Heterogeneous Catalysis and Diffusion - Chemical Reaction Engineering - Chemical Engineering Previous Year Questions

1

2008 · Chemical Engineering · Chemical Reaction Engineering · Heterogeneous Catalysis and Diffusion

Chemical Engineering (CH) 2008

A species \( A \) reacts on a solid catalyst to produce \( R \) and \( S \) as follows:
1) \( A \rightarrow R \)    \( r_R = k_1 C_A^2 \)
2) \( A \rightarrow S \)    \( r_S = k_2 C_A^2 \)
Assume film resistance to mass transfer is negligible. The ratio of instantaneous fractional yield of \( R \) in the presence of pore diffusion to that in the absence of pore diffusion is

A

1

B

>1

C

<1

D

Zero

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2

2009 · Chemical Engineering · Chemical Reaction Engineering · Heterogeneous Catalysis and Diffusion

Chemical Engineering (CH) 2009

For a solid-catalyzed reaction, the Thiele modulus is proportional to

A

\(\sqrt{\frac{\text{intrinsic reaction rate}}{\text{diffusion rate}}} \)

B

\(\sqrt{\frac{\text{diffusion rate}}{\text{intrinsic reaction rate}}} \)

C

\(\frac{\text{intrinsic reaction rate}}{\text{diffusion rate}} \)

D

\(\frac{\text{diffusion rate}}{\text{intrinsic reaction rate}} \)

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3

2009 · Chemical Engineering · Chemical Reaction Engineering · Heterogeneous Catalysis and Diffusion

Chemical Engineering (CH) 2009

The active component of catalysts used in steam reforming of methane to produce synthesis gas is

A

Nickel

B

Iron

C

Platinum

D

Palladium

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4

2010 · Chemical Engineering · Chemical Reaction Engineering · Heterogeneous Catalysis and Diffusion

Chemical Engineering (CH) 2010

For a first order isothermal catalytic reaction, \( A \rightarrow P \), occurring in an infinitely long cylindrical pore, the relationship between effectiveness factor, \( \varepsilon \), and Thiele modulus, \( \phi \), is

A

\(\varepsilon = \frac{1}{\phi^2} \)

B

\(\varepsilon = \phi \)

C

\(\varepsilon = 1 \)

D

\(\varepsilon = \frac{1}{\phi} \)

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5

2011 · Chemical Engineering · Chemical Reaction Engineering · Heterogeneous Catalysis and Diffusion

Chemical Engineering (CH) 2011

Consider an irreversible, solid catalysed, liquid phase first order reaction. The diffusion and the reaction resistances are comparable. The overall rate constant (\(k_o\)) is related to the overall mass transfer coefficient (\(k_m\)) and the reaction rate constant (\(k\)) as

A

\(k_o = \frac{k k_m}{k + k_m}\)

B

\(k_o = \frac{k + k_m}{k k_m}\)

C

\(k_o = \frac{k + k_m}{2}\)

D

\(k_o = k + k_m\)

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6

2011 · Chemical Engineering · Chemical Reaction Engineering · Heterogeneous Catalysis and Diffusion

Chemical Engineering (CH) 2011

For a first order catalytic reaction the Thiele modulus (φ) of a spherical pellet is defined as
\[ \phi = \frac{R_p}{3} \sqrt{\frac{k \rho_p}{D_e}} \]
where
ρ_p = pellet density, R_p = pellet radius
D_e = effective diffusivity, k = first order reaction rate constant
If φ > 5, then the apparent activation energy (E_a) is related to the intrinsic (or true) activation energy (E) as

A

E_a = E^0.3

B

E_a = 0.5E

C

E_a = 2E

D

E_a = E²

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7

2012 · Chemical Engineering · Chemical Reaction Engineering · Heterogeneous Catalysis and Diffusion

Chemical Engineering (CH) 2012

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 component \( i \) and \( K_i \) is the adsorption equilibrium constant of component \( i \), then the form of the Langmuir-Hinshelwood rate expression will be

A

\(\text{rate} \propto \frac{P_A P_B}{1 + K_A P_A + K_B P_B + K_C P_C} \)

B

\(\text{rate} \propto \frac{P_A P_B}{(1 + K_A P_A + K_B P_B + K_C P_C)^2} \)

