Diffusion and Mass-transfer Theories - Mass Transfer - Chemical Engineering Previous Year Questions

1

2007 · Chemical Engineering · Mass Transfer · Diffusion and Mass-transfer Theories

Chemical Engineering (CH) 2007

The following figure depicts steady one-dimensional diffusion of water vapour from the surface of water taken in a conical flask at room temperature. Derive the governing equation for determining the concentration profile of water vapour in the gas medium. Neglect change of level of water due to condensation. The temperatures of the gas and the liquid media are identical and constant.

A

\(\frac{d}{dz} \left[ r^2 \frac{C D_{WA}}{1 - x_W} \frac{dx_W}{dz} \right] = 0\)

B

\(\frac{d}{dz} \left[ \frac{C D_{WA}}{1 - x_W} \frac{dx_W}{dz} \right] = 0\)

C

\(\frac{d}{dz} \left[ r \frac{C D_{WA}}{1 - x_W} \frac{dx_W}{dz} \right] = 0\)

D

\(\frac{d}{dz} \left[ r C D_{WA} \frac{dx_W}{dz} \right] = 0\)

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2

2008 · Chemical Engineering · Mass Transfer · Diffusion and Mass-transfer Theories

Chemical Engineering (CH) 2008

A rectangular slab of thickness 2b along the x axis and extending to infinity along the other directions is initially at concentration c_{A0}. At time t=0, both surfaces of the slab (x = ± b) have their concentrations increased to c_{AW} and maintained at that value. Solute A diffuses into the solid. The dimensionless concentration C is defined as
\[ C = \frac{c_A - c_{A0}}{c_{AW} - c_{A0}} \]
The diffusivity of A inside the solid is assumed constant. At a certain time instant, which ONE of the following is the correct representation of the concentration profile?

A

[Image: (A) concentration profile C vs x/b, C=1 at boundaries, increases from center]

B

[Image: (B) concentration profile C vs x/b, linear V shape]

C

[Image: (C) concentration profile C vs x/b, U shape with C=1 at boundaries]

D

[Image: (D) concentration profile C vs x/b, U shape with C=1 at boundaries]

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3

2008 · Chemical Engineering · Mass Transfer · Diffusion and Mass-transfer Theories

Chemical Engineering (CH) 2008

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

A

\(\exp(-\frac{k_c A}{V} t) = 0.99\)

B

\(\exp(-\frac{k_c A}{V} t) = 0.01\)

C

\(\frac{V}{A k_c} \exp(-0.99) = t\)

D

\(\frac{V}{A k_c} \exp(0.01) = t\)

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4

2008 · Chemical Engineering · Mass Transfer · Diffusion and Mass-transfer Theories

Chemical Engineering (CH) 2008

Air concentrated with solute P is brought in contact with water. At steady state, the bulk concentrations of P in air and water are 0.3 and 0.02 respectively. The equilibrium equation relating the interface compositions is
\[ y_{P,i} = 0.25 x_{P,i} \]
Assume that the mass transfer coefficients \( F_G \) and \( F_L \) are identical. The gas phase mole fraction of P at the interface (\( y_{P,i} \)) is

A

0.0663

B

0.075

C

0.16

D

0.3

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5

2008 · Chemical Engineering · Mass Transfer · Diffusion and Mass-transfer Theories

Chemical Engineering (CH) 2008

If the exit average concentration in the liquid is measured to be 1.4 × 10^-2 kmol/m³, the total mass transfer rate (in kmol/s) of the sparingly soluble gas into the liquid is

A

0.133 × 10^-4

B

0.434 × 10^-7

C

3.4 × 10^-2

D

17 × 10^-2

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6

2008 · Chemical Engineering · Mass Transfer · Diffusion and Mass-transfer Theories

Chemical Engineering (CH) 2008

The mass transfer coefficient k_c,avg (in m/s), averaged along the length of the vertical surface is

A

2.94 × 10^-6

B

2.27 × 10^-6

C

1.94 × 10^-6

D

1.65 × 10^-6

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7

2009 · Chemical Engineering · Mass Transfer · Diffusion and Mass-transfer Theories

Chemical Engineering (CH) 2009

According to the penetration theory of mass transfer, the mass transfer coefficient (k) varies with diffusion coefficient (D) of the diffusing species as

A

\(D \)

B

\(D^{-1/2} \)

C

\(D^{1/2} \)

D

\(D^{3/2} \)

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8

2009 · Chemical Engineering · Mass Transfer · Diffusion and Mass-transfer Theories

Chemical Engineering (CH) 2009

Species A is diffusing at steady state from the surface of a sphere (radius = 1 cm) into a stagnant fluid. If the diffusive flux at a distance \(r = 3\) cm from the center of the sphere is 27 mol/cm²·s, the diffusive flux (in mol/cm²·s) at a distance \(r = 9\) cm is

A

1

B

3

C

9

D

27

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9

2010 · Chemical Engineering · Mass Transfer · Diffusion and Mass-transfer Theories

Chemical Engineering (CH) 2010

At 25°C and 90% relative humidity, water evaporates from the surface of a lake at the rate of 1.0 kg/m²/h. The relative humidity that will lead to an evaporation rate of 3.0 kg/m²/h, with other conditions remaining the same, is

A

30%

B

50%

C

60%

D

70%

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10

2010 · Chemical Engineering · Mass Transfer · Diffusion and Mass-transfer Theories

