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QUESTION: 1

Fick’s law is given by the formula

Solution:

Explanation: Experimental evidences shows that molecular diffusion is goverened by the empirical relation suggested by Fick.

QUESTION: 2

Figure shows equimolal diffusion between species B and C. Identify the correct molar diffusion rate

Solution:

Explanation: Equimolal diffusion between species B and C of a binary gas system implies that each molecule of component B is replaced by each molecule of constituent C.

QUESTION: 3

What is the unit of diffusion coefficient?

Solution:

Explanation: D = – N/ (d C/ d x).

QUESTION: 4

What is the molecular weight of Sulphur-dioxide?

Solution:

Formula of Sulphur-dioxide is SO _{2}.

QUESTION: 5

What is the molecular volume of air at normal boiling point?

Solution:

Explanation: Air contains some dust particles due to which its molecular volume decreases by a small factor.

QUESTION: 6

What is the value of Schmidt number for hydrogen?

Solution:

Explanation: Schmidt number = v/D.

QUESTION: 7

Estimate the diffusion coefficient for ammonia in air t 25 degree Celsius temperature and one atmospheric pressure.

For ammonia,

Molecular weight = 17

Molecular volume = 25.81 cm^{3}/gm mole

For air,

Molecular weight = 29

Solution:

Explanation: D = 0.0043 T ^{3/2}/p _{t} (V _{b}^{1/3}_{ }+ V _{c}^{1/3}) ^{2 }[1/M _{b }+ M _{c}]^{ ½}.

QUESTION: 8

Estimate the diffusion coefficient of carbon monoxide through air in which the mole fractions of each constituents are

O _{2} = 0.18

N _{2} = 0.72

CO = 0.10

The gas mixture is at 300 K and 2 atmosphere total pressure. The diffusivity values are

D _{CO }= 18.5 * 10 ^{-6 }m^{2}/s at 273 K, 1 atm

D _{CN }= 19.2 * 10 ^{-6 }m^{2}/s at 288 K, 1 atm

The subscripts C is carbon monoxide, O is oxygen and N is nitrogen

Solution:

Explanation: (T _{1}/T _{2})^{ 3/2 }(p _{2}/p _{1}) = D _{1}/D _{2}.

QUESTION: 9

What is the molecular weight of Sulphur-dioxide?

Solution:

Explanation: Formula of Sulphur-dioxide is SO _{2}.

QUESTION: 10

The dimension of diffusion coefficient is given by

Solution:

Explanation: Unit is m^{2}/s

QUESTION: 11

For what kind of mixtures D_{AB}=D_{BA} holds?

Solution:

Explanation: None.

QUESTION: 12

In the expression for molar flux N_{A}=(N_{A}+N_{B})C_{A}/C – D_{AB}dC_{A}/dz, the terms representing bulk flow and molecular diffusion are, respectively

Solution:

Explanation: None.

QUESTION: 13

Consider loss of ethanol vapor by diffusion from a half-filled open test tube. At what point in the diffusion path will the contribution of the bulk flow term to the molar flux be maximum?

Solution:

Explanation: At the liquid-gas interface concentration will be maximum.

Bulk liquid is not a part of the diffusion path.

QUESTION: 14

A reaction 3A+2B+C=1.5D+E occurs in a reactor at steady state. What will be the value of the flux ratio N_{A}/N_{D }

Solution:

Explanation: N_{A}/N_{D}= (rate of disappearance of A)/(rate of appearance of D)

= -3/1.5

= -2.

QUESTION: 15

For a component A of a mixture, concentration as a function of x is given:

C_{A}=5e^{-10x} (x is in cm and C_{A} in mol/liter)

Calculate the value of diffusion velocity (m/s)of the component A at the point x=0, if diffusivity of A in the mixture is 2.567*10^{-5}m^{2}/s.

Solution:

Explanation: By Fick’s law, J_{A}=(-)D_{AB}*dC/dx

C_{A}(u_{A}-U)= (-)D_{AB}dC/dx…………1

Diffusion velocity= (u_{A}-U)=(-D_{AB}dC/dx)/C_{A}

dC/dx = -50e^{-10x}

C_{A}= 5 mol/lit

Put all the values in equation 1.

QUESTION: 16

A sheet of Fe 1.0 mm thick is exposed to a oxidizing gas on one side and a deoxidizing gas on the other at 725°C. After reaching steady state, the Fe membrane is exposed to room temperature, and the C concentrations at each side of the membrane are 0.012 and 0.075 wt%. Calculate the diffusion coefficient (m^{2}/sec) if the diffusion flux is 1.4×10^{-8}kg/m^{2}-sec.

Solution:

Explanation: Convert from wt% to kg/m^{3} .

Concentration in kg/m^{3}=[C_{1}/(C_{1}/ρ_{1}+C2/ρ_{2})]*1000

0.012% and 0.075% in kg/m^{3} are 0.270 and 1.688 respectively.

Putting all the values in the equation J_{A}=(-)D_{AB}dC/dx.

QUESTION: 17

At which condition molar flux with respect to a stationary observer and with respect to a observer moving with molar average velocity?

Solution:

Explanation: In a very dilute solution, the contribution of the bulk flow term becomes negligible.

N_{A}= (N_{A}+N_{B})C_{A}/C – D_{AB}dC_{A}/dz (general equation)

(N_{A}+N_{B})C_{A}/C =0 (in dilute solution)

N_{A}= -D_{AB}dC_{A}/dz = J_{A}.

QUESTION: 18

Which among the following is the statement of the ‘Fick’s Law’?

Solution:

Explanation: None.

QUESTION: 19

Fick’s law is given by the formula

Solution:

Experimental evidences shows that molecular diffusion is goverened by the empirical relation suggested by Fick.

QUESTION: 20

In industries titanium is hardened through diffusion of carbon. The concentration of carbon at 1mm into the surface of the titanium slab is 0.25kg/m^{3} and at 3mm the concentration is 0.68kg/m^{3}. The rate at which the carbon is entering into its surface is 1.27*10-9kg/m^{2}.s. calculate the value of diffusion coefficient of carbon.

Solution:

Explanation: J=-D(∂C/∂x)

∂C/∂x= Δc/Δx=(0.25-0.68)/(0.003-0.001)=-215kg/m^{4}

1.27*10^{-19}kg/m^{2}.s= -D*(-215kg/m^{4})

D=5.91*10^{-12}m^{2}/s.

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