Reaction Engineering - GATE-CH Questions

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Heterogeneous Reactions

0700-2-cre-1mark

0700-2-cre

Thiele modulus is defined as

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

1988-7-b-iii-cre

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:

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

1995-1-k-cre

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

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

1996-1-17-cre

The Knudsen diffusivity is dependent on

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

1996-1-21-cre

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


[Index]



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

1996-2-11-cre

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 \(A\))

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

1997-2-15-cre

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

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

2000-1-21-cre

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

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

2005-70-cre

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

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

2008-59-cre

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


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

2009-15-cre

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

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

2010-4-cre

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

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

2011-21-cre

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

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

2014-40-cre

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

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

2017-18-cre

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


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

2017-19-cre

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

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

2013-23-cre

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 ____________

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

2006-80-81-cre

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

1998-21-cre

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?

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

2003-74-cre

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


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

2004-25-cre

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

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

2007-56-cre

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

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

2007-57-cre

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?

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

2011-42-cre

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

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

2012-36-cre

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


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

2015-47-cre

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

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

BT-2018-52-cre

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 ____________

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

1994-23-b-cre

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 (\(C_0\)).

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

1996-25-cre

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.

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

2002-17-cre

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.


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Last Modified on: 01-May-2024

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