CH_Chemical-Reaction-Engineering (1).pdf

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GATE SOLVED PAPER Chemical Engineering Chemical Reaction Engineering Copyright © By NODIA & COMPANY

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GATE SOLVED PAPER - CH CHEMICAL REACTION ENGINEERING

YEAR 2011 Q. 1

ONE MARK

Reactant R forms three products X , X , Y and Y and Z irreversibly, Z irreversibly, as shown below.

Y N A P M O C & A I ^ h ^ h D ^h O N © 1.5

The reaction rates are given by rX = kX C R , rY = kY C R and rZ = kZ C R . The activation energies for formation of X , X , Y Y and Z 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 X are (A) high temperature, high concentration of R (B) high temperature, temp erature, low concentration of R (C) low temperature, high concentration of R (D) low temperature, low concentration of R Q. 2

Consider an irreversible, solid catalysed, liquid phase first order reaction. The diffusion and the reaction resistances are comparable. The overall rate constant K C k m C is related to the overall mass transfer coefficient m and the reaction rate constant k as (A)

k c =

(C)

k c =

kk m k + k m k + k m

2

k + k m kk m

(B)

k c =

(D)

kc = k + k m

YEAR 2011 Q. 3

TWO MARKS

^h

For a first order catalytic reaction, the Thiele modulus φ of a spherical pellet is defined as φ

where,

=

Rp

3

k ρ p D e

ρ p = pellet

density R p = pellet radius D e e = effective diffusivity k = first order reaction rate constant If φ > 5 , then the apparent activation energy E a a is related to the intrinsic (or true) activation energy E as (A) Ea = E 0.5 (B) Ea = 0.5 E (C) Ea = 2E (D) Ea = E 2

^h

^ h

GATE SOLVED PAPER - CH

Q. 4

CHEMICAL REACTION ENGINEERING

The following figures show the outlet tracer concentration profiles (cvst) for a pulse input.

Match the figures in Group I with the reactor configurations in Group II. Group I

Group II

Y N A P M O C & A I D O N © P. Figure 1

I.

PFR

Q. Figure 2

II. CSTR

R. Figure 3

III. PFR and CSTR in series

IV. PFR and CSTR in parallel (B) P-IV, Q-III, R-I (D) P-I, Q-III, R-II

(A) P-II, Q-IV, R-III (C) P-III, Q-IV, R-II

Statement For Linked Answer Q. 5 and 6 : Q. 5

In an aqueous solution, reaction P Q occurs under isothermal conditions following first order kinetics. The feed rate is 500 cm3 / min and concentration of P in the feed is 1.5 # 10 4 mol/cm3 . The reaction is carried out in a 5 L 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 "

-

Q. 6

The 5 L CSTR is replaced by five CSTRs in series. If the capacity of each new CSTR is 1 L, then the overall conversion (in percentage) is (A) 65 (B) 67 (C) 73 (D) 81 YEAR 2010

Q. 7

ONE MARK

For a first order isothermal catalytic reaction A P , occurring in an infinitely long cylindrical pore, the relationship between effectiveness factor ε , and Thiele modulus φ , is "

(A) ε = (C)

ε

=

1

φ2

1

(B) ε = φ (D) ε = 1

φ

YEAR 2010 Q. 8

-

TWO MARKS

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

^h


(A)

(C)

* *

1 t2

1 t1

c

0

t − t 1 exp −

exp

c

t 2

0 −

t − t 1 t 2


for t # t 1

m for t

>

t 1

(B)

for t > t 2

m for t

>

t 2

(D)

* *

1 t1

c

0

t − t 2 exp − t 1

t2

exp

m for t

>

t 2

for t # t 1

0 1

for t # t 2

c t m for t −

t 1

>

t 2

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

Q. 9

"

^ h

Y N A P M O C & A I D O N ©

Statement For Linked Answer Q. 10 and 11 :

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 mol/L , and the outlet concentration "

is 1 mol/L . The rate law for the reaction is Q. 10

Q. 11

The value of K in mol/L, is (A) 11 (C) 5

− r A =

kC A where, K + C A

(B) 9 (D) 2

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 mol/L, required to attain an outlet concentration of A of 1 mol/L , is (A) 2.64 (B) 2.00 (C) 1.64

(D) 0.54

YEAR 2009 Q. 12

k = 5 mol/L -s.

ONE MARK

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)

dC j dt

(B)

-

c dC m dt j



dN j (C) 1

(D)

V dt

Q. 13

-

cV 1 dN m dt j

The half-life of a first order liquid phase reaction is in min 1 , is (A) 0.0231 (B) 0.602 (C) 1.386 (D) 2.0

30 s .

