Page 260 - Introduction to chemical reaction engineering and kinetics

9.2 Gas-Liquid Systems 241
where the liquid-film mass transfer coefficient is defined by

'be = DA&% (9.2-7)
(4) There is equilibrium at the interface, which is another way of assuming that there
is no resistance to mass transfer at the interface. The equilibrium relation may
be expressed by means of Henry’s law:

PAi = HACAi (9.2-8)

where HA is the Henry’s law constant for species A.
The rate of mass transfer of A may also be characterized in terms of overall mass
transfer coefficients KAg and KA, defined by

NA = KA&'A - 6~) (9.2-9)
= KA&~ - cA) (9.2-10)

where pi is the (fictitious) partial pressure of A in equilibrium with a liquid phase of
concentration CA,

Pi = HACA (9.2-11)
and, correspondingly, CL is the liquid-phase concentration of A in equilibrium with a
gas-phase partial pressure of PA,

PA =HAC~ (9.2-12)

KAs and KAe may each be related to kAg and kAo. From equations 9.2-3, -6, and -9,

1
-= ‘+HA (9.2-13)
KAY kg kAC

and from equations 9.2-3, -6, and -10,
1 - 1 - 1
- - HAkAg + kA, (9.2-14)
KA,
Each of these last two equations represents the additive contribution of gas- and
liquid-film resistances (on the right) to the overall resistance (on the left). (Each mass
transfer coefficient is a “conductance” and its reciprocal is a “resistance.“)
Special cases arise from each of equations 9.2-13 and -14, depending on the relative
magnitudes of kAg and k,,. For example, from equation 9.2-13, if kAg is relatively large
so that Ilk,, << HAlkAe, then KAs (and hence NA) is determined entirely by kAe, and
we have the situation of “liquid-film control.” An important example of this is the situ-
ation in which the gas phase is pure A, in which case there is no gas film for A to diffuse
through, and kAg --+ W. Conversely, we may have “gas-film control.” Similar conclu-
sions may be reached from consideration of equation 9.2-14 for KAe. In either case, we
obtain the following results:

NA = kAe(PAjHA - CA); liquid-film control (9.2-15)

NA = kAg(pA - HA CA); gas-film Control (9.2-16)