Mass Transfer - GATE-CH Questions

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Convective Mass Transfer

0600-2-mt-1mark
0600-2-mt

Sherwood number in mass transfer is analogous to the following dimensionless group in heat transfer

Graetz number

Grashoff number

Nusselt number

Prandtl number

GATE-CH-1990-5-i-mt-2mark
1990-5-i-mt

In the absorption of a solute gas from a mixture containing inerts in a solvent, it has been found that the overall gas transfer coefficient is nearly equal to the
individual gas film transfer coefficient. It may therefore be concluded that:

the process is liquid film controlled

the gas is sparingly soluble in the solvent

the transfer rate can be increased substantially by reducing the thickness of the liquid film

the transfer rate can be increased substantially by reducing the thickness of the gas film

GATE-CH-1994-1-p-mt-1mark
1994-1-p-mt

Mass transfer coefficient, k, according to penetration theory varies with mass diffusivity as
0.5
D

1/D

1.5
D

GATE-CH-1995-2-p-mt-2mark
1995-2-p-mt

For absorbing sparingly soluble gas in a liquid

gas side mass transfer coefficient should be increased

liquid side mass transfer coefficient should be increased

liquid side mass transfer coefficient should be decreased

mass transfer coefficient must be kept constant

GATE-CH-1997-1-16-mt-1mark
1997-1-16-mt

For turbulent mass transfer in pipes, the Sherwood number depends upon the Reynolds number(Re) as
0.33
Re

0.53
Re

0.83
Re

Re

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 GATE-CH-1997-2-13-mt-2mark
1997-2-13-mt

According to the film theory of mass transfer, the mass transfer coefficient is proportional to (where D is the molecular diffusivity)

2
D

0.5
D

1/D

GATE-CH-1998-1-16-mt-1mark
1998-1-16-mt

The mass transfer coefficient for a solid sphere of radius �a�, dissolving in a large volume of quiescent liquid, in which D is the diffusivity of the solute, is

D/a

D/(2a)

proportional to D
0.5

dependent on the Reynold’s number

GATE-CH-1998-1-17-mt-1mark
1998-1-17-mt

In an interphase mass transfer process, the lesser the solubility of a given solute in a liquid, the higher are the chances that the transfer process will be

liquid phase resistance controlled

gas phase resistance controlled

impossible

driven by a nonlinear driving force

GATE-CH-1998-2-14-mt-2mark
1998-2-14-mt

If the Prandtl number is greater than the Schmidt number,

the thermal boundary layer lies inside the concentration boundary layer

the concentration boundary layer lies inside the thermal boundary layer

the thermal and concentration boundary layers are of equal thickness

the hydrodynamic (i.e., momentum) boundary layer is thicker than the other two

GATE-CH-1998-2-19-mt-2mark
1998-2-19-mt

In an interphase heat transfer process, the equilibrium state corresponds to equality of temperatures in the two phases, while the condition for equilibrium in an
interpahse mass transfer process is

equality of concentrations

equality of chemical potentials

equality of activity coefficients

equality of mass transfer coefficients

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 GATE-CH-1999-1-19-mt-1mark
1999-1-19-mt

Penetration theory states that the mass transfer coefficient is equal to (where De is diffusivity and t is time)
1/2
(D e t)

1/2
(D e /t)

1/2
(4D e /(πt))

1/2
(4D e t)

GATE-CH-2001-1-11-mt-1mark
2001-1-11-mt

The surface renewal frequency in Danckwerts� model of mass transfer is given by (k L : mass transfer coefficient, m/s)

2
√k DA
L

2
k DA
L

2
k /D A
L

2
k L /D
A

GATE-CH-2001-1-12-mt-1mark
2001-1-12-mt

For gas absorption the height of a transfer unit, based on the gas phase, is given by (G: superficial molar gas velocity; L: superficial molar liquid velocity; FG :

mass transfer coefficient, mol/m2.s; a: interfacial area per unit volume of tower)

FG a

FG

Ga

Ga

FG

FG G

GATE-CH-2002-1-24-mt-1mark
2002-1-24-mt

The dimensionless group in mass transfer that is equivalent to Prandtl number in heat transfer is

Nusselt number

Sherwood number

Schmidt number

Stanton number

GATE-CH-2002-1-25-mt-1mark
2002-1-25-mt

The Reynolds analogy for momentum, heat and mass transfer is best applicable for

Gases in turbulent flow

Gases in laminar flow

 Liquids in turbulent flow

Liquids and gases in laminar flow

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GATE-CH-2003-64-mt-2mark
2003-64-mt

The Reynolds number of the liquid was increased 100 fold for a laminar film used for gas-liquid contacting. Assuming penetration theory is applicable, the fold-
increase in the mass transfer coefficient (k c ) for the same system is

100

10

GATE-CH-2005-21-mt-1mark
2005-21-mt

For turbulent flow past a flat plate, when no form drag is present, the friction factor f and the Chilton-Colburn factor jD are related as

f and jD cannot be related

f is equal to jD

f is greater than jD

f is less than jD

GATE-CH-2005-65-mt-2mark
2005-65-mt

Match the variation of mass transfer coefficient given by the theory in Group I with the appropriate variation in Group II.

