Equimolar Counter Diffusion Of A and B (NA =-NB) Chemical Engineering Notes | EduRev

Mass Transfer

Chemical Engineering : Equimolar Counter Diffusion Of A and B (NA =-NB) Chemical Engineering Notes | EduRev

The document Equimolar Counter Diffusion Of A and B (NA =-NB) Chemical Engineering Notes | EduRev is a part of the Chemical Engineering Course Mass Transfer.
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Equimolar counter-diffusion of A and B (NA =-NB) 
Equimolar Counter Diffusion Of A and B (NA =-NB) Chemical Engineering Notes | EduRev  → Gas phase                (3.19)
Equimolar Counter Diffusion Of A and B (NA =-NB) Chemical Engineering Notes | EduRev → Liquid phase                                        (3.20)

For gas phase diffusion we know, 
Equimolar Counter Diffusion Of A and B (NA =-NB) Chemical Engineering Notes | EduRev                                                                                     (3.21)

Equating Equation (3.19) and Equation (3.21),
Equimolar Counter Diffusion Of A and B (NA =-NB) Chemical Engineering Notes | EduRev                                                                                                     (3.22)

Again,

Equimolar Counter Diffusion Of A and B (NA =-NB) Chemical Engineering Notes | EduRev                                                        (3.23)

Equating Equation (3.19) and Equation (3.23),
Equimolar Counter Diffusion Of A and B (NA =-NB) Chemical Engineering Notes | EduRev                                                                                                     (3.24)
Also,
Equimolar Counter Diffusion Of A and B (NA =-NB) Chemical Engineering Notes | EduRev                                                          (3.25)
Equating Equation (3.19) and Equation (3.25),
Equimolar Counter Diffusion Of A and B (NA =-NB) Chemical Engineering Notes | EduRev                                                                                                       (3.26)

For liquid phase diffusion the flux can be written as
Equimolar Counter Diffusion Of A and B (NA =-NB) Chemical Engineering Notes | EduRev                                                                         (3.27)
Equating Equation (3.20) and Equation (3.27), Equimolar Counter Diffusion Of A and B (NA =-NB) Chemical Engineering Notes | EduRev                  (3.28)
Also, 
Equimolar Counter Diffusion Of A and B (NA =-NB) Chemical Engineering Notes | EduRev                                           (3.29)
Equimolar Counter Diffusion Of A and B (NA =-NB) Chemical Engineering Notes | EduRev                                                                                                    (3.30)

Equating Equation (3.8) and Equation (3.17),
Conversions:    Equimolar Counter Diffusion Of A and B (NA =-NB) Chemical Engineering Notes | EduRev 

Example problem 3.1:
Hydrochloric acid (A) diffuses through a thin film of water (B) 4.0 mm thick at 283 K. The concentration of HCl at point 1 on one boundary of the film is 12 wt% and on the other boundary, at point 2 is 4 wt%. The diffusivity of HCl in water is 2.5 x 10-9 m2/s. Calculate the flux of HCl considering water to be stagnant. Density of the solutions at points 1 and 2 are 1060.7 kg/m3 and 1020.15 kg/m3 respectively.

Solution 3.1: Molecular weight of HCl, MA = 36.5 and MB = 18
At point 1, mole fraction of HCl
Equimolar Counter Diffusion Of A and B (NA =-NB) Chemical Engineering Notes | EduRev Therefore, xB1 = 1- 0.0629 = 0.9371
Average molecular weight at point 1
Equimolar Counter Diffusion Of A and B (NA =-NB) Chemical Engineering Notes | EduRev

At point 2, mole fraction of HCl 
Equimolar Counter Diffusion Of A and B (NA =-NB) Chemical Engineering Notes | EduRev
Average molecular weight at point 2 
Equimolar Counter Diffusion Of A and B (NA =-NB) Chemical Engineering Notes | EduRev
z = 4 mm = 0.004 m
Flux of HCl,
Equimolar Counter Diffusion Of A and B (NA =-NB) Chemical Engineering Notes | EduRev

3.2 Mass transfer under laminar flow condition 
Mass transfer coefficient does not play a big role in laminar flow condition as molecular diffusion exists there. In laminar flow regime, the average liquid phase mass transfer coefficient, kL,av is correlated with Sherwood number (Sh) and DAB as follows:
Equimolar Counter Diffusion Of A and B (NA =-NB) Chemical Engineering Notes | EduRev                                                                                         (3.31)
Equimolar Counter Diffusion Of A and B (NA =-NB) Chemical Engineering Notes | EduRev                                                                                    (3.32) 

3.3 Mass transfer under turbulent flow past solids
Mass transfer under flow past solid is a practically useful situation. Several theories have attempted to clarify the behavior of mass transfer coefficients. All the theories have some assumptions and some drawbacks. Hence, these are revised frequently. In turbulent flow medium, small fluid an element of different sizes, called eddies, move randomly. These eddies form, interact among others and disappear in the flow path. The total molar flux of a solute ‘A’ due to molecular diffusion and eddy diffusion, JA is as follows:
Equimolar Counter Diffusion Of A and B (NA =-NB) Chemical Engineering Notes | EduRev                                                                            (3.33)
where DE is eddy diffusivity. Eddy diffusivity depends on intensity of local turbulence.

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