN₂ = 10, with small PCO and PNO.

Which of the following are true?

  1. Reaction is irreversible.

  2. CO2 is weakly adsorbed.

  3. Reaction is at equilibrium.

  4. CO is weakly adsorbed.

  5. NO is weakly adsorbed.

  Go To Solution #4
































































5) 

\( \text{NO} + \text{CO} \rightleftharpoons \text{CO}_2 + \frac{1}{2} \text{N}_2 \)

For a fixed concentration of NO which of the following curves describes the rate law for the case when PNO is very very small? 

A B
-r'CO vs PCO showing saturation behavior. Linear increase of -r'CO with PCO.
C D
Flat line showing -r'CO independent of PCO. Bell-shaped curve of -r'CO vs PCO.

E

Decreasing curve of -r'CO vs PCO.

      Go To Solution #5        


 

 

 

 

 

 

Solution #1

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

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

\( \text{A is True} \)

Similarly,

\( \frac{r_{\text{ADNO}}}{k_{\text{NO}}} \sim 0, \quad r_{\text{CO}_2} \sim 0\)

\( C_{\text{NO}S} = K_{\text{NO}} P_{\text{NO}} C_{\nu} \)

\( \text{B is True} \)

\( C_{\text{CO}^2S} = K_{\text{CO}_2} P_{\text{CO}_2} C_{\nu} \)

\( \text{D is True} \)

But,

\( \frac{r_{\text{SN}_2}}{k_{\text{S2}}} \sim 0 = C_{\text{N}_2}^2 S - P_{\text{N}_2} C_{\nu}^2 K_{\text{N}_2} = 0 \)

\( C_{\text{N}_2}^2 S = P_{\text{N}_2} C_{\nu}^2 K_{\text{N}_2} \)

\( C_{\text{NS}} = K_{\text{N}_2}^{1/2} P_{\text{N}_2}^{1/2} C_{\nu} \)

\( \text{E is True} \)

\( \text{C is False} \)

Back to Problem #1

Problem #2

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Solution #2

The rate law is

\( r_S = k_{S1} \left[ C_{\text{NO}S} C_{\text{CO}S} - \frac{C_{\text{N}S} C_{\text{CO}S}}{K_S} \right] \)

and

\( C_{\text{NO}S} = K_{\text{NO}} P_{\text{NO}} C_{\nu} \)

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

\( C_{\text{CO}_2S} = K_{\text{CO}_2} P_{\text{CO}_2} C_{\nu} \)

\( C_{\text{N}S} = K_{\text{N}_2}^{1/2} P_{\text{N}_2}^{1/2} C_{\nu} \)

Substituting for \( C_{\text{NO}S} \), \( C_{\text{CO}S} \), \( C_{\text{CO}_2S} \), and \( C_{\text{N}S} \) in the rate law

We obtain

\( r_S = k_S K_{\text{NO}} K_{\text{CO}} P_{\text{CO}} P_{\text{NO}} \left[ \frac{P_{\text{CO}_2}^{1/2} P_{\text{N}_2}}{K_P} \right] \)

\( C_t = C_{\nu} + C_{\text{CO}S} + C_{\text{NO}S} + C_{\text{CO}_2S} + C_{\text{N}S} \)

\( = C_{\nu} \left[ 1 + K_{\text{CO}} P_{\text{CO}} + K_{\text{NO}} P_{\text{NO}} + K_{\text{CO}_2} P_{\text{CO}_2} + K_{\text{N}_2}^{1/2} P_{\text{N}_2}^{1/2} \right] \)

\( -r'_{\text{CO}} = \frac{k P_{\text{CO}} P_{\text{NO}} \left[ \frac{P_{\text{CO}_2}^{1/2} P_{\text{N}_2}}{K_P} \right]}{ \left[ 1 + K_{\text{CO}} P_{\text{CO}} + K_{\text{NO}} P_{\text{NO}} + K_{\text{CO}_2} P_{\text{CO}_2} + K_{\text{N}_2}^{1/2} P_{\text{N}_2}^{1/2} \right]^2} \)