Group I Group II
(P) Film Theory (1) ∝ D AB

2/3
(Q) Penetration theory (2) ∝ D
AB

1/2
(R) Boundary layer theory (3) ∝ D
AB

P-1, Q-2, R-3

P-2, Q-1, R-3

P-1, Q-3, R-2

P-3, Q-2, R-1

GATE-CH-2006-43-mt-2mark
2006-43-mt

Experiments conducted with a sparingly dissolving cylinder wall in a flowing liquid yielded the following correlation for the Sherwood number

0.83 1/3
Sh = 0.023(Re) (Sc)

Assuming the applicability of the Chilton-Colburn analogy, the corresponding correlation for heat transfer is
0.83 1/3
St = 0.023(Gr) (Pr)

0.83 1/3
Nu = 0.023(Re) (Pr)

0.83 2/3
j H = 0.023(Re) (Pr)

0.5 4/3
Nu = 0.069(We) (Pr)
 GATE-CH-2010-3-mt-1mark
2010-3-mt

The ratio of the thermal boundary layer thickness to the concentration boundary layer thickness is proportional to

Nu

Le

Sh

Pr

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GATE-CH-2011-20-mt-1mark
2011-20-mt

Simultaneous heat and mass transfer is occurring in a fluid flowing over a flat plate. The flow is laminar. The concentration boundary layer will COINCIDE with the
thermal boundary layer, when

Sc = Nu

Sh = Nu

Sh = Pr

Sc = Pr

GATE-CH-2011-40-mt-2mark
2011-40-mt

A gas mixture is in contact with a liquid. Component P in the gas mixture is highly soluble in the liquid. Possible concentration profiles during absorption of P are
shown in choices, where

x : mole fraction of P in bulk liquid

y : mole fraction of P in bulk gas
x i : mole fraction of P at the interface in liquid
y i : mole fraction of P at the interface in gas

y : equilibrium gas phase mole fraction corresponding to

∗
xi

The CORRECT profile is

 GATE-CH-2012-18-mt-1mark
2012-18-mt

For which of the following operations, does the absorption operation become gas-film controlled?

[P.] The solubility of gas in the liquid is very high

[Q.] The solubility of gas in the liquid is very low

[R.] The liquid-side mass transfer coefficient is much higher than the gas-side mass transfer coefficient

[S.] The liquid-side mass transfer coefficient is much lower than the gas-side mass transfer coefficient

P&Q

P&R

P&S

Q&R

GATE-CH-2014-19-mt-1mark
2014-19-mt

Assuming the mass transfer coefficients in the gas and the liquid phases are comparable, the absorption of CO2 from reformer gas (CO2+H2) into an aqueous
solution of diethanolamine is controlled by

gas phase resistance

liquid phase resistance

both gas and liquid phase resistances

composition of the reformer gas

 GATE-CH-2014-20-mt-1mark
2014-20-mt

Which ONE of the following statements is CORRECT for the surface renewal theory?

Mass transfer takes place at steady state

Mass transfer takes place at unsteady state

Contact time is same for all the liquid elements

Mass transfer depends only on the film resistance

[Index] [Detailed Solutions to the Above in our Online Courses...]

GATE-CH-2016-12-mt-1mark
2016-12-mt

Match the dimensionless numbers in Group-1 with the ratios in Group-2.

Group-1 Group-2
buoyancy f orce
P. Biot number I.
viscous f orce

internal thermal resistance of a solid

Q. Schmidt number II.
boundary layer thermal resistance

momentum dif f usivity

R. Grashof number III.
mass dif f usivity

P-II, Q-I, R-III

P-I, Q-III, R-II

P-III, Q-I, R-II

P-II, Q-III, R-I

GATE-CH-2017-16-mt-1mark
2017-16-mt

Consider steady state mass transfer of a solute A from a gas phase to a liquid phase. The gas phase bulk and interface mole fractions are y A,G and y A,i ,

(x A,i − x A,L )
respectively. The liquid phase bulk and interface mole fractions are x A,L and x A,i , respectively. The ratio is very close to zero. This implies that
(y A,G − y A,i )

mass transfer resistance is

negligible in the gas phase only

negligible in the liquid phase only

negligible in both the phases

considerable in both the phases

GATE-CH-2017-43-mt-2mark
2017-43-mt

The Sherwood number (Sh L ) correlation for laminar flow over a flat plate of length L is given by

