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

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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5

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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6

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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7

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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8

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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9

2009 · Chemical Engineering · Chemical Reaction Engineering · Reaction Kinetics and Ideal Reactors

Chemical Engineering (CH) 2009

For a homogeneous reaction system, where
\( C_j \) is the concentration of \( j \) at time \( t \)
\( N_j \) is the number of moles of \( j \) at time \( t \)
\( V \) is the reaction volume at time \( t \)
\( t \) is the reaction time
The rate of reaction for species \( j \) is defined as

A

\(\frac{dC_j}{dt} \)

B

\(-\left( \frac{dC_j}{dt} \right) \)

C

\(\frac{1}{V} \frac{dN_j}{dt} \)

D

\(-\left( \frac{1}{V} \frac{dN_j}{dt} \right) \)

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10

2009 · Chemical Engineering · Chemical Reaction Engineering · Reaction Kinetics and Ideal Reactors

Chemical Engineering (CH) 2009

The half-life of a first order liquid phase reaction is 30 seconds. Then the rate constant, in \( min^{-1} \), is

A

0.0231

B

0.602

C

1.386

D

2.0

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11

2009 · Chemical Engineering · Chemical Reaction Engineering · Reaction Kinetics and Ideal Reactors

Chemical Engineering (CH) 2009

An isothermal pulse test is conducted on a reactor and the variation of the outlet tracer concentration with time is shown below :
The mean residence time of the fluid in the reactor (in minutes) is

A

5.0

B

7.5

C

10.0

D

15.0

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12

2009 · Chemical Engineering · Chemical Reaction Engineering · Reaction Kinetics and Ideal Reactors

Chemical Engineering (CH) 2009

The rate constant (\( k \)) for this reaction at 50 °C is

A

\(0.2 \left( \frac{\text{gmol}}{\text{liter}} \right)^{0.5} \cdot \text{min}^{-1} \)

B

\(0.2 \left( \frac{\text{liter}}{\text{gmol}} \right)^{0.5} \cdot \text{min}^{-1} \)

C

\(0.4 \left( \frac{\text{gmol}}{\text{liter}} \right)^{0.5} \cdot \text{min}^{-1} \)

D

\(0.4 \left( \frac{\text{liter}}{\text{gmol}} \right)^{0.5} \cdot \text{min}^{-1} \)

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13

2009 · Chemical Engineering · Chemical Reaction Engineering · Reaction Kinetics and Ideal Reactors

Chemical Engineering (CH) 2009

The concentration of A (in gmol/liter) at the exit of the plug flow reactor is

A

0.5

B

1.0

C

2.0

D

2.5

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14

2010 · Chemical Engineering · Chemical Reaction Engineering · Reaction Kinetics and Ideal Reactors

Chemical Engineering (CH) 2010

Two reactors (reactor 1 and reactor 2) with average residence times, τ_1 and τ_2, respectively, are placed in series. Reactor 1 has zero dispersion and reactor 2 has infinite dispersion. The residence-time distribution, E(t) of this system, is given by

A

\(\begin{cases} 0 & t \le \tau_1 \\ \frac{1}{\tau_2} \exp\left(-\frac{t - \tau_1}{\tau_2}\right) & t > \tau_1 \end{cases}\)

B

\(\begin{cases} 0 & t \le \tau_2 \\ \frac{1}{\tau_1} \exp\left(-\frac{t - \tau_2}{\tau_1}\right) & t > \tau_2 \end{cases}\)

C

\(\begin{cases} 0 & t \le \tau_1 \\ \frac{1}{\tau_2} \exp\left(-\frac{t - \tau_1}{\tau_2}\right) & t > \tau_1 \end{cases}\)

D

\(\begin{cases} 0 & t \le \tau_2 \\ \frac{1}{\tau_2} \exp\left(-\frac{t}{\tau_2}\right) & t > \tau_2 \end{cases}\)

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15

2010 · Chemical Engineering · Chemical Reaction Engineering · Reaction Kinetics and Ideal Reactors

Chemical Engineering (CH) 2010

An autocatalytic liquid phase reaction, A + R → 2R is conducted in an isothermal batch reactor with a small initial concentration of R. Assume that the order of reaction with respect to both reactants is positive. The rate of reaction (−r_A) versus concentration, C_A, as the reaction proceeds, is depicted by

A

B

C

D

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16

2010 · Chemical Engineering · Chemical Reaction Engineering · Reaction Kinetics and Ideal Reactors

Chemical Engineering (CH) 2010

A liquid phase reaction, A → B, is conducted isothermally in a CSTR having a residence time of 2 s. The inlet concentration of species A is 2 moles/litre, and the outlet concentration is 1 mole/litre. The rate law for the reaction is −r_A = kC_A/(K + C_A) where k = 5 moles/litre/s.
The value of K, in moles/litre, is

A

11

B

9

C

5

D

2

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17

2010 · Chemical Engineering · Chemical Reaction Engineering · Reaction Kinetics and Ideal Reactors

Chemical Engineering (CH) 2010

If the same reaction is conducted in a series of two CSTRs with residence times 1 s and 0.2 s, then the inlet concentration of A, in moles/litre, required to attain an outlet concentration of A of 1 mole/litre, is

A

2.64

B

2.00

C

1.64

D

0.54

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18

2011 · Chemical Engineering · Chemical Reaction Engineering · Reaction Kinetics and Ideal Reactors

Chemical Engineering (CH) 2011

Reactant R forms three products X, Y and Z irreversibly, as shown below. The reaction rates are given by \(r_X = k_X C_R\), \(r_Y = k_Y C_R^{1.5}\) and \(r_Z = k_Z C_R\). The activation energies for formation of X, Y and Z are 40, 40 and 5 kJ/mol respectively. The pre-exponential factors for all reactions are nearly same. The desired conditions for MAXIMIZING the yield of X are

A

high temperature, high concentration of R

B

high temperature, low concentration of R

C

low temperature, high concentration of R

D

low temperature, low concentration of R

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19

2011 · Chemical Engineering · Chemical Reaction Engineering · Reaction Kinetics and Ideal Reactors

Chemical Engineering (CH) 2011

The following figures show the outlet tracer concentration profiles (c vs. t) for a pulse input.
Match the figures in Group I with the reactor configurations in Group II.
GROUP I
P. Figure 1
Q. Figure 2
R. Figure 3
GROUP II
I. PFR
II. CSTR
III. PFR and CSTR in series
IV. PFR and CSTR in parallel

A

P – II, Q – IV, R – III

B

P – IV, Q – III, R – I

C

P – III, Q – IV, R – II

D

P – I, Q – III, R – II

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20

2011 · Chemical Engineering · Chemical Reaction Engineering · Reaction Kinetics and Ideal Reactors

Chemical Engineering (CH) 2011

In an aqueous solution, reaction \(P \rightarrow Q\) occurs under isothermal conditions following first order kinetics. The feed rate is 500 cm\(^3\)/min and concentration of P in the feed is \(1.5\times10^{-3}\) mol/cm\(^3\). The reaction is carried out in a 5 litre CSTR. At steady state, 60 % conversion is observed. The rate constant (in min\(^{-1}\)) is

A

0.06

B

0.15

C

0.21

D

0.28

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