0700-2-cre-1mark

Thiele modulus is defined as

• \(D/k\)

• \(k/D\)

• \(L(k/D)^{0.5}\)

• \(Lk/D\)

GATE-CH-1988-7-b-iii-cre-2mark

The reaction \(A \rightarrow B\) occurs in an isothermal catalyst pellet under steady state conditions. If the diffusion of \(A\) into the pellet is the rate controlling step, the rate of diffusion of \(A\) is:

• faster than the rate of reaction

• equal to the rate of reaction

• slower than the rate of reaction

• may be faster or slower, depending on the kinetics

GATE-CH-1995-1-k-cre-1mark

A first order reaction \(A \rightarrow B\) occurs in an isothermal porous catalyst pellet of spherical shape. If the concentration of \(A\) at the centre of the pellet is much less than that at the external surface, the process is limited by

• diffusion within the pellet

• reaction

• external mass transfer

• none of the above

GATE-CH-1996-1-17-cre-1mark

The Knudsen diffusivity is dependent on

• the molecular velocity only

• the pore radius of the catalyst only

• the molecular mean free path only

• the molecular velocity and pore radius of the catalyst

GATE-CH-1996-1-21-cre-1mark

For a first order chemical reaction in a porous catalyst, the Thiele modulus is 10. The effectiveness factor is approximately equal to

• 1

• 0.5

• 0.1

• 0

GATE-CH-1996-2-11-cre-2mark

The rate expression for a heterogeneous catalytic reaction is given by \[ -r_{A} = k k_{A} P_{A} / (1 + k_{A} P_{A} + k_{R} P_{R}) \] where \(k\) is the surface reaction rate constant and \(k_{A}\) and \(k_{R}\) are adsorption equilibrium constants of \(A\) and \(R\) respectively. If \(k_{R} P_{R} \gg ( 1 + k_{A} P_{A})\) the apparent activation energy \(E_{A}\) is equal to (given \(E\) is the activation energy for the reaction, and \(\Delta H_{R}\) and \(\Delta H_{A}\) are the activation energies of adsorption of \(R\) and \(A\))

• \(E\)

• \(E + \Delta H_{A}\)

• \(E + \Delta H_{A} - \Delta H_{R}\)

• \(\Delta H_{A} + \Delta H_{R}\)

GATE-CH-1997-2-15-cre-2mark

For a first-order isothermal chemical reaction in a porous catalyst, the effectiveness factor is 0.3. The effectiveness factor will increase if the

• catalyst size is reduced or the catalyst diffusivity is reduced

• catalyst size is reduced or the catalyst diffusivity is increased

• catalyst size is increased or the catalyst diffusivity is reduced

• catalyst size is increased or the catalyst diffusivity is increased

GATE-CH-2000-1-21-cre-1mark

In solid catalysed reactions the diffusional effects are more likely to affect the overall rate of reaction for

• fast reactions in catalysts of small pore diameter

• fast reactions in catalysts of large pore diameter

• slow reactions in catalysts of small pore diameter

• slow reactions in catalysts of large pore diameter

GATE-CH-2005-70-cre-2mark

Match the items in Group I with those in Group II:

Group I	Group II
(P) Porous catalyst	(1) Selectivity
(Q) Parallel reactions	(2) Shrinking core model
(R) Non-ideal tubular reactor	(3) Thiele modulus
(S) Gas-solid non-catalytic reaction	(4) Dispersion number

• P-3, Q-1, R-4, S-2

• P-1, Q-3, R-2, S-4

• P-1, Q-4, R-2, S-3

• P-3, Q-4, R-1, S-2

GATE-CH-2008-59-cre-2mark

The irreversible zero order reaction \(A \rightarrow B\) takes place in a porous cylindrical catalyst that is sealed at both ends as shown in the figure. Assume dilute concentration and neglect any variations in the axial direction.

The steady state concentration profile is \[ \frac {C_A}{C_{AS}} = 1 + \frac {\phi _o^2}{4}\left [\left (\frac {r}{R}\right )^2-1\right ] \] where \(\phi _o\) is the Thiele modulus. For \(\phi _o=4\), the range of \(r\) where \(C_A=0\) is

• \(0<r<\dfrac {R}{4}\)

• \(0<r<\dfrac {R}{2}\)

• \(0\le r \le \sqrt {\dfrac {3}{4}}R\)

• \(0\le r\le R\)

GATE-CH-2009-15-cre-1mark

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

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

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

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

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

GATE-CH-2010-4-cre-1mark

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

• \(\xi =\dfrac {1}{\phi ^2}\)

• \(\xi =\phi \)

• \(\xi =1\)

• \(\xi =\dfrac {1}{\phi }\)

GATE-CH-2011-21-cre-1mark

Consider an irreversible, solid catalyzed, liquid phase first order reaction. The diffusion and 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