Then the rate constant

-

Q. 14

For a solid-catalyzed reaction, the Thiele modulus is proportional to (A)

Intrinsic reaction rate Diffusion rate

(B)

Intrinsic reaction rate Diffusion rate

Diffusion rate Intrinsic reaction rate Diffusion rate Intrinsic reaction rate

Y N A P M O C & A I D O N © (C)

(D)

YEAR 2009

Q. 15

TWO MARKS

The liquid-phase reaction A B is conducted in an adiabatic plug flow reactor. Data Inlet concentration of A = 4.0 kmol/m3 Density of reaction moisture (independent of temperature) = 1200 kg/m 3 Average heat capacity of feed stream (independent of temperature) 2000 J/ kg K Heat of reaction (independent of temperature) 120 kJ/mol of A reacting If the maximum allowable temperature in the reactor is 800 K , then the feed temperature (in cK ) should not exceed. (A) 400 (B) 500 (C) 600 (D) 700 "

=

−

=−

Q. 16

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 min) is (A) 5.0 (B) 7.5 (C) 10.0 (D) 15.0

Statement For Linked Answer Q. 17 and 18 : The liquid-phase reaction A B + C is conducted isothermally at 50cC in a Continuous stirred Tank Reactor (CSTR). The inlet concentration of A is 8.0 g-mol/L . At a space time of 5 min, the concentration of A at the exit of CSTR is 4.0 g-mol/L . The kinetics of the reaction is 0.5 - r A kC A g mol/L min A plug flow reactor of the same volume is added in series after the existing CSTR. "

=

−

−


Q. 17

^h

The rate constant k for this reaction at

cg g (C) 0.4 c

- mol

0.5

-

0.5

m L mol m L

(A) 0.2

Q. 18


50cC is

cg (D) 0.4 c g

. min-1 -1

. min

0.5

m L m mol

L - mol

(B) 0.2

0.5

-

. min-1 . min-1

The concentration of A (in g-mol/L) at the exit of the plug flow reactor is (A) 0.5 (B) 1.0 (C) 2.0 (D) 2.5 YEAR 2008

Q. 19

ONE MARK

^h

A species A reacts on a solid catalyst to produce R and S as follows 2 1. A R rR = k1 C A 2 2. A S rS = k 2 C A Assume film resistance to mass transfer is negligible. The ratio of 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 "

Y N A P M O C & A ^ I D O N © "

YEAR 2008

Q. 20

Q. 21

TWO MARKS

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 l . It is found that the concentration of A remains the same throughout the reactor Which one of the following ratios of inlet molar rate FA, in : FB, in : F l , 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 "

h

The elementary liquid phase series paallel reaction scheme A

"

B

A

"

R

"

C

is to be carried out in an isothermal CSTR. The rate laws are given by rR = K'C A rB

=

kCA

−

kCB

Feed is pure A. The space time of the CSTR which results in the maximum exit concentration of B is given by (A) (C) Q. 22

1

kk '

1

^k k h + '

(B)

(D)

1

^ h k ^k k h k' k + k ' 1

+ '

^ h

1/2 The liquid phase reaction A Products is governed by the kinetics, rA k C A If the reaction undergoes 75% conversion of A in 10 min in an isothermal batch reactor, the time (in min) for complete conversion of A is (A) 40/3 (B) 20 (C) 30 (D) infinite "

−

=


Q. 23

The homogeneous reaction A + B C is conducted in an adiabatic CSTR at 8000 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 J/(mol K ), C p, C 150 J/ mol K 100 kJ/mol C p, B 50 J/ mol K , ∆h rxn 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 "

=

^

=

Q. 24


−

−

h

^

=

−

h

=−

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 concentration and neglect any variations in the axial direction. "

Y N A P M O C &:a k D A I D O N © z

The steady state concentration profile is 2

φ0 C A =1+ 4 C AS

r R

2

−1

,

where φ 0 is the Thiele modulus. For φ 0 = 4 , the range of r , where C A = 0 , is

(A)

0 < r <

R 4

(C) 0 # r # R

(B)

0 < r <

R 2

(D) 0 # r # R

Common Data For Questions. 25 and 26 :

A liquid is flowing through a reactor at a constant flow rate. A step input of 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.

^h

Q. 25

The volumetric flow rate of the liquid through the reactor (in L/min) is (A) 1 (B) 2 (C) 1.5 (D) 4

Q. 26

The mean residence time of the fluid in the reactor (in min) is (A) 1 (B) 2



(C) 3

(D) 4

Statement For Linked Answer Q. 27 and 28 : The liquid phase reaction A Products 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 L. Pure A is fed to the CSTR at a concentration C A0 = 2 mol/L and a volumetric flow rate of 4 L/min. The kinetics of the reaction is given by 0.1 C A2 mol/L min - r A "

=

Q. 27

Q. 28

−

The conversion achieved by the CSTR is (A) 40% (B) 50% (C) 60% (D) 80%

Y N A P M O C & A I D O N © ^ h The volume of the PFR required (in litre) is (A) 380 (B) 350 (C) 75 (D) 35 YEAR 2007

Q. 29

Q. 30

Q. 31

TWO MARKS

A well-stirred reaction vessel is operated as a semibatch 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 L/min having feed concentration equal to 1 mol/L . 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 "

=

−

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 - ∆H , volume of the reactor V , initial concentration as C A , 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) Tci

=

T

−

(C) Tci

=

T

−

−

h h

∆H VkC A

UA

0

∆H VCA e

UAt

(B)