C

\(\text{rate} \propto \frac{P_A P_B}{(1 + K_A P_A + K_B P_B + K_C P_C)^{0.5}} \)

D

\(\text{rate} \propto \frac{P_A P_B}{P_C} \)

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8

2013 · Chemical Engineering · Chemical Reaction Engineering · Heterogeneous Catalysis and Diffusion

Chemical Engineering (CH) 2013

The overall rates of an isothermal catalytic reaction using spherical catalyst particles of diameters 1 mm and 2 mm are \(r_{A1}\) and \(r_{A2}\) (in mol (kg-catalyst)⁻¹ h⁻¹), respectively. The other physical properties of the catalyst particles are identical. If pore diffusion resistance is very high, the ratio \(r_{A2}/r_{A1}\) is __________

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9

2014 · Chemical Engineering · Chemical Reaction Engineering · Heterogeneous Catalysis and Diffusion

Chemical Engineering (CH) 2014

A vapour phase catalytic reaction (Q + R → S) follows Rideal mechanism (R and S are not adsorbed). Initially, the mixture contains only the reactants in equimolar ratio. The surface reaction step is rate controlling. With constants a and b, the initial rate of reaction (−r₀) in terms of total pressure (P_T) is given by

A

\(-r_0 = \frac{aP_T}{1+bP_T}\)

B

\(-r_0 = \frac{aP_T}{1+bP_T^2}\)

C

\(-r_0 = \frac{aP_T^2}{1+bP_T}\)

D

\(-r_0 = \frac{aP_T^2}{(1+bP_T)^2}\)

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10

2017 · Chemical Engineering · Chemical Reaction Engineering · Heterogeneous Catalysis and Diffusion

Chemical Engineering (CH) 2017

Consider a first order catalytic reaction in a porous catalyst pellet.
Given \(R\) – characteristic length of the pellet; \(D_e\) – effective diffusivity; \(k_c\) – mass transfer coefficient; \(k_1\) – rate constant based on volume of the catalyst pellet; \(C_s\) – concentration of reactant on the pellet surface.
The expression for Thiele modulus is

A

\(\frac{k_c R}{D_e}\)

B

\(R \sqrt{\frac{k_1}{D_e}}\)

C

\(R \sqrt{\frac{k_1 C_s}{D_e}}\)

D

\(R \sqrt{\frac{D_e}{k_1}}\)

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11

2017 · Chemical Engineering · Chemical Reaction Engineering · Heterogeneous Catalysis and Diffusion

Chemical Engineering (CH) 2017

For a solid-catalyzed gas phase reversible reaction, which of the following statements is ALWAYS TRUE?

A

Adsorption is rate-limiting

B

Desorption is rate-limiting

C

Solid catalyst does not affect equilibrium conversion

D

Temperature does not affect equilibrium conversion

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12

2018 · Chemical Engineering · Chemical Reaction Engineering · Heterogeneous Catalysis and Diffusion

Chemical Engineering (CH) 2018

Liquid phase isomerization of o-xylene to p-xylene using a zeolite catalyst was carried out in a CSTR. Three sets of kinetic data at different temperatures and stirring speeds were obtained as shown below.

	set A			set B			set C
temperature (K)	500	500	500	600	600	600	700	700	700
stirring speed (rpm)	1000	2000	3000	1000	2000	3000	1000	2000	3000
reaction rate (mol L-1 s-1)	0.020	0.025	0.025	0.037	0.047	0.047	0.069	0.078	0.086

The operating condition at which the reaction rate is not controlled by external mass transfer resistance is

A

T = 500 K; rpm = 3000

B

T = 600 K; rpm = 1000

C

T = 700 K; rpm = 1000

D

T = 700 K; rpm = 2000

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13

2019 · Chemical Engineering · Chemical Reaction Engineering · Heterogeneous Catalysis and Diffusion

Chemical Engineering (CH) 2019

For a first order reaction in a porous spherical catalyst pellet, diffusional effects are most likely to lower the observed rate of reaction for

A

slow reaction in a pellet of small diameter

B

slow reaction in a pellet of large diameter

C

fast reaction in a pellet of small diameter

D

fast reaction in a pellet of large diameter

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14

2020 · Chemical Engineering · Chemical Reaction Engineering · Heterogeneous Catalysis and Diffusion