0.5 1/3
Sh L = 0.664 Re Sc
L

where Re L and Sc represent Reynolds number and Schmidt number, respectively. This correlation, expressed in the form of Chilton-Colburn jD factor, is

j D = 0.664

−0.5
j D = 0.664 Re
L

j D = 0.664 Re L

0.5 2/3
j D = 0.664 Re Sc
L
 GATE-CH-1994-3-k-mt-1mark
1994-3-k-mt

Forced convection is relatively more effective in increasing the rate of mass transfer if Schmidt number is larger. (True/False)

True

False

GATE-CH-1994-20-mt-5mark
1994-20-mt

A stream of air at 100 kPa pressure and 300 K is flowing on the top surface of a thin flat sheet of solid naphthalene of length 0.2 m with a velocity of 20 m/s.
The other data are:
Mass diffusivity of naphthalene vapor in air = 6 × 10 −6 m 2 /s
Kinematic viscosity of air = 1.5 × 10 −5 m 2 /s
Concentration of naphthalene at the air-solid naphthalene interface = 1 × 10 kmol/m 3
−5

Note: For heat transfer over a flat plate, convective heat transfer coefficient for laminar flow can be calculated by the equation:

1/2 1/3
Nu = 0.664Re Pr
L

You may use analogy between mass and heat transfer.

Calculate:
(a) the average mass transfer coefficient( in m/s) over the flat plate
{#1}

(b) the rate of loss of naphthalene from the surface per unit width (in mol.m −1 .h −1 )
{#2}

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GATE-CH-2004-19-20-mt-2mark
2004-19-20-mt

Pure aniline is evaporating through a stagnant air film of 1 mm thickness at 300 K and a total pressure of 100 kPa. The vapor pressure of aniline at 300 K is 0.1
kPa. The total molar concentration under these conditions is 40.1 mol/m3. The diffusivity of aniline in air is 0.74 × 10 m2/s.
−5

(i) The numerical value of the mass transfer coefficient is 7.4 × 10

−3
. Its units are

{#1}

(ii) The rate of evaporation of aniline is . Its units are

−4
2.97 × 10

{#2}

GATE-CH-2000-2-14-mt-2mark
2000-2-14-mt

The individual mass transfer coefficients (mol/m2.s) for absorption of a solute from a gas mixture into a liquid solvent are kx =4.5 and ky = 1.5. The slope of the
equilibrium line is 3. Which of the following resistance(s) is (are) controlling?

liquid-side

gas-side

interfacial

both liquid and gas side

GATE-CH-2001-2-12-mt-2mark
2001-2-12-mt

The interfacial area per unit volume of dispersion, in a gas-liquid contactor, for fractional hold-up of gas = 0.1 and gas bubble diameter = 0.5 mm is given by (in
m2/m3)

500
 1200

900

800

GATE-CH-2005-64-mt-2mark
2005-64-mt

Two solid discs of benzoic acid (molecular weight = 122) of equal dimensions are spinning separately in large volumes of water and air at 300 K. The mass
transfer coefficients for benzoic acid in water and air are 0.9 × 10 −5 and 0.47 × 10 −2 m/s respectively. The solubility of benzoic acid in water is 3 kg/m3 and the
equilibrium vapor pressure of benzoic acid in air is 0.04 kPa. Then the disc

dissolves faster in air than in water

dissolves faster in water than in air

dissolves at the same rate in both air and water

does not dissolve either in water or in air

GATE-CH-2008-52-mt-2mark
2008-52-mt

A sparingly soluble solute in the form of a circular disk is dissolved in an organic solvent as shown in the figure. The area available for mass transfer from the disk
is A and the volume of the initially pure organic solvent is V . The disk is rotated along the horizontal plane at a fixed rpm to produce a uniform concentration of
the dissolving solute in the liquid. The convective mass transfer coefficient under these conditions is k c . The equilibrium concentration of the solute in the solvent
is C ∗ . The time required for the concentration to reach 1% of the saturation value is given by

kc A
exp (− t) = 0.99
V

kc A
exp (− t) = 0.01
V

V
exp(−0.99) = t
Ak c

V
exp(0.01) = t
Ak c

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GATE-CH-2014-31-mt-2mark
2014-31-mt
A spherical ball of benzoic acid (diameter = 1.5 cm) is submerged in a pool of still water. The solubility and diffusivity of benzoic acid in water are 0.03 kmol/m3
and 1.25 × 10 −9 m2/s respectively. Sherwood number is given as Sh = 2.0 + 0.6Re Sc . The initial rate of dissolution (in kmol/s) of benzoic acid
0.5 0.33

approximately is
−11
3.54 × 10

−12
3.54 × 10

−13
3.54 × 10

−14
3.54 × 10

GATE-CH-1991-6-i-mt-2mark
1991-6-i-mt

The diffusion rate of ammonia from an aq.solution to the gas phase is 10 −3 kmol/m 2 .s. The interface equilibrium pressure of NH 3 is 660 N/m 2 and the
concentration of NH 3 in the gas phase is 5%. If the total pressure is 101 N/m 2 , temperature is 295 K and diffusivity of NH 3 is 0.24 cm 2 /s, the gas film thickness
is ____________(μm).