Tci

−

=

T

−

=

T

−

kt

−

0

(D) Tci

^ ^

−

h h

0

∆H VkCA e

kt

−

0

UA

∆H VC A

0

UAt

The following liquid phase reaction is taking place in an isothermal CSTR k k k A B C ; 2A D Reaction mechanism is same as the stoichiometry given above. Given k 1 1 min 1 ; k 2 1 min 1 ; k 3 0.5 L/mol min ; C A = 10 mol/L , C B = 0 mol/L and 1 C B = 1 mol/L , the solution for F/V (flow rate/reactor volume in min ) yields (A) 6.7 (B) 6 and 0.5 (C) 2 and 4/3 (D) 8 1

3

2

=

=

−

=

−

0

0

-

−


Q. 32


A pulse of concentrated KCl solution is introduced as tracer into the fluid entering a reaction vessel having volume equal to 1 m 3 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, volume of plug flow reactor V p , mixed flow volume V m , and dead space V d , are

Y N A P M O C & A I D O N © (A) V p = 1/6 m 3 , V m = 1/2 m 3 , V d = 1/3 m 3 (B) Vp = Vm = V d = 1/3 m 3 (C) V p = 1/3 m 3 , V m = 1/2 m 3 , V d = 1/6 m 3 (D) V m = 5/6 m 3 , V d = 1/6 m 3

Q. 33

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 A is 100 and W is fixed. Agitation rate was found to have no effect on conversion. d p

F A0

X A

4

2

0.8

0

6 4 0.4 (A) Strong pore diffusion control (B) Diffusion free (C) Intermediate role by pore diffusion (D) External mass transfer

Q. 34

Q. 35

Q. 36

A packed bed reactor converts A to R by first order reaction with 9 mm pellets in 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 The following rate concentration data are calculated from experiment. Find the activation energy temperature E/R of the first order reaction.

^ h

d p

C A

- r A

T

1

20

1

480

2

40

2

480

2 (A) 2432.8 (C) 9731.2

40

3

500 (B) 4865.6 (D) 13183.3

Determine the level of C A (high, low, intermediate), temperature profile (high, low, increasing, decreasing), which will favour the formation of the desired product indicated in the reaction scheme given below 0


1

A

3

R

n 1


S (desired); A

E 1

n 2

2

U

E 2

n 3

E 3

2 25 1 35 3 (A) High C A , increasing T , plug flow reactor (B) Low C A , increasing T , plug flow reactor (C) High C A , decreasing T , mixed flow reactor (D) High C A , decreasing T , plug flow reactor

45

0

0

0

0

Common Data For Questions. 37 and 38 : The following liquid phase reaction is taking place in an isothermal batch reactor

^

k1 first order

A

Q. 38

B

^

k 2 zero order

h

C

Y N c m c m A P c m c m M O C & A I D O N ^ h © ^ h

Feed concentration Q. 37

h

=

1 mol/L

The time at which the concentration of by (A)

t =

(C)

t =

Β

will reach its maximum value is given

k 1 1 ln k1 k 2

(B)

t

k 2 1 ln k2 k 1

(D)

t =

=

1

k2

−

k1

ln

k 2 k 1

k 1 1 ln k2 k 2

The time at which the concentration of B will become zero is given by the following equation (A) 1 e k t k2 t (B) t = 3 (C) t = 1 (D) t = 1 −

−

1

=

k 2

k 1

YEAR 2006

Q. 39

ONE MARK

The reaction 2A + B 2C occurs on a catalyst surface. The reactants A and B diffuse to the catalyst surface and get converted completely to the product C , which diffuses back. The steady state molar fluxes of A, B and C are related by (A) NA = 2NB = N C (B) NA 1/2 NB N C (C) NA 2NB (D) NA = 1/2 NB = N C N C "

=−

=

=−

=−

Q. 40

An irreversible gas phase reaction A 5B is conducted in an isothermal batch reactor at constant pressure in the presence of an inert. The feed contains no B . If the volume of the gas at complete conversion must not exceed three times the initial volume, the minimum mol % of the inert in the feed must be (A) 0 (B) 20 (C) 33 (D) 50

Q. 41

A first order reversible reaction A k B occurs in a batch reactor. The exponential decay of the concentration of A has the time constant (A) 1 (B) 1 k 1 k 2

"

k 1

2

(C)

1 k1 - k 2

(D)

1 k1 +

k 2



YEAR 2006 Q. 42

TWO MARKS

The rate, at which an antiviral drug acts, increases with its concentration in the blood C , according to the equation r

=

kC C 50 + C

where, C 50 is the concentration at which the rate is 50% of the maximum rate k . Often, the concentration C 90 , when the rate is 90% of the maximum, is measured instead of C 50 . The rate equation then becomes (A)

1.8 kC C 90 + C

(B)

r =

kC

b

C 90 + C 9

l

Y N A P M O C & A I ^ D h O N ^ h © (C)