Chemical Engineering (CH) 2020

The square of Thiele modulus, M_T, is given by M_T^2 = L^2 k / D_eff, where L is the characteristic length of the catalyst pellet, k is the rate constant of a first order reaction, and D_eff is the effective diffusivity of the species in the pores. M_T is a measure of

A

rate of pore diffusion / time scale of reaction

B

rate of pore diffusion / rate of reaction

C

time scale of pore diffusion / rate of reaction

D

rate of reaction / rate of external mass transfer

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15

2021 · Chemical Engineering · Chemical Reaction Engineering · Heterogeneous Catalysis and Diffusion

Chemical Engineering (CH) 2021

Ethylene adsorbs on the vacant active sites V of a transition metal catalyst according to the following mechanism.
\[ \mathrm{C_2H_4 + 2V \rightleftharpoons \begin{array}{c} \mathrm{C_2H_4} \\ | \\ \mathrm{V} \end{array} \begin{array}{c} \mathrm{C_2H_4} \\ | \\ \mathrm{V} \end{array} } \]
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

A

\(N_T = N_V + N_{C_2H_4} \)

B

\(N_T = N_V + 2N_{C_2H_4} \)

C

\(N_T = 2N_V + N_{C_2H_4} \)

D

\(N_T = N_V + 0.5N_{C_2H_4} \)

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16

2022 · Chemical Engineering · Chemical Reaction Engineering · Heterogeneous Catalysis and Diffusion

Chemical Engineering (CH) 2022

The reaction \( A \rightarrow B \) is carried out isothermally on a porous catalyst. The intrinsic reaction rate is \( kC_A^2 \), where \( k \) is the rate constant and \( C_A \) is the concentration of \( A \). If the reaction is strongly pore-diffusion controlled, the observed order of the reaction is

A

1

B

2

C

\(\frac{3}{2} \)

D

\(\sqrt{2} \)

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17

2023 · Chemical Engineering · Chemical Reaction Engineering · Heterogeneous Catalysis and Diffusion

Chemical Engineering (CH) 2023

Match the reactions in Group 1 with the catalysts in Group 2 listed in the table below.

A

P-III, Q-IV, R-II, S-I

B

P-III, Q-IV, R-I, S-II

C

P-IV, Q-II, R-I, S-III

D

P-IV, Q-III, R-I, S-II

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18

2023 · Chemical Engineering · Chemical Reaction Engineering · Heterogeneous Catalysis and Diffusion

Chemical Engineering (CH) 2023

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?

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

\(\frac{K_{CO}p_{CO}}{K_{H_2}p_{H_2}}\)

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19

2024 · Chemical Engineering · Chemical Reaction Engineering · Heterogeneous Catalysis and Diffusion

Chemical Engineering (CH) 2024

A first-order heterogeneous reaction \(A \rightarrow B\) is carried out using a porous spherical catalyst. Assume isothermal conditions, and that intraparticle diffusion controls the reaction rate. At a bulk A concentration of \(0.3 \text{ mol L}^{-1}\), the observed reaction rate in a 3 mm diameter catalyst particle is \(0.2 \text{ mol s}^{-1} \text{ L}^{-1}\) catalyst volume. At a bulk A concentration of \(0.1 \text{ mol L}^{-1}\), the observed reaction rate, in mol s^{-1} L^{-1} catalyst volume, in a 6 mm diameter catalyst particle, is

A

0.011

B

0.033

C

0.022

D

0.005

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20

2025 · Chemical Engineering · Chemical Reaction Engineering · Heterogeneous Catalysis and Diffusion

Chemical Engineering (CH) 2025

Choose the CORRECT ordering of the diameter \(d\) of the different types of pores in a solid catalyst.

A

\(d_{\text{micro-pore}} < d_{\text{macro-pore}} < d_{\text{meso-pore}}\)

B

\(d_{\text{macro-pore}} < d_{\text{meso-pore}} < d_{\text{micro-pore}}\)

C

\(d_{\text{meso-pore}} < d_{\text{micro-pore}} < d_{\text{macro-pore}}\)

D

\(d_{\text{micro-pore}} < d_{\text{meso-pore}} < d_{\text{macro-pore}}\)

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