Chemical Reaction Engineering GATE-2008

Q 1: A species (A) reacts on a solid catalyst to produce R and S as follows:

A\rightarrow R;\;\;r_R=k_1C_A^2\;\;\;\;(1) A\rightarrow S;\;\;r_S=k_2C_A^2\;\;\;\;(2)

Assume film resistance to mass transfer is negligible. The ratio of the 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) 0

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Q 2: The gas phase reaction A + 3B → 2C is conducted in a PFR at constant temperature and pressure. The PFR achieves a conversion of 20 % of A. The feed is a mixture of A, B, and an inert I. It is found that the concentration of A remains the same throughout the reactor.

Which ONE of the following ratios of inlet molar rate (F_A,in: F_B,in: F_I,in) is consistent with this observation? Assume the reaction mixture is an ideal gas mixture.

A) 2 : 3 : 0
B) 2 : 2 : 1
C) 3 : 2 : 1
D) 1 : 2 : 1

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Q 3: The elementary liquid phase series parallel reaction scheme

A\rightarrow B\rightarrow C A\rightarrow R

is to be carried out in an isothermal CSTR. The rate laws are given by

r_R=k'C_A r_B=kC_A-kC_B

Feed is pure A. The space-time of the CSTR which results in the maximum exit concentration of B is given by

A) \sqrt{\frac1{kk'}}
B) \sqrt{\frac1{k'\left(k+k'\right)}}
C) \frac1{k+k'}
D) \sqrt{\frac1{k\left(k+k'\right)}}

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Q 4: The liquid phase reaction A → Products is governed by the kinetics

-r_A=kC_A^{1/2}

If the reaction undergoes 75 % conversion of A in 10 minutes in an isothermal batch reactor, the time (in minutes) for complete conversion of A is

A) 40/3
B) 20
C) 30
D) ∞

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Q 5: The homogeneous reaction A + B → C is conducted in an adiabatic CSTR at 800 K so as to achieve a 30 % conversion of A. The relevant specific heats and enthalpy change of reaction are given by

C_{P,A}=100\frac J{mol\;K},\;C_{P,C}=150\frac J{mol\;K} C_{P,B}=50\frac J{mol\;K},\;\triangle h^{rxn}=-1000\frac{kJ}{mol}

If the feed, a mixture of A and B, is available at 550 K, the mole fraction of A in the feed that is consistent with the above data is

A) 5/7
B) 1/4
C) 1/2
D) 2/7

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Q 6: The irreversible zero-order reaction A → B takes place in a porous cylindrical catalyst that is sealed at both ends as shown in the figure. Assume dilute concentrations and neglect any variations in the axial direction.

The steady-state concentration profile is

\frac{C_A}{C_{AS}}=1+\frac{\phi_0^2}4\left[\left(\frac rR\right)^2-1\right]

where ϕ_o is the Thiele modulus. For ϕ_o = 4, the range of r where C_A = 0 is

A) 0<r<\frac R4
B) 0<r<\frac R2
C) 0\leq r\leq\sqrt{\frac34}R
D) 0\leq r\leq R

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Common data for questions Q 7 & 8:

A liquid is flowing through a reactor at a constant flow rate. A step input of the tracer at a molar flow rate of 1 mol/min is given to the reactor at time t = 0. The time variation of the concentration (C) of the tracer at the exit of the reactor is as shown in the figure:

Q 7: The volumetric flow rate of the liquid through the reactor (in L / min) is

A) 1
B) 2
C) 1.5
D) 4

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Q 8: The mean residence time of the fluid in the reactor (in minutes) is

A) 1
B) 2
C) 3
D) 4

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Statement linked questions Q 9 & 10:

The liquid phase reaction A → P is to be carried out at constant temperature in a CSTR followed by a PFR in series. The overall conversion of A achieved by the reactor system (CSTR + PFR) is 95 %. The CSTR has a volume of 75 liters. Pure A is fed to the CSTR at a concentration C_A0 = 2 mol/liter and a volumetric flow rate of 4 liters/min. The kinetics of the reaction is given by

-r_A=0.1C_A^2\frac{mol}{liter.min}

Q 9: The conversion achieved by the CSTR is

A) 40 %
B) 50 %
C) 60 %
D) 80 %

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Q 10: The volume of the PFR required (in liters) is

A) 380
B) 350
C) 75
D) 35

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