Q. 43

r =

r =

kC C 90

(D)

r =

0.9 kC C 90

Consider the following reactions between gas A and two solid spherical particles B and C of the same size. k gaseous product, A + B k ash A + C The ash does not leave the particle C . Let t 1 and t 2 be the times required for A to completely consume particles B and C , respectively. If k 1 and k 2 are equal at all temperatures and the gas phase mass transfer resistance is negligible, then (A) t1 = t 2 at all temperatures (B) t1 = t 2 at high temperatures (C) t1 > t 2 at high temperatures (D) t1 < t 2 at high temperatures 1

2

Q. 44

Q. 45

A reaction A B is to be conducted in two CSTRs in series. The steady state conversion desired is X f . The reaction rate as a function of conversion is given by r = − 1/ 1 + X . If the feed contains no B , then the conversion in the first reactor that minimizes the total volume of the two reactors is (A) 1 - X f (B) 0.2 X f (C) 0.5 X f (D) 0.5 1 - X f "

Consider the following elementary reaction network

The activation energies for the individual reactions are E 1 = 100 kJ/mol , E 2 = 150 kJ/mol , E 3 = 100 kJ/mol , and E 4 = 200 kJ/mol . If the feed is pure A and the desired product is C , then the desired temperature profile in a plug flow reactor in the direction of flow should be (A) constant at low temperature (B) constant at high temperature (C) increasing (D) decreasing Q. 46

^h

t / 1 e The exit gage distribution in a stirred reactor is given by E t . Fluid elements e 1 and e 2 enter the reactor at times t = 0 and t = θ > 0 , respectively. The probability that e 2 exits the reactor before e 1 is (A) 12 (B) 12 e θ/τ (C) e θ/τ (D) 0 -

-

=

−

t

t



YEAR 2005 Q. 47

ONE MARK

For the reaction 2R + S T , the rates of formation r R , r S and r T of the substances R, S and T respectively, are related by (A) 2rR = rS = r T (B) 2rR rS r T (C) rR = 2rS = 2r T (D) rR 2rS 2r T "

=

=

Q. 48

Q. 49

=−

=−

For the liquid phase reaction A P , in a series of experiments in a batch reactor, the half-life t 1/2 was found to be inversely proportional to the square ro ot of the initial concentration of A. The order of the reaction is "

^ h

(A)

3 2

(C)

+

(B) 1 1 2

(D)

-

1 2

Y ^h N A P M O C & A I ^ h^ h ^ h^ D ^ h^ ^ h^ h O N ©

Which is the correct statement from the following statements on the Arrhenius model of the rate constant k Ae E/RT ? (A) A is always dimensionless (B) For two reactions 1 and 2, if A1 = A2 and E1 > E 2 , then k1 T > k2 T (C) For a given reaction, the percentage change of k with respect to temperature is higher at lower temperatures (D) The percentage change of k with respect to temperature is higher for higher A −

=

YEAR 2005

^h

TWO MARKS

2

Q. 50

k1 C A

The rate expression for the reaction of A is given by − r A = 1/2 . The units 1 + k 2 C A of k 1 and k 2 are respectively, (A) mol 1 m3 s 1 , mol 1/2 m 3/2 (B) mol 1 m3 s 1 , mol1/2 m3/2 (C) mol m 3 s 1 , mol1/2m 3/2 s 1 (D) mol 1 m3 s 1 , mol 1/2 m3/2 s 1/2 -

-

-

Q. 51

-

-

-

-

-

-

-

-

-

h

-

h

The first order liquid phase reaction A P is to be carried out isothermally in the following ideal reactor configurations (P) A 1 m3 CSTR followed by a 1 m3 PFR, (Q) A 2 m3 CSTR (R) A 1 m3 PFR followed by a 1 m 3 CSTR, (S) A 1 m3 CSTR followed by a 1 m3 CSTR, The overall exit conversions X , for the above configurations P , Q , R and S , assuming indentical inlet conditions and temperature, are related as (A) XP > XR > XS > XQ (B) XP = XR > XS > XQ (C) XP = XS = XQ = XR (D) XQ > XP > XR > XS "

Q. 52

The gas phase reaction A B + C is carried out in an ideal PFR achieving 40% conversion of A. The feed has 70 mol% A and 30 mol% inerts. The inlet temperature is 300 K and the outlet temperature is 400 K . The ratio of te outlet to inlet molar concentration of A (assuming ideal gas mixture and uniform pressure) is (A) 0.60 (B) 0.30 (C) 0.47 (D) 0.35

Q. 53

Match the items in Group I with those in Group II.

"



Group I

Group II

P. Porous catalyst

I.

