xA* is the concentration
(mole fraction) in liquid phase that is in equilibrium with yAG.
yA* is the concentration (mole fraction) in vapor
phase that is in equilibrium with xAL.
Overall Mass Transfer Coefficients
The previous definitions for molar flux NA require the knowledge of the interface concentrations. Since experimental sampling of the concentrations at the interface is very difficult or virtually impossible; it is more useful to define the mass transfer equation using overall mass transfer coefficients KX and KY :
xA* is the concentration (mole fraction) in liquid phase that is in equilibrium with yAG.
yA* is the concentration (mole fraction) in vapor phase that is in equilibrium with xAL.
Driving force for mass transfer: ( yAG - yA* ) in the gas phase (as indicated by line PC) and ( xA* - xAL ) in the liquid phase (line PD). See the Figure below.
NOTE : for most situations the asterisk '*' is not shown.
[ Again, there is similarity to heat transfer - the overall heat transfer coefficient which can be defined based on outer surface area of the tube (UO) or on the inner surface area of the tube (Ui). Here we have the overall mass transfer coefficient based on the gas side or based on the liquid side ]
Relationship between film and overall mass transfer coefficients:
It can be shown that kx, ky, KX, and KY are related through the following equations:
where m" is the slope of line segment DM, and m' is the slope of line segment MC as shown. If the equilibrium line is straight, then m' = m".
kx , ky , KX , and KY all change with positions in the tower.
The above equations can be used in gas solubility analysis. Click here for more information.
NOTE: units for kx , ky , KX , and KY varies with the way the mass transfer equation is written (vapor phase or liquid phase) and the driving forces used, e.g. mole fractions ( y or x ), mole ratios ( X or Y ), weight fraction, partial pressures (p), or concentrations (c) etc.