Chemical Reaction Engineering GATE-1999

Q 1: Overall order of reaction for which rate constant has units of (mol/L)^–(3/2) sec^–1 is

A) -3/2
B) 1/2
C) 3/2
D) 5/2

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Q 2: For the reaction A+B\rightarrow2B+C ,

A) r_A = r_B
B) r_A = -r_B
C) r_A = 2r_B
D) r_A = r_B/2

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Q 3: The exit age distribution curve E(0) for an ideal CSTR with the average residence time τ, is given by

A) e^{-t/\tau}
B) (1/\tau)e^{-t/\tau}
C) 1-e^{-t/\tau}
D) 1-\left(1/\tau\right)e^{-t/\tau}

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Q 4: An endothermic second-order reaction is carried out in an adiabatic plug flow reactor. The rate of heat generation is

A) maximum at the inlet of the reactor
B) maximum at the exit of the reactor
C) maximum at the centre of the reactor
D) constant throughout the reactor

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Q 5: For the liquid phase zero-order irreversible reaction A → B, the conversion of A in a CSTR is found to be 0.3 at a space velocity of 0.1 min^–1. What will be the conversion for a PFR with a space velocity of 0.2 mm^–1? Assume that all the other operating conditions are the same for CSTR and PFR.

A) 0.15
B) 0.3
C) 0.6
D) 0.9

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Q 6: Consider the n^th order irreversible liquid phase reaction A→ B. Which one of the following plots involving half-life of the reaction (t_1/2) and the initial reactant concentration (C_A0) gives a straight-line plot?

A) C_A0 vs. t_1/2
B) In C_A0 vs. t_1/2
C) C_A0 vs. In t_1/2
D) In C_A0 vs. In t_1/2

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Q 7: At a given value of E/R (ratio of activation energy and gas constant), the ratio of the rate constants at 500 K and 400 K is 2 if the Arrhenius law is used. What will be this ratio if transition state theory is used with the same value of E/R?

A) 1.6
B) 2
C) 2.24
D) 2.5

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Q 8: Two parallel first-order reactions A → B and A → C are taking place in the liquid phase in a well-mixed batch reactor. After 60 min of operation, 80 % of A has reacted while 2 moles of B per mole of C was detected in the reactor. Calculate the rate constants k₁ and k₂ for the two reactions. Assume that no B and C were initially present in the reactor.

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Q 9: An isothermal plug flow reactor is designed to give 80 % conversion of A for a second-order liquid phase reaction A → B. Pure A at a concentration 1 kmol/m³ is fed to the reactor at a flow rate of 5 m³/hr The rate constant for the reaction at a specified operating temperature is 0.5 m³/kmol h. When the reactor is actually operated based on this design, it was found that 30 % of the initial reactor behaved as a well-mixed reactor while the remaining behaved as a plug flow reactor. Calculate the conversion obtained in such a reactor.

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Q 10: For an exothermic reaction A → B, 90 kmol of B are to be produced while achieving 90 % conversion of A in an isothermal batch reactor operated at 500 K. The reaction is to be started with pure A at a concentration of 10 kmol/m3. Determine the volume of the reactor, duration of the batch operation, and the total heat removed during the isothermal operation. The heat of the reaction at 500 K is – 40 kJ/mol of A reacted. Following additional information is available to determine the order and rate constant of the reaction. Laboratory experiments conducted at 500 K with 1 kmol/m³ initial concentration of pure A showed that 20 % conversion is obtained in 20 min. while 50 % conversion is obtained in 80 min. The reaction is suspected to be either first or second order.

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