• \(\displaystyle k_o = \frac {k?k_m}{k+k_m}\)

• \(\displaystyle k_o = \frac {k+k_m}{k?k_m}\)

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

• \(k_o = {k+k_m}\)

GATE-CH-2014-40-cre-2mark

Match the following:

Group 1	Group 2
P. Tank in series model	I. Non-isothermal reaction
Q. Liquid-liquid extraction	II. Mixer-settler
R. Optimum temperature progression	III. PFR with axial mixing
S. Thiele modulus	IV. Solid catalyzed reaction

• P-II, Q-IV, R-I, S-III

• P-I, Q-I, R-III, S-IV

• P-III, Q-I, R-II, S-IV

• P-III, Q-II, R-I, S-IV

GATE-CH-2017-18-cre-1mark

Consider a first order catalytic reaction in a porous catalyst pellet.
Given: \(R\) - characteristic length of the pellet; \(\mathcal {D}_e\) - 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

• \(\dfrac {k_cR}{\mathcal {D}_e}\)

• \(\displaystyle R\sqrt {\frac {k_1}{\mathcal {D}_e}}\)

• \(\displaystyle R\sqrt {\frac {k_1C_s}{\mathcal {D}_e}}\)

• \(\displaystyle R\sqrt {\frac {\mathcal {D}_e}{k_1}}\)

GATE-CH-2017-19-cre-1mark

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

• Adsorption is rate-limiting

• Desorption is rate-limiting

• Solid catalyst does not affect equilibrium conversion

• Temperature does not affect equilibrium conversion

GATE-CH-2013-23-cre-1mark

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 ____________

• Answer

GATE-CH-2006-80-81-cre-4mark

Consider the diffusion of a reactant \(A\) through a cylindrical catalyst pore of radius \(R\) and length \(L \gg R\). Reactant \(A\) undergoes a zeroth order reaction on the cylindrical surface of the pore. The following equation describes changes in the concentration of \(A\) within the pore due to the axial diffusion of \(A\) and the disappearance of \(A\) due to reaction \[ \frac {d^2C_A}{dx^2} = K \] where \(C_A\) is the concentration of \(A\) at a distance of \(x\) from the pore entrance, and \(K\) is a constant.

(i) If the concentration of \(A\) at the pore entrance (\(x=0\)) is \(C_{A0}\), and \(x=L\) is a dead end where no reaction occurs, the concentration profile of \(A\) in the pore is given by

{#1}

(ii) The minimum pore length for \(A\) to be completely converted within the pore is

{#2}

GATE-CH-1998-21-cre-5mark

A particular metal reacts with a certain liquid and the product passes into solution. Three non-porous solid spheres of same metal and of diameters 10, 20 and 30 mm respectively were placed in a very large liquid pool of reactive liquid at the same time. After an hour, it was found that the pool had only two spheres of diameter 10 and 20 mm, respectively. After another hour, the pool had only one sphere of diameter 10 mm. This sphere also disappeared after another hour. Explain these observation through appropriate derivation using a more likely rate controlling step out of the following two:
(a) Film mass transfer, (b) Surface reaction.
Which is the rate controlling step?

• Film mass transfer

• Surface reaction

GATE-CH-2003-74-cre-2mark

Following isothermal kinetic data are obtained in a basket type of mixed flow reactor for a porous catalyst. Determine the role of pore diffusion and external mass transfer processes.

Run Number	Pellet diameter	Leaving concentration	Spinning rate	\((-r_A')\)
		of the reactant	of basket
1	1	1	high	2
2	2	1	low	1
3	2	1	high	1

• Strong pore diffusion control and mass transfer not controlling

• Both pore diffusion and mass transfer not controlling

• Both pore diffusion and mass transfer controlling

• Mass transfer controlling

GATE-CH-2004-25-cre-1mark

First order gaseous phase reaction is catalyzed by a non-porous solid. The kinetic rate constant and the external mass transfer coefficient are \(k\) and \(k_g\), respectively. The effective rate constant (\(k_{\text {eff}}\)) is given by

• \(k_{\text {eff}} = k+k_g\)

• \(\displaystyle k_{\text {eff}}= \frac {(k+k_g)}{2} \)

• \(k_{\text {eff}} = (k k_g)^{1/2} \)

• \(\displaystyle \frac {1}{k_{\text {eff}}} = \frac {1}{k} + \frac {1}{k_g} \)

GATE-CH-2007-56-cre-2mark

The first order reaction of \(A\) to \(R\) is run in an experimental mixed flow reactor. Find the role played by pore diffusion in the run given below. \(C_{A0}\) is 100 and \(W\) is fixed. Agitation rate was found to have no effect on conversion.