Ans: D

Back to Problem #2

Problem #3

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Solution #3

\( \text{CO} + \text{NO} \rightleftharpoons \text{CO}_2 + \frac{1}{2} \text{N}_2 \)

\( -r'_{\text{CO}} = \frac{k P_{\text{CO}} P_{\text{NO}} \left[ P_{\text{CO}_2}^{1/2} P_{\text{N}_2} - \frac{P_{\text{CO}_2}^{1/2} P_{\text{N}_2}}{K_P} \right]}{ \left( 1 + K_{\text{NO}} P_{\text{NO}} + K_{\text{CO}} P_{\text{CO}} + K_{\text{CO}_2} P_{\text{CO}_2} + \sqrt{K_{\text{N}_2} P_{\text{N}_2}} \right)^2} \)

Rate law suggests

For \( P_{\text{CO}_2} \) and \( P_{\text{NO}} \) small,

\( -r_{\text{CO}}' \sim \frac{1}{P_{\text{N}_2}} \)

Rate law curve vs flat data for -r'CO,0 vs PN2.

\( K_{\text{N}_2} \sim 0 \)

Ans: B, \( \text{N}_2 \) weakly adsorbed

Back to Problem #3

Problem #4

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Solution #4

\( -r_{\text{CO},0} = \frac{k P_{\text{CO},0} P_{\text{NO},0} \left( 1 + K_{\text{NO}} P_{\text{NO},0} + K_{\text{CO}} P_{\text{CO},0} + K_{\text{CO}_2} P_{\text{CO}_2,0} + 0.0001 \right)}{\left( 1 + K_{\text{NO}} P_{\text{NO},0} + K_{\text{CO}} P_{\text{CO},0} + K_{\text{CO}_2} P_{\text{CO}_2,0} \right)^2} \)

1) Reaction is irreversible.

2) \( \text{CO}_2 \) is weakly adsorbed.

\( -r_{\text{CO},0} = \frac{k P_{\text{CO},0} P_{\text{NO},0}}{ \left( 1 + K_{\text{NO}} P_{\text{NO},0} + K_{\text{CO}} P_{\text{CO},0} \right)^2 } \)

1 and 2 are true, all others are false.

Back to Problem #4

Problem #5

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Solution #5

\( -r_{\text{CO}}' = \frac{k P_{\text{CO}} P_{\text{NO}}}{ \left( 1 + K_{\text{NO}} P_{\text{NO}} + K_{\text{CO}} P_{\text{CO}} \right)^2 } \)


Low Partial Pressure CO

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

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

Linear increase of -r'CO with PCO.

High Partial Pressure CO

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

\( -r_{\text{CO}}' \sim \frac{P_{\text{CO}}}{P_{\text{CO}}^2} \sim \frac{1}{P_{\text{CO}}} \)

Rate -rAO decreases with PCO.

Combining

Rate -r′CO peaks at a specific PCO.

Ans: D

Differentiating the rate law in with respect PCO to find the maximum

\( \frac{d \left( -r_{\text{CO}}' \right)}{d P_{\text{CO}}} = 0 = \frac{k P_{\text{NO}} \left[ 1 + K_{\text{NO}} P_{\text{NO}} + K_{\text{CO}} P_{\text{CO}} \right] - k P_{\text{CO}} P_{\text{NO}} \left[ 1 + K_{\text{NO}} P_{\text{NO}} + K_{\text{CO}} P_{\text{CO}} \right]^2 K_{\text{CO}}}{\left[ 1 + K_{\text{NO}} P_{\text{NO}} + K_{\text{CO}} P_{\text{CO}} \right]^4} \)

Solving

\( P_{\text{CO}} = \frac{1 + K_{\text{NO}} P_{\text{NO}}}{K_{\text{C}}} \)

Back to Problem #5

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