Chemical Reaction Engineering GATE-2007

Q 1: A well-stirred reaction vessel is operated as a semi-batch reactor in which it is proposed to conduct a liquid phase first-order reaction of the type A → B. The reactor is fed with the reactant A at a constant rate of 1 litre/min having feed concentration equal to 1 mol/litre. The reactor is initially empty. Given k = 1 min^-1, the conversion of reactant A based on moles of A fed at t = 2 min is

A) 0.136
B) 0.43
C) 0.57
D) 0.864

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Q 2: A liquid phase exothermic first-order reaction is being conducted in a batch reactor under isothermal conditions by removing heat generated in the reactor with the help of cooling water. The cooling water flows at a very high rate through a coil immersed in the reactor such that there is a negligible rise in its temperature from the inlet to the outlet of the coil. If the rate constant is given as k, the heat of reaction (–ΔH), volume of the reactor, V, initial concentration as CA0, overall heat transfer coefficient, U, and heat transfer area of the coil is equal to A, the required cooling water inlet temperature, T_ci is given by the following equation:

A) T_{ci}=T-\frac{\left(-\triangle H\right)VkC_{A0}}{UA}
B) T_{ci}=T-\frac{\left(-\triangle H\right)VkC_{A0}e^{-kt}}{UA}
C) T_{ci}=T-\frac{\left(-\triangle H\right)VC_{A0}e^{-kt}}{UAt}
D) T_{ci}=T-\frac{\left(-\triangle H\right)VC_{A0}}{UAt}

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Q 3: The following liquid phase reaction is taking place in an isothermal CSTR

A\xrightarrow{k_1}B\xrightarrow{k_2}C 2A\xrightarrow{k_3}D

The reaction mechanism is the same as the stoichiometry given above. Given k₁ = 1 min^-1; k₂ = 1 min^-1; k₃ = 0.5 lit/(mol)(min); C_A0 = 10 mol/litre, C_B0 = 0 mol/litre and C_B = 10 mol/litre, the solution for F/N (flow rate/reactor volume in min^-1) yields

A) 6.7
B) 6 and 0.5
C) 2 and 4/3
D) 8

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Q 4: A pulse of concentrated KCl solution is introduced as a tracer into the fluid entering a reaction vessel having a volume equal to 1 m³ and flow rate equal to 1 m³/min. The concentration of tracer measured in the fluid leaving the vessel is shown in the figure given below.

The flow model parameters that fit the measured RTD in terms of one or all of the following mixing elements, namely, the volume of plug flow reactor, V_p, mixed flow volume, V_m, and dead space, V_d, are  

A) V_p = 1/6 m³, V_m = 1/2 m³, V_d= 1/3 m³
B) V_p = V_m = V_d = 1/3 m³
C) V_p = 1/3 m³, V_m = 1/2 m³, V_d = 1/6 m³
D) V_m = 5/6 m³, V_d = 1/6 m³

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Q 5: 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.

dp	FA0	XA
4	2	0.8
6	4	0.4

A) Strong pore diffusion control
B) Diffusion free
C) Intermediate role by pore diffusion
D) External mass transfer

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Q 6: A packed bed reactor converts A to R by first-order reaction with 9 mm pellets in a strong pore diffusion regime to 63.2 % level. If 18 mm pellets are used what is the conversion?

A) 0.39
B) 0.61
C) 0.632
D) 0.865

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Q 7: The following rate-concentration data are calculated from the experiment. Find the activation energy temperature (E/R) of the first-order reaction.

dp	CA	-rA	T
1	20	1	480
2	40	2	480
2	40	3	500

A) 2432.8
B) 4865.6
C) 9731.2
D) 13183.3

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Q 8: Determine the level of C_A0 (high, low, intermediate), and temperature profile (high, low, increasing, decreasing), which will favor the formation of the desired product indicated in the reaction scheme given below.

A\xrightarrow1R\xrightarrow3S_{desired} A\xrightarrow2U

n1	E1	n2	E2	n3	E3
2	25	1	35	3	45

A) High C_A0, increasing T, Plug flow reactor
B) Low C_A0, increasing T, Plug flow reactor
C) High C_A0, decreasing T, Mixed flow reactor
D) High C_A0, decreasing T, Plug flow reactor

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Common data for questions Q 9 & 10:

Q 9: The following liquid phase reaction is taking place in an isothermal batch reactor

A\xrightarrow{k_1\left(first\;order\right)}B\xrightarrow{k_2\left(zero\;order\right)}C

Feed concentration = 1 mol/litre. The time at which the concentration of B will reach its maximum value is given by

A) t=\frac1{k_1}\ln\left(\frac{k_1}{k_2}\right)
B) t=\frac1{k_2-k_1}\ln\left(\frac{k_2}{k_1}\right)
C) t=\frac1{k_2}\ln\left(\frac{k_2}{k_1}\right)
D) t=\frac1{k_2}\ln\left(\frac{k_1}{k_2}\right)

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Q 10: The time at which the concentration of B will become zero is given by the following equation:

A) (1-e^{-k_1t})=k_2t
B) t=\infty
C) t=\frac1{k_2}
D) t=\frac1{k_1}