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3.1 Introduction to Heterogeneous Processes 71

where K ov f v erall coef is an oicient (in m/s):

1 1 H 1  1 
H   (3.52)
K ov k g fg k f k  s s k 

w It is noteorthy that not all the resistances are significant in eery case. If only a pure gas v
constitutes the gas phase and for slightly soluble gases, the resistance to the mass transfer
on the liquid side of the interface is predominant. Under these conditions, C G C G,i and
v the aboe equation reduces to

1 1  1 1 
H   (3.53)
K ov fg  k f k k s s 

Even when the gaseous reactant is in a mixture with other components in the b ubbles, k g
appears to be much larger than k fg /H and thus, the last equation is applicable.

Derivation of an oall gas transfer r ver ate
In many three-phase systems, the two resistances in the gas–liquid interface are combined
v
in one oerall gas mass transfer coef f icient K L . To do this, we combine the follo wing
rates:
r k C ( G C G,i ) (bulk g to bubble i nt erface) (3.54)
as
g
g
r fg k C ( L,i C ) (bubble inte to bulk liquid) (3.55)
e
rfa
c
L
fg
If equilibrium exists at the bubble–liquid interface, C G,i and C L,i are related by Henry’s law:
C G,i HC L,i (3.56)
Then
kC g G k C fg L
C L,i k (3.57)
k g
fg
H
The rate becomes

Hk k gf g C  
r fg k C ( L,i C )  G C L  (3.58)
fg
L
k fg Hk g H  
Defining an oerall gas-phase mass transfer coef icient v f K L (in m/s),
Hk k gf g 1 1 1
K (3.59)
L
k Hk K Hk k
fg g L g fg