Q. Parallel reactions

II. Shrinking core model

R. Non-ideal tubular reactor

III. Thiele modulus

S. Gas-solid non-catalytic reaction (A) P-3, Q-1, R-4, S-2 (C) P-1, Q-4, R-2, S-3 Q. 54

Selectivity

IV. Dispersion number (B) P-1, Q-3, R-2, S-4 (D) P-3, Q-4, R-1, s-2

^

h

The rate of the liquid phase reversible reaction A 2B in kmol/m3-min at 298 K , is rA 0.02 CA 0.01C B where the concentrations C A and C B are expressed in kmol/m3 . What is the maximum limiting conversion of A achievable in an isothermal CSTR at 298 K, assuming pure A is fed at the inlet? (A) 1 (B) 2/3 (C) 1/2 (D) 1/3

Y N A P M ^h O C & A I D O N © ^

−

=

−

h

Statement For Linked Answer Q. 55 and 56 :

The residence time distribution E t (as shown below) of a reactor is zero until 3 min and then increases linearly to a maximum value E at 8 min after which it decreases linearly back to zero at 15 min . max

Q. 55

Q. 56

What is the value of E (A) 1/6 (C) 1/4

max

? (B) 1/8 (D) 1/3

What is the value of the mean residence time in min? (A) 5.7 (B) 8 (C) 8.7 (D) 12 YEAR 2004

Q. 57

ONE MARK

The rate expression for the gaseous phase reaction CH 3OH is

CO + 2H 2

given by γ

β α r k1 p co pH k 2 p CH OH Which of the following is not possible? (A) α = 1, β = 1, γ = 1 (B) (C) α = 1/3 , β = 2/3 , γ = 1/3 (D) =

2

−

3

1, β = 2 , γ = 1 α = 1/2 , β = 1, γ = 1/2 α

=


Q. 58


The rate of ammonia synthesis for the reaction 2NH 3 is

N 2 + 3H 2

3 r 0.8pN p H If the reaction is represented as, =

2

1 3 N2 + H2 2 2

2

2

−

=

Q. 59

Q. 60

^

2

−

2

2

0.6p NH

3

1 NH 3 , 2

The rate of ammonia synthesis is (A) r 0.8 p N0.5 p H1.5 0.6 p NH 2 (C) r 0.5 0.8 p N p H3 0.6 p NH =

given by

3

2

−

3

h

(B) (D)

r r

3

=

=

0.8 p N p H

^

2

2

2

0.6 p NH

−

0.5 1. 5 p N2 p H2

0.5 0.8

−

3

0.6 p NH

3

h

An endothermic aqueous phase first order irreversible reaction is carried out in an adiabatic plug flow reactor. The rate of reaction (A) is maximum at the inlet of the reactor (B) goes through a maximum along the length of the reactor (C) goes through a minimum along the length of the reactor (D) is maximum at the exit of the reactor

Y N A ^ M h P ^ h O ^ h C & A I D O N ©

A first order gaseous phase reaction is catalyzed by a non-porous solid. The kinetic rate constant and the external mass transfer coefficient are k and k g , respectively. The effective rate constant k eff is given by k + k g (A) k eff = k + k g (B) k eff = 2

(D) 1 k eff

1 2

(C) k eff = kk g

Q. 61

=

1

k

+

1

k g

For a packed bed reactor, the presence of a long tail in the residence time distribution curve is an indication of (A) ideal plug flow (B) bypass (C) dead zone (D) channeling YEAR 2004

Q. 62

TWO MARKS

The following has phase reaction is taking place in a plug flow reactor, A+

1 B 2

"

C

A stoichiometric mixture of A and B at 300 K is fed to the reactor. At 1 m along the length of the reactor, the temperature is 360 K . the pressure drop is negligible and an ideal gas behaviour can be assumed. Identify the correct expression relating the concentration of A at the inlet C A , concentration of A at 1 m C A and the corresponding conversion of A X .

^ h

(A) CA (C) CA Q. 63

=

=

1.2 C A

^ h ^h ^ h ^ h ^ h ^ h 0

^ ^ ^ ^

1

0

0.83C A

1

−

−

0.33 X

1

0

1

h h h h

X

−

−

X

0.33X

(B) (D)

CA CA

=

=

1.2 C A

1

0

0.83C A

1

−

−

1

0

1

X

0.5 X −

−

X

0.5X

A second order liquid phase reaction A B is carried out in a mixed flow reactor operated in semi-batch mode (no exit stream). The reactant A at concentration C AF is fed to the reactor at a volumetric flow rate of F . The volume of the reacting mixture is V and the density of the liquid mixture is constant. The mass balance for A is "


(A) (C)

^ h ^ h

d VC A dt

^

=−

F CAC

=−

FCA

d VC A dt


−

−

h

CA 2

−

kC A V

2

kC A V

(B) (D)

^ h ^ ^ h

d VC A dt

=

F CAF

=

FCAF

d VC A dt

−

−

h

CA

−

2

kC A V

2

kC A V

Q. 64

For an isothermal second order aqueous phase reaction A B , the ratio of the time required for 90% conversion to the time required for 45% conversion is (A) 2 (B) 4 (C) 11 (D) 22

Q. 65

An isothermal aqueous phase reversible reaction P R is to be carried out in a mixed flow reactor. The reaction rate in kmol/m3-h is given by r 0.5 C p 0.125 C R . A stream containing only P enters the reactor. The residence time required (in hour) for 40% conversion of P is (A) 0.80 (B) 1.33 (C) 1.60 (D) 2.67

"