Chemical Engineering (CH) 2010

A liquid flows over a flat naphthalene plate of length L, at a Reynolds number (Re_L = Lρu∞/μ) of 1500, as shown in the figure. The surface concentration of naphthalene is C_As > C_A∞, and the surface temperature is T_s > T_∞. Assume Pr = Sc = 1.
If, at x = L, \(\left|\frac{\partial C_A^*}{\partial y^*}\right|_{y^*=0} = 10\) where \(C_A^* = \frac{C_A - C_{A\infty}}{C_{As} - C_{A\infty}}\) and \(y^* = \frac{y}{L}\), then the Nusselt number and the friction coefficient at x = L, are

A

10, 1/75

B

10, 10

C

20, 10

D

1/75, 5

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11

2011 · Chemical Engineering · Mass Transfer · Diffusion and Mass-transfer Theories

Chemical Engineering (CH) 2011

Ammonia (component 1) is evaporating from a partially filled bottle into surrounding air (component 2). The liquid level in the bottle and the concentration of ammonia at the top of the bottle are maintained constant. \(N_1\) is the molar flux relative to a fixed location in space and \(J_1\) is the molar flux with respect to the average molar velocity of the constituent species in the gas phase. Assume that air in the bottle is stagnant. Which ONE of the following is CORRECT?

A

\(N_1 = \text{constant}, N_2 = 0, J_1 + J_2 = 0\)

B

\(N_1 + N_2 = 0, J_1 + J_2 = 0\)

C

\(N_1 + N_2 = 0, J_1 = \text{constant}, J_2 = 0\)

D

\(N_1 = \text{constant}, N_2 = 0, J_1 = \text{constant}, J_2 = 0\)

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12

2011 · Chemical Engineering · Mass Transfer · Diffusion and Mass-transfer Theories

Chemical Engineering (CH) 2011

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 the 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 x_i

The CORRECT profile is

A

Gas: y_i is below y*, y_i is above y; Liquid: x_i is near interface then decreases to x

B

Gas: y_i is below y*, y_i is above y; Liquid: x_i is near interface then increases to x

C

Gas: y_i is above y*, y_i is above y; Liquid: x_i is near interface then increases to x

D

Gas: y_i is above y*, y_i is above y; Liquid: x_i is near interface then decreases to x

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13

2012 · Chemical Engineering · Mass Transfer · Diffusion and Mass-transfer Theories

Chemical Engineering (CH) 2012

For which of the following combinations, 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

A

P & Q

B

P & R

C

P & S

D

Q & R

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14

2013 · Chemical Engineering · Mass Transfer · Diffusion and Mass-transfer Theories

Chemical Engineering (CH) 2013

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 \(Sh = 0.025 Re^{0.8} Sc^{0.33}\). If the velocity of the fluid and the diameter of the pipe are both doubled, what is the new value of \(k_c\) in mm/s, up to 2 digits after the decimal point? ______

Check answer

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15

2014 · Chemical Engineering · Mass Transfer · Diffusion and Mass-transfer Theories

Chemical Engineering (CH) 2014

A spherical storage vessel is quarter-filled with toluene. The diameter of the vent at the top of the vessel is 1/20\(^{th}\) of the diameter of the vessel. Under the steady state condition, the diffusive flux of toluene is maximum at

A

the surface of the liquid

B

the mid-plane of the vessel

C

the vent

D

a distance 20 times the diameter of the vent away from the vent

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16

2014 · Chemical Engineering · Mass Transfer · Diffusion and Mass-transfer Theories

Chemical Engineering (CH) 2014

Assuming the mass transfer coefficients in the gas and the liquid phases are comparable, the absorption of \(CO_2\) from reformer gas (\(CO_2+H_2\)) into an aqueous solution of diethanolamine is controlled by

A

gas phase resistance

B

liquid phase resistance

C

both gas and liquid phase resistances

D

composition of the reformer gas

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17

2014 · Chemical Engineering · Mass Transfer · Diffusion and Mass-transfer Theories

Chemical Engineering (CH) 2014

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

A

Mass transfer takes place at steady state

B

Mass transfer takes place at unsteady state

C

Contact time is same for all the liquid elements

D

Mass transfer depends only on the film resistance

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18

2014 · Chemical Engineering · Mass Transfer · Diffusion and Mass-transfer Theories

Chemical Engineering (CH) 2014

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 x 10⁻⁹ m²/s respectively. Sherwood number is given as Sh = 2.0 + 0.6 Re⁰.⁵ Sc⁰.³³. The initial rate of dissolution (in kmol/s) of benzoic acid approximately is

A

3.54×10⁻¹¹

B

3.54×10⁻¹²

C

3.54×10⁻¹³

D

3.54×10⁻¹⁴

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19

2016 · Chemical Engineering · Mass Transfer · Diffusion and Mass-transfer Theories

Chemical Engineering (CH) 2016

Consider the following two cases for a binary mixture of ideal gases A and B under steady state conditions. In Case 1, the diffusion of A occurs through non-diffusing B. In Case 2, equimolar counter diffusion of A and B occurs. In both the cases, the total pressure is 100 kPa and the partial pressures of A at two points separated by a distance of 10 mm are 10 kPa and 5 kPa. Assume that the Fick’s first law of diffusion is applicable. What is the ratio of molar flux of A in Case 1 to that in Case 2?

A

0.58

B

1.08

C

1.58

D

2.18

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20

2017 · Chemical Engineering · Mass Transfer · Diffusion and Mass-transfer Theories

Chemical Engineering (CH) 2017

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 \(y_{A,i}\), respectively. The liquid phase bulk and interface mole fractions are \(x_{A,L}\) and \(x_{A,i}\), respectively. The ratio \(\frac{(x_{A,i} - x_{A,L})}{(y_{A,G} - y_{A,i})}\) is very close to zero.
This implies that mass transfer resistance is

A

negligible in the gas phase only

B

negligible in the liquid phase only

C

negligible in both the phases

D

considerable in both the phases

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