Applications of Chemical Kinetics in Environmental Systems - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 285

The rate of mass transfer from gas to liquid through the gas film is given by

k G C G i −

G i

C int r 1 = (6.47)

and that through the liquid film by

k L C int C L i .

r 2 =

L i −

(6.48)

At steady state, the rate at which the mass reaching the interface from the gas side
should equal that leaving through the liquid film, that is, r 1 = r 2 ,

k G C G i −

G i

k L C int C L i .

C int =

L i −

(6.49)

Since C int

G i and C int L i are not known or obtainable from experiments, we need to

eliminate these using the air-water partition equilibrium to obtain

k G C G i +

k L C L i

C int

G i =

(k L /K aw )) .

(6.50)

(k G +

Hence,

C G i

K aw − C L i

1
(( 1 /k L ) + ( 1 /k G K aw ))

r 1 = (6.51)

is the rate of transfer from gas to liquid ( absorption ). If the transfer is from liquid to
gas ( stripping ), the rate is

C L i − .

C G i
K aw

1

r 1 = (6.52)

(( 1 /k L ) + ( 1 /k G K aw ))

If the rate of absorption is expressed in the form
r 1 = K L C G i

K aw − C L i ,

(6.53)

where K L is the overall mass transfer coefficient based on the bulk-phase concentra-
tions, we