Question

1. Write very briefly about the following:                                                                        

a)  Fick’s second law and its application

b) Different Mass transfer coefficients

c) Raoult’s law and Henry’s law and their applications  

d) Give the j_D correlation for mass transfer in flow parallel to flat plate

e)  Chilton – Colburn analogy

f) Capacity coefficients and their use

g) Marangony effect

2. Explain and derive the Mass transfer flux equation for molecular diffusion in gases for the case of (i) Equimolar counter diffusion and (ii) A is diffusing through stagnant non diffusing B.
3. a) Explain the diffusion through a varying cross sectional area and derive the equation for mass transfer flux.

        4)   a) Explain briefly about the diffusivities in gases

                                                            

b) Explain briefly about the diffusivities in liquids

1. Explain the diffusivities of electrolytes in liquids              

                                    

b) Predict the diffusion coefficients of dilute electrolytes for the following cases:

i) For  KCl at 25 ⁰C, calculate  .

ii) For  KCl at 18.5 ⁰C, calculate  .             

iii) For  CaCl₂ at 25 ⁰C, calculate  . Also predict Di of ion Ca⁺² and of  Cl^-.

Data: λ₊(K⁺) =73.5, λ_-(Cl^-) =76.3, λ₊(Ca²⁺/2) = 59.5

       6)   Explain (a) The two film theory and (b) The penetration theory.                       

      7)   Explain the mass transfer in the laminar boundary layer when the fluid is in laminar flow over a flat plate.

                    

8).Explain the following briefly.

1. Individual and overall mass transfer coefficients.
2. Reynolds analogy.   

Answer 1

As we know that ficks first law is applicable for steady state molecular diffusion but ficks second law is applicable for unsteady state molecular diffusion. It means here accumulation of concentration within volume is there.

By ficks second law,

dCa/dt = Dab*d2Ca/dt2

It is applicable for one dimensional unsteady state molecular diffusion.

Ca - concentration of diffusing component.

Dab is the diffusivity of A and B.

t is the time.

Application : this law is applicable for all unsteady state mass transfer operations. It tells us how much flux is gone through the system and what is the accurate time. Equation having time and space simultaneously so it tells both .

b) we have different - different mass transfer coefficients:

Flux = mass transfer coefficient * concentration difference

Mass transfer coefficient basis of Diffusing A and Non diffusing B (Nb = 0)

Na = kg*(ΔP) = ky(Δy) = kc(ΔC)

kg - mass transfer coefficient in terms of gas pressure.

ky - mass transfer coefficient in terms of mole fractions in gas phase.

kc - mass transfer coefficient in terms of concentration in gas phase.

Similarly for liquid phase,

Na = kx*(Δx) = kL(ΔC)

kx - mass transfer coefficient in terms of mole fraction in liquid phase.

kL - mass transfer coefficient in terms of concentration in liquid phase.

Equimolar countercurrent mass transfer (Na = - Nb)

All mass transfer coefficient is based on equimolar countercurrent mass transfer.

Na = kg'(ΔP) = ky'(Δy) = k'c(ΔC)

kg', ky' , kc' - mass transfer coefficients are based on pressure, mole fraction, and concentration in gas phase.

Na = k'x(Δx) = kL'(ΔC)

kx', kL' are mass transfer coefficients are based on mole fraction and concentration in liquid phase.

C) roults law and henry law and their application :

Roults law - it is applicable for all ideal solutions of liquid and vapor. Here solute is very much soluble into the solvent.

If gas and liquid are in equilibrium then

yP = xP*

y =(P*/P )* x = mx

Where y is the mole fraction of solute in gas phase.

x is the mole fraction of solute in liquid phase.

P is the total pressure.

P* is the vapor pressure of liquid in that temperature.

Application : this law is so much applicable in mass transfer operations in chemical industry for using equilibrium relation in distillation column and other mass transfer operations.

Where we found data between more volatile and less volatile component and by which we get separation themselves.

Henrys law: it is applicable for solute which having less solubility into the gases. It is used for finding solubility of liquid into the gases.

y = Hx

H is the henry law coefficient.

Application : this law is used to find out the solubility of the liquid and gas into the other solvents. Like O2 solubility into the water and so. Much examples which are found out by this law and also use in mass transfer operations and chemical Operation in industry.

D) Jd corellation for mass transfer in flow parallel to flat plate

As we know that

Mass transfer factor Jd =( Std) *(Sc) ^(2/3

Where (Std) is the Stanton number for diffusion.

Std = Sh/ReSc

For parallel flat plate,

Sh = 0.664*Re^0.5 * Sc^(1/3)

Std = (0.664*Re^0.5 * Sc^(1/3)/ReSc = 0.664Re^-0.5 * Sc(-2/3)

Then

Jd = 0.664*Re^-0.5