^

Y N A P M O C & A I D O N ^h © =

Q. 66

Q. 67

h

−

A pollutant P degrades according to first order kinetics. An aqueous stream containing P at 2 kmol/m3 and volumetric flow rate 1 m3 /h requires a mixed flow reactor of volume V to bring down the pollutant level to 0.5 kmol/m3 . The inlet concentration of the pollutant is now doubled and the volumetric flow rate is tripled. If the pollutant level is to be brought down to the same level of 0.5 kmol/m3 , the volume of the mixed flow reactor should be increased by a factor of (A) 7 (B) 6 (C) 3 (D) 7/3 Consider a reversible exothermic reaction in a plug flow reactor. The maximum and minimum permissible temperatures are T and T min , respectively. Which of the following temperature T profiles will require the shortest residence time to achieve the desired conversion? max


Q. 68


An irreversible aqueous phase reaction A + B P is carried out in an adiabatic mixed flow reactor. A feed containing 4 kmol/m 3 of each A and B enters the reactor at 8 m3 /h . If the temperature of the exit stream is never to exceed 390 K , what is the maximum feed inlet temperature allowed? Data: Heat of reaction 50 kJ/mol , density of the reacting mixture = 1000 kg/m3 , specific heat of reacting mixture 2 J/ kg K . The above data can be assumed to be independent of composition and temperature. (A) 190 K (B) 290 K (C) 390 K (D) 490 K "

=−

=

Q. 69

−

Pick the wrong design guideline for a reactor in which the reactions A R (desired) and A S (undesired) are to take place. The ratio of the reaction rate is "

r R r S

"

c m

k 1 a C A k 2

Y N A P M O C & A I D O ^ h ^ h N^ h ^ h © ^ h ^ h =

−

b

(A) use high pressure and eliminate inerts when a > b (B) avoid recycle when a > b (C) use batch reactor of plug flow reactor when a > b (D) use CSTR with a high conversion when a > b YEAR 2003

Q. 70

For a series of reactions be approximated as k (A) A B

A

k1

B

k 2

C having

1

(C)

Q. 71

k 2

C

A

(D)

A

k1 % k 2 , the reaction system can k 2

B

k 1

C

An elementary liquid phase decomposition reaction out in a CSTR. The design equation is (A) (C)

Q. 72

A

(B)

k τ

k τ

=

=

X A

1

−

X A

X A

1

−

X A

2

(B)

k τ =

A

XA

k

2B is to be carried

1 + X A

1 − X A 2 XA / 1 + X A (D) kτ C AB = 1 − X A 2

Find a mechanism that is consistent with the rate equation and reaction given below 2A + B rA k CA CB A2 B , (A) A + B (B) A + B AB ; AB + A A 2 B AB ; AB + A A2 B

^ h

"

−

=

"

(C) A + A

"

AA ;

AA + B

"

"

(D) A + A

A 2 B

YEAR 2003 Q. 73

ONE MARK

"

AA ;

AA + B

"

A2 B

TWO MARKS

A CSTR is to be designed in which an exothermic liquid phase first order reaction of the type A R is taking place. The reactor is to be provided with a jacket in which coolant is flowing. Following data is given 3 C A0 = 5 kmol/m ; X A = 0.5 ; feed temperature = reactor temperature = 40cC ; rate constant at 40cC 1 min 1 ; ∆H 40 kJ/mol ; ρ = 1000 kg/m3 ; C p 4 J/g cC ; q 10 3 m 3 /min ( ρ and C p are same for the reactant and product streams). The amount of heat to be removed is "

=

=

−

=

−

−

^ h

=−



(A) 2/3 kW (C) 5/3 kW Q. 74

(B) (D)

1 kW 4 kW

A liquid phase reaction is to be carried out under isothermal conditions. The reaction rate as a function of conversion has been determined experimentally and is shown in figure given below. What choice of reactor or combination of reactors will require the minimum overall reactor volume, if a conversion of 0.9 is desired?

Y N A P M O C & A I D O N ^ h ^ h © (A) CSTR followed by a PFR (B) PFR followed by a CSTR (C) CSTR followed by a PFR followed by CSTR (D) PFR followed by a CSTR followed by a PFR

Common Data For Questions. 75 and 76 :

The following gas phase reactions are carried out isothermally in a CSTR 2R ; r1 = k1 pA ; k 1 20 mol/ s m 3 bar A 3S ; r2 = k 2 pA ; k 2 40 mol/ s m 3 bar A Total pressure = 1 bar ; F A = 1 mol/s ; feed is pure A "

=

−

−

"

=

−

−

0

Q. 75

What is the maximum possible value of F R (mol/s)? (A) 1/3 (B) 1/2 (C) 2/3

(D) 2

Q. 76

The volume of a CSTR required for a fractional conversion of A equal to 0.3 due to the first reaction is (A) 0.011 (B) 0.021 (C) 0.275 (D) 0.375

Q. 77

A step input tracer test is used to explore the flow pattern of fluid through a vessel of total volume equal to 1 m3 having a feed rate of 1 m3 /min .



Identify for each curve in Group I a suitable flow model from the list given under Group II. Group I

Group II

Y N A P M O C & A I D O N © P. Curve 1

1.