Answer

GATE-CH-2001-13-mt-5mark
2001-13-mt

A sugary substance A is added to a pot of milk (initially containing no A) and stirred vigorously by a spoon so that the concentration of A, C A , is uniform
everywhere. The mass transfer coefficient for the transfer of A into the liquid is k sl = 1 × 10 −4 m/s. Solid A is added in great excess compared to the saturation
capacity of milk to dissolve A. Assume that the solid-liquid interfacial area stays constant throughout the dissolution process and is given by a = 1000 cm 2 .
Derive the expression for C A versus time, t. The time (in s) taken for C A /C A∗
= 0.95 ___________

kmol/m 3 ; = 1000 cm 3 .
∗ −2
C = 5 × 10 VL
A

Answer

GATE-CH-2002-12-mt-5mark
2002-12-mt

The mass flux from a 5 cm diameter naphthalene ball, placed in stagnant air at 40 C and atmospheric pressure, is 1.47 × 10
∘
mol/m .s. Assume the vapor
−3 2

pressure of naphthalene to be 0.15 atm at 40 ∘ C and negligible bulk concentration of naphthalene in air. If air starts blowing across the surface of naphthalene ball
at 3 m/s, by what factor will the mass transfer rate increase, all other conditions remaining the same? _______________

For spheres:

0.5 0.33
Sh = 2.0 + 0.6(Re) (Sc)

where Sh is the Sherwood number and is the Schmidt number. The viscosity and density of air are kg/m.s and 1.123 kg/m 3 , respectively and the
−5
Sc 1.8 × 10

gas constant is 82.06 cm 3 .atm/mol.K

Answer

GATE-CH-2013-39-mt-2mark
2013-39-mt

A study was conducted in which water was pumped through cylindrical pipes made of a sparingly soluble solid. For a given pipe and certain flow conditions, the
mass transfer coefficient k c has been calculated as 1 mm/s using the correlation Sh = 0.025Re Sc . If the velocity of the fluid and the diameter of the pipe
0.6 0.33

are both doubled, what is the new value of k c in mm/s, up to 2 digits after the decimal point? ____________

Answer

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GATE-CH-1990-15-iii-mt-6mark
1990-15-iii-mt

Consider a system in which component A is being transferred from a gas phase to a liquid phase. The equilibrium relation is given by y A = 0.75x A where y A and
x A are mole fractions of A in gas and liquid phase respectively. At one point in the equipment, the gas contains 10 mole % A and liquid 2 mole % A. Gas film
 mass transfer coefficient ky at this point is 10 kmol/(h.m 2 .Δy A ) and 60% of the resistance is in the gas film. Calculate:
(a) the overall mass transfer coefficient in kmol/(h.m 2 .Δy A ).
{#1}

(b) mass flux of A in kmol/(h.m 2 ).

{#2}

(c) the interfacial gas concentration of A in mole fraction.

{#3}

GATE-CH-1988-5-a-ii-mt-1mark
1988-5-a-ii-mt

A pure gas is absorbed in a solvent in which the gas is highly soluble. The controlling resistance is in the ����- film.

Answer

GATE-CH-1989-5-i-b-mt-1mark
1989-5-i-b-mt

Schmidt number is the ratio of ����- diffusivity to ����- diffusivity.

Answer

GATE-CH-1989-5-i-c-mt-1mark
1989-5-i-c-mt

Reynolds analogy between momentum and mass transfer is applicable when ����- number is equal to ����- .

Answer

GATE-CH-1992-6-c-mt-2mark
1992-6-c-mt

����- number in mass transfer corresponds to Nusselt number in heat transfer and ����- number to Prandtl number.

Answer

GATE-CH-1993-12-c-mt-2mark
1993-12-c-mt

Associate the following dimensionless groups, with heat transfer, mass transfer and momentum transfer.

Sherwood number

Prandtl number

Nusselt number

Schmidt number

Answer

GATE-CH-1994-2-o-mt-1mark
1994-2-o-mt

The Reynolds analogy for mass transfer is given by ����- and is applicable when Schmidt number is ����-

Answer

[Index] [Detailed Solutions to the Above in our Online Courses...]

Last Modified on: 24-Oct-2022

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