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2.3 Gas–Liquid Interfacial Behavior 55

Fig. 2.10 Interfacial mass Driving
transfer diving force y force Equilibrium
line
Driving
Gas force
phase
mole y*
ratio, y

x x*
Liquid phase molar ratio, x

0
n ¼ K y y y Þ gas phase ð2:83Þ
ð
0
n ¼ K x x xð Þ liquid phase ð2:84Þ
where K x , K y = Overall mass transfer coefficients for the liquid and gas phases
2
respectively (mol/m s). x ; y ¼ Hypothetical mole fraction corresponding to y, x

in the bulk fluids, and they are determined by the Henry’s law as
y ¼ Hx ð2:85Þ

y ¼ Hx ð2:86Þ
The difference between the hypothetical mole fraction and the corresponding
actual mole fraction results in the driving force illustrated in Fig. 2.10.
If we consider gas phase only in Eq. (2.83) above, the total mass transfer rate
2
(mole/m s) is described as
0
ð
½
n ¼ K y y yð Þ ¼ K y y y i Þ þ y i y ފ ð2:87Þ
ð
Dividing both sides by K y gives,
n 0
ð
¼ y y i Þ þ Hx i xÞ ð2:88Þ
ð
K y
The single-phase mass transfer Eqs. (2.81) and (2.84) above also give
n 0 n 0
¼ y y i and ¼ x i x ð2:89Þ
k y k x

Substitute Eq. (2.89) into (2.88) and dividing both sides with n , one can get
0
1 1 H
¼ þ ð2:90Þ
K y k y k x