Reaction Kinetics and Ideal Reactors - Chemical Reaction Engineering - Chemical Engineering Previous Year Questions

1

2007 · Chemical Engineering · Chemical Reaction Engineering · Reaction Kinetics and Ideal Reactors

Chemical Engineering (CH) 2007

Vapor phase hydration of C₂H₄ to ethanol by the following reaction
C₂H₄ (g) + H₂O (g) ↔ C₂H₅OH (g)
attains equilibrium at 400 K and 3 bar. The standard Gibbs free energy change of reaction at these conditions is ΔG° = 4000 J/mol. For 2 moles of an equimolar feed of ethylene and steam, the equation in terms of the extent of reaction ε (in mols) at equilibrium is

A

\(\frac{\varepsilon(2-\varepsilon)}{(1-\varepsilon)^2} - 0.3 = 0\)

B

\(\frac{(1-\varepsilon)^2}{\varepsilon(2-\varepsilon)} - 0.9 = 0\)

C

\(\frac{\varepsilon}{(1-\varepsilon)^2} - 0.3 = 0\)

D

\(\frac{\varepsilon(2-\varepsilon)}{(1-\varepsilon)} - 0.9 = 0\)

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2

2007 · Chemical Engineering · Chemical Reaction Engineering · Reaction Kinetics and Ideal Reactors

Chemical Engineering (CH) 2007

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 liter/min having feed concentration equal to 1 mol/liter. 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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3

2007 · Chemical Engineering · Chemical Reaction Engineering · Reaction Kinetics and Ideal Reactors

Chemical Engineering (CH) 2007

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 negligible rise in its temperature from inlet to outlet of the coil. If the rate constant is given as k, heat of reaction (-ΔH), volume of the reactor, V, initial concentration as C_A0, overall heat transfer coefficient, U, 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

\(T_{ci} = T - \frac{(-\Delta H)V k C_{A0}}{UA}\)

B

\(T_{ci} = T - \frac{(-\Delta H)V k C_{A0} e^{-kt}}{UA}\)

C

\(T_{ci} = T - \frac{(-\Delta H)V C_{A0} e^{-kt}}{UAt}\)

D

\(T_{ci} = T - \frac{(-\Delta H)V C_{A0}}{UAt}\)

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4

2007 · Chemical Engineering · Chemical Reaction Engineering · Reaction Kinetics and Ideal Reactors

Chemical Engineering (CH) 2007

The following liquid phase reaction is taking place in an isothermal CSTR
\[ A \xrightarrow{k_1} B \xrightarrow{k_2} C \]
\[ 2A \xrightarrow{k_3} D \]
Reaction mechanism is 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 = 1 mol/litre, the solution for F/V (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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5

2007 · Chemical Engineering · Chemical Reaction Engineering · Reaction Kinetics and Ideal Reactors

Chemical Engineering (CH) 2007

The following rate-concentration data are calculated from 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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6

2007 · Chemical Engineering · Chemical Reaction Engineering · Reaction Kinetics and Ideal Reactors

Chemical Engineering (CH) 2007

Determine the level of C_A0 (high, low, intermediate), temperature profile (high, low, increasing, decreasing) which will favor the formation of the desired product indicated in the reaction scheme given below.
A --(1)--> R --(3)--> S_desired
A --(2)--> U

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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7

2007 · Chemical Engineering · Chemical Reaction Engineering · Reaction Kinetics and Ideal Reactors

Chemical Engineering (CH) 2007

The following liquid phase reaction is taking place in an isothermal batch reactor
\[ A \xrightarrow{k_1 \text{ (first order)}} B \xrightarrow{k_2 \text{ (zero order)}} C \]
Feed concentration = 1mol/litre
The time at which the concentration of B will reach its maximum value is given by

A

\(t = \frac{1}{k_1} \ln \left( \frac{k_1}{k_2} \right) \)

B

\(t = \frac{1}{k_2 - k_1} \ln \left( \frac{k_2}{k_1} \right) \)

C

\(t = \frac{1}{k_2} \ln \left( \frac{k_2}{k_1} \right) \)

D

\(t = \frac{1}{k_2} \ln \left( \frac{k_1}{k_2} \right) \)

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8

2007 · Chemical Engineering · Chemical Reaction Engineering · Reaction Kinetics and Ideal Reactors

Chemical Engineering (CH) 2007

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

A

\(\left( 1 - e^{-k_1 t} \right) = k_2 t \)

B

\(t = \infty \)