PFR and CSTR in series

Q. Curve 2

2.

CSTR with dead space

3.

PFR in series with a CSTR and dead space

4.

CSTR (B) P-4, Q-1 (D) P-2, Q-1

(A) P-4, Q-3 (C) P-2, Q-3

Q. 78

Following isothermal kinetic data are obtained in a basket type of mixed flow reactor for a porous catalyst. Determine the role of pore diffusion and external mass transfer processes. Pellet diameter

Leaving concentration of the reactant

Spinning rate of basket

^ h

1

1

high

2

2

1

log

1

2 1 high (A) Strong pore diffusion control and mass transfer not controlling (B) Both pore diffusion and mass transfer not controlling (C) Both pore diffusion and mass transfer controlling (D) Mass transfer controlling YEAR 2002

'

- r A

1

ONE MARK

Q. 79

For an ideal plug flow reactor the value of the Peclet number is (A) 0 (B) 3 (C) 1 (D) 10

Q. 80

The extent of a reaction is (A) different for reactants and products (B) dimensionless (C) dependent on the stoichiometric coefficients (D) All of the above

Q. 81

An exothermic reaction takes place in an adiabatic reactor. The product



temperature ... the reactor feed temperature. (A) is always equal to (B) is always greater than (C) is always less than (D) may be greater or less than YEAR 2002 Q. 82

Q. 83

TWO MARKS

A pulse tracer is introduced in an ideal CSTR (with a mean residence time τ ) at time = 0 . The time taken for the exit concentration of the tracer to reach half of its initial value will be (A) 2τ (B) 0.5τ (C) τ/0.693 (D) 0.693τ


A batch adiabatic reactor at an initial temperature of 373 K is being used for the reaction A B . Assume the heat of reaction is - 1 kJ/mol at 373 K and the heat capacity of both A and B to be constant and equal to 50 J/mol-K . The temperature rise after a conversion of 0.5 will be (A) 5cC (B) 10cC (C) 20cC (D) 100cC "

Q. 84

In the hydrodealkylation of toluence to benzene, the following reactions occur C7 H8 + H2

"

C 6 H 6 + CH 4

2C 6 H 6

C 12 H 10 + H 2

Toluence and hydrogen are fed to a reactor in a molar ratio 1 : 5. 80% of the toluence gets converted and the selectivity of benzene (defined as moles of benzene formed/per moles of toluene converted) is 90%. The fractional conversion of hydrogen is (A) 0.16 (B) 0.144 (C) 0.152

(D) 0.136

YEAR 2001

Q. 85

ONE MARK

The conversion for a second order, irreversible reaction (constant volume) k A B , in batch mode is given by 2

(A) (C)

1 1 + k 2 CA t

(B)

0

^

h

0

1 + k 2 CA t

(D)

0

Q. 86

^

k2 CA t 0

h

1 + k 2 CA t 0

2

The reaction rate constants at two different temperatures T 1 and T 2 are related by

c m c m (C) exp c m c 1 1 m

(A)

ln

k 2 k 1

k 2 k 1

Q. 87

0

2

k 2 CA t 0

k 2 CA t 1 + k 2 CA t

=

E 1 R T2

=

−

E R T1

1 T 1

−

T 2

c m c m (D) exp c m c1 1m (B)

ln

k 2 k 1

k 2 k 1

=

E 1 R T1

=

−

E R T2

1 T 2

−

T 1

The E -curve for a non-ideal reactor defines the fraction of fluid having age between t and t + dt (A) at the inlet (B) at the outlet (C) in the reactor (D) averaged over the inlet and outlet



YEAR 2001 Q. 88

TWO MARKS

The mean conversion in the exit stream, for a second order, liquid phase reaction in a non-ideal flow reactor is given by 3

(A)

#

^h

0

0

0 3

(C)

#

1

1 + k 2 CA t 0

0

Q. 89

1−E t

Q. 93

(D)

# exp1 ^

− k 2 CA0 t

+ k 2 C A 0

0

− r A =

kpA ps 1 + KA pA + K p p p

(B)

E t dt

kpA ps 1 + KA pA + KB p B + K p p p

(D)

− r A =

kp A2 − k1 p p 1 + KA pA + K p p p

Y N A ^ h^ h P ^ h^ ^ h M ^ h ^ h O C & A I D O N © − r A =

− r A =

kpA ps 1 + KA pA

k 1

The first-order, gas phase reaction A 2B is conducted isothermally in batch mode. The rate of change of conversion with time is given by (A)

dX A = k1 1 − XA dt

(C)

dX A dt

=

k1

1

−

YEAR 2000

Q. 92

0

3

dt

^h h ^h

1 E t dt 1 + k 2 CA t

"

(C)

Q. 91

# 0

^ h@

6

(B)

For a vapour phase catalytic reaction A + B P which follows the Rideal mechanism and the reaction step is rate controlling, the rate of reaction is given by (reaction step is irreversible, product also adsorbs) (A)

