Distillation

Unit 1 Distillation 
Contents 
1. Concept of diffusion. (definition) 
2. Fick’s law of diffusion. 
3. Steady state diffusion through a stagnant gas film. 
4. Steady state equimolar counter diffusion. 

  Learning Objective/ Key learning 
State the role of diffusion in the given mass transfer. 
►What is Diffusion? 
►Define Fick’s Law. 
►Derive the equation for Steady state diffusion through a stagnant gas film. 
►Derive the equation for Steady state equimolar counter diffusion. 
 
WHAT ID DIFFUSION? 
    ►Diffusion is the tendency of molecules to move toward areas of lower concentration until the concentration is uniform throughout. 
 It is movement of an individual component through a mixture from a region of higher concentration to region of lower concentration at fixed temp & press with or without the help of external force.

 ►FICK’S LAW OF DIFFUSION : 
    First law of diffusion (Steady state Law) Adolf Fick (1955) first described the molecular diffusion in an isothermal, isobaric, binary system of components A and B. ►According to his idea of molecular diffusion, the molar flux of a species relative to an observer moving with molar average velocity is proportional to the concentration gradient in a certain direction. ►EQUATION FOR FICK’S LAW OF DIFFUSION 
 JA= - DAB DCA/Dz  
►Where, JA is the molar flux of component A in the Z direction. 
►CA is the concentration of A and Z is the distance of diffusion. 
►The proportionality constant, DAB is the diffusion coefficient of the molecule A in B. This is valid only at steady state condition of diffusion. 
►The Equation is called Fick’s first law of diffusion.

Concept of Diffusion

                       

   1. A Cylindar Of Air  And a Cylindar of Bromine Vapor are sealed Together
   2. Bromine Vapor Diffuses upward through the air
   3. After several hours  Bromine vapour reaches top of column.

Derivation Of the equation for steady State diffusion through a stagnant gas Film

Assume steady state diffusion in the Z direction without any chemical reaction in a binary gaseous mixture of species A and B. For one dimensional diffusion of species A, the Equation of molar flux can be written as

 NA=-CD AB dyA/Dz  + yA(NA + NB) 

Separating  the variables in equation

-dyA/NA -yA (NA +NB) = dz/CDAB

For the gaseous mixture, at constant pressure and temperature C and DAB are constant, independent of position and composition. Also all the molar fluxes are constant in Equation. Therefore the Equation can be integrated between two boundary conditions as follows 

at Z=Z1     YA= YA1
    Z=Z2       YA=YA2

Derivation of the equation for Steady state diffusion through a stagnant gas film…..cont
 where 1 indicates the start of the diffusion path and 2 indicates the end of the diffusion path. After integration with the above boundary conditions the Equation for diffusion for the said condition can be expressed as

NA=NA/(NA + NB)     CDAB/Z2-Z1     In[NA/NA + NB) - yA2/NA/(NA=NB)-YA1]

For steady state one dimensional diffusion of A through non-diffusing B, NB = 0 and NA = constant. Therefore NA /(NA + NB ) =1 . Hence Equation becomes

NA= CDAB/Z2-Z1  In[1-yA2/1-YA1]

Since for an ideal gas C=p/RT and for mixture of ideal gases yA=pA /P, the Equation can be expressed in terms of partial pressures as 

NA=PDAB/(Z2-Z1)RT  In(P-PA2/P-PA1]

 









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