C

\(t = \frac{1}{k_2} \)

D

\(t = \frac{1}{k_1} \)

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9

2008 · Chemical Engineering · Chemical Reaction Engineering · Reaction Kinetics and Ideal Reactors

Chemical Engineering (CH) 2008

Air (79 mole % nitrogen and 21 mole % oxygen) is passed over a catalyst at high temperature. Oxygen completely reacts with nitrogen as shown below
\( 0.5 N_{2(g)} + 0.5 O_{2(g)} \rightarrow NO_{(g)} \)
\( 0.5 N_{2(g)} + O_{2(g)} \rightarrow NO_{2(g)} \)
The molar ratio of NO to NO\(_2\) in the product stream is 2:1. The fractional conversion of nitrogen is

A

0.13

B

0.20

C

0.27

D

0.40

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10

2008 · Chemical Engineering · Chemical Reaction Engineering · Reaction Kinetics and Ideal Reactors

Chemical Engineering (CH) 2008

The standard Gibbs free energy change and enthalpy change at 25°C for the liquid phase reaction \( CH_3COOH_{(l)} + C_2H_5OH_{(l)} \rightarrow CH_3COOC_2H_{5(l)} + H_2O_{(l)} \) are given as \( \Delta G^\circ_{298} = -4650 \) J/mol and \( \Delta H^\circ_{298} = -3640 \) J/mol. If the solution is ideal and enthalpy change is assumed to be constant, the equilibrium constant at 95°C is

A

0.65

B

4.94

C

6.54

D

8.65

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11

2008 · Chemical Engineering · Chemical Reaction Engineering · Reaction Kinetics and Ideal Reactors

Chemical Engineering (CH) 2008

The gas phase reaction \( A + 3 B \rightarrow 2 C \) 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 rates (\( F_{A,in}: F_{B,in}: F_{I,in} \)) 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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12

2008 · Chemical Engineering · Chemical Reaction Engineering · Reaction Kinetics and Ideal Reactors

Chemical Engineering (CH) 2008

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
\[ r_R = k' C_A \]
\[ r_B = k C_A - k C_B \]
Feed is pure A. The space time of the CSTR which results in the maximum exit concentration of B is given by

A

\(\frac{1}{\sqrt{k k'}} \)

B

\(\frac{1}{\sqrt{k' (k + k')}} \)

C

\(\frac{1}{(k + k')} \)

D

\(\frac{1}{\sqrt{k (k + k')}} \)

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13

2008 · Chemical Engineering · Chemical Reaction Engineering · Reaction Kinetics and Ideal Reactors

Chemical Engineering (CH) 2008

The liquid phase reaction \( A \rightarrow \) Products is governed by the kinetics
\[ -r_A = k C_A^{1/2} \]
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

\(\infty \)

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14

2008 · Chemical Engineering · Chemical Reaction Engineering · Reaction Kinetics and Ideal Reactors

Chemical Engineering (CH) 2008

The selectivity for desired product relative to undesired product is

A

2.3

B

3.5

C

7

D

8

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15

2008 · Chemical Engineering · Chemical Reaction Engineering · Reaction Kinetics and Ideal Reactors

Chemical Engineering (CH) 2008

The fractional yield of CO2 is (where fractional yield is defined as the ratio of moles of the desired product formed to the moles that would have been formed if there were no side reactions and the limiting reactant had reacted completely)

A

0.7

B

0.88

C

1

D

3.5

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16

2008 · Chemical Engineering · Chemical Reaction Engineering · Reaction Kinetics and Ideal Reactors

Chemical Engineering (CH) 2008

The fractional conversion of methane is

A

0.4

B

0.5

C

0.7

D

0.8

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17

2008 · Chemical Engineering · Chemical Reaction Engineering · Reaction Kinetics and Ideal Reactors

Chemical Engineering (CH) 2008

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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18

2008 · Chemical Engineering · Chemical Reaction Engineering · Reaction Kinetics and Ideal Reactors

Chemical Engineering (CH) 2008

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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19

2008 · Chemical Engineering · Chemical Reaction Engineering · Reaction Kinetics and Ideal Reactors

Chemical Engineering (CH) 2008

The conversion achieved by the CSTR is

A

40%

B

50%

C

60%

D

80%

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20

2008 · Chemical Engineering · Chemical Reaction Engineering · Reaction Kinetics and Ideal Reactors

Chemical Engineering (CH) 2008

The volume of the PFR required (in liters) is

A

380

B

350

C

75

D

35

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