\(d_p\)	\(F_{A0}\)	\(X_A\)
4	2	0.8
6	4	0.4

• strong pore diffusion control

• diffusion free

• intermediate role by pore diffusion

• external mass transfer

GATE-CH-2007-57-cre-2mark

A packed bed reactor converts \(A\) to \(R\) by first order reaction with 9 mm pellets in strong pore diffusion regime to 63.2% level. If 18 mm pellets are used what is the conversion?

• 0.39

• 0.61

• 0.632

• 0.865

GATE-CH-2011-42-cre-2mark

For a first order catalytic reaction the Thiele modulus (\(\phi \)) of a spherical pellet is defined as \[ \phi = \frac {R_s}{3} \sqrt {\frac {k\rho _p}{D_e}} \] where

\(\rho _p\) = pellet density
\(R_s\) = pellet radius
\(D_e\) = effective diffusivity
\(k\) = first order reaction rate constant

If \(\phi >5\), then the apparent activation energy (\(E_a\)) is related to the intrinsic (or true) activation energy (\(E\)) as

• \(E_a=E^{0.5}\)

• \(E_a=0.5E\)

• \(E_a=2E\)

• \(E_a=E^2\)

GATE-CH-2012-36-cre-2mark

The rate-controlling step for the solid-catalyzed irreversible reaction \(A+B\rightarrow C\) 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

• \(\displaystyle \text {rate} \propto \frac {P_AP_B}{1+K_AP_A+K_BP_B+K_CP_C}\)

• \(\displaystyle \text {rate} \propto \frac {P_AP_B}{\big (1+K_AP_A+K_BP_B+K_CP_C\big )^2}\)

• \(\displaystyle \text {rate} \propto \frac {P_AP_B}{\big (1+K_AP_A+K_BP_B+K_CP_C\big )^{0.5}}\)

• \(\displaystyle \text {rate} \propto \frac {P_AP_B}{P_C}\)

GATE-CH-2015-47-cre-2mark

A catalyst slab of half-thickness \(L\) (the width and length of the slab \(\gg L\)) is used to conduct the first order reaction \(A\rightarrow B\). At 450 K, the Thiele modulus for this system is 0.5. The activation energy for the first order rate constant is 100 kJ/mol. The effective diffusivity of the reactant in the slab can be assumed to be independent of temperature, and external mass transfer resistance can be neglected. If the temperature of the reaction is increased to 470 K, then the effectiveness factor at 470 K (up to two decimal places) will be ____________

Value of universal gas constant = 8.314 J/mol.K

• Answer

GATE-CH-BT-2018-52-cre-2mark

First order deactivation rate constants for soluble and immobilized amyloglucosidase enzyme are 0.03 min^-1 and 0.005 min^-1, respectively. The ratio of half-life of the immobilized enzyme to that of the soluble enzyme is ____________

• Answer

GATE-CH-1994-23-b-cre-5mark

A gaseous reactant diffuses through a gas film and reacts on the surface of a non-porous spherical catalyst particle. The rate of surface reaction is \(k_1C_s\), where \(C_s\) is the reactant concentration on the catalyst surface. The reaction rate constant (\(k_1\)) = \(0.83 \times 10^{-4}\) m/s and the gas film mass transfer coefficient (\(k_m\)) = \(1.66 \times 10^{-4}\) m/s. Derive the reaction rate expression in terms of bulk gas phase concentration (\(C_0\)).

• Answer

GATE-CH-1996-25-cre-5mark

Cis-2-butene (\(A\)) isomerizes to trans-2-butene (\(B\)) on a solid catalyst under isothermal conditions according to the reaction \(A \rightleftharpoons B\). Assuming desorption of \(B\) from the surface of the catalyst to be rate controlling, derive an expression for the intrinsic rate of reaction per unit mass of catalyst. Sketch rate of reaction vs. total pressure (at constant composition) for the above mechanism.

• Answer

GATE-CH-2002-17-cre-5mark

An enzyme immobilized on the surface of a non-porous solid catalyzes a single-substrate reaction according to the first order rate equation given by \[\nu = \frac{V_m}{K_m} S\] Where \(V_m\) and \(K_m\) are the reaction parameters and \(S\) is the substrate (reactant) concentration at the surface of the solid.

1. If reaction rate is inhibited by liquid-film mass transfer resistance, find the overall rate expression for enzyme catalysis at steady state in terms of \(V_m, K_m\), the bulk liquid substrate concentration \(S_0\) and the film mass transfer coefficient \(k_s\).

2. If the reaction rate is of first order even at the bulk liquid concentration, what will be the value of the effectiveness factor for the following values of the reaction parameters: \(V_m = 10^{-10}\) mol/cm\(^2\).s, \(K_m = 2\times10^{-3}\) mol/litre, \(k_s = 5\times10^{-5}\) cm/s.

• Answer