Q. 90

3

k 2 CA t E t dt 1 + k 2 CA t

X A

2

1 + 2X A

(B)

dX A = k1 1 − XA 1 + 0.5X A dt

(D)

k1 1 − X A dX A = dt 1 + X A

h

ONE MARK

The experimentally determined overall order for the reaction A + B C + D is two. Then the (A) reaction is elementary with a molecularity of 2 (B) molecularity of the reaction is 2 but the reaction may not be elementary (C) reaction may be elementary with a molecularity of 2 (D) reaction is elementary but the molecularity may not be 2 "

The reaction A B is conducted in a isothermal batch reactor. If the conversion of A increases linearly with holding time, then the order of the reaction is (A) 0 (B) 1 (C) 1.5 (D) 2 "

For the liquid phase parallel reactions 2 A R , rR = k1 C A ; E 1 = 80 kJ/mol A S , rS = k 2 C A ; E 2 = 120 kJ/mol The desired product is R. A higher selectivity of R will be achieved, if the reaction is conducted at (A) low temperature in a CSTR (B) high temperature in a CSTR (C) low temperature in a PFR (D) high temperature in a PFR " "

Q. 94

In solid catalysed reactions, the diffusional effects are more likely to affect the overall rate of reaction for (A) fast reactions in catalysts of small pore diameter (B) fast reactions in catalysts of large pore diameter



(C) slow reactions in catalysts of small pore diameter (D) fast reactions in catalysts of large pore diameter YEAR 2000 Q. 95

Q. 96

TWO MARKS

The conversion for a first-order liquid-phase reaction A B in a CSTR is 50%. If another CSTR of the same volume is connected in series, then the percentage conversion at the exit of the second reactor will be (A) 60 (B) 75 (C) 90 (D) 100 "


The following half-life data are available for the irreversible liquid phase reaction, A products: "

Initial concentration (kmol/m3)

Half-life (min)

2

2

8 1 The overall order of the reaction is (A) 0.5 (C) 1.5

Q. 97

k1

(B) 1 (D) 2 k 2

The first order series reaction A B C is conducted in a batch reactor. The initial concentrations of A, B and C (C A , C B , C C respectively) are all nonzero. The variation of C B with reaction time will not show a maximum, if (A) K2 CB > K1 C A (B) K1 CA > K 2 CB (C) CB > C A (D) CA > C B 0

0

0

Q. 98

0

0

0

0

0

0

0

0

The reaction A B is conducted in an adiabatic Plug Flow Reactor (PFR). Pure A at a concentration of 2 kmol/m3 is fed to the reactor at the rate of 0.01 m3 /s and at a temperature of 500 K . If the exit conversion is 20%, then the exit temperature (in kelvin) is (A) 400 (B) 500 (C) 600 (D) 1000 Given, Heat of reaction at 298 K 50000 kJ/kmol of A reacted. Heat capacities, CPA C PB 100 kJ/kmol K (may be assumed to be independent of temperature). "

=−

=

Q. 99

=

−

The rate controlling step for the heterogeneous irreversible catalytic reaction A g +B g C g is the surface reaction of absorbed A with absorbed B to give absorbed C . The rate expression for this reaction can be written as

^h ^h

^h

"

K KA pA p B 1 + KA p A + KB pB K KA KB p Ap B (C) 1 + KA pA + KB pB + KC pC

(A)

6 6

@

@

K KA KB p Ap B 1 + KA pA + KB p B K KA KB p Ap B (D) 1 + KA pA + KB pB + KC pC

(B)

6 6

**********

@

@






ANSWER KEY CHEMICAL REACTION ENGINEERING

1

2

3

4

5

6

7

8

9

10

(B)

(A)

(B)

(A)

(B)

(C)

(C)

(A)

(A)

(B)

11

12

13

14

15

16

17

18

19

20

(C)

(C)

(C)

(A)

(C)

(C)

(C)

(B)

(C)

(C)

21

22

23

24

25

26

27

28

29

30

(D)

(B)

(A)

(C)

(A)

(C)

(C)

(B)

(C)

(B)

31

32

33

34

35

36

37

38

39

40

(B)

(C)

(A)

(D)

(B)

(A)

(A)

(A)

(C)

(D)

41

42

43

44

45

46

47

48

49

50

(D)

(B)

(D)

(C)

(D)

(B)

(D)

(A)

(C)

(A)

51

52

53

54

55

56

57

58

59

60

(B)

(C)

(A)

(C)

(A)

(B)

(A)

(B)

(A)

(D)

61

62

63

64

65

66

67

68

69

70

(C)

(C)

(A)

(C)

(C)

(A)

(B)

(B)

(B)

(D)

71

72

73

74

75

76

77

78

79

80

(A)

(C)

(C)

(D)

(C)

(B)

(A)

(A)

(A)

(D)

81

82

83

84

85

86

87

88

89

90

(B)

(A)

(A)

(C)

(B)

(B)

(B)

(A)

(A)

(C)

91

92

93

94

95

96

97

98

99

(A)

(C)

(C)

(B)

(C)

(A)

(C)

(D)

(A)


CH_Chemical-Reaction-Engineering (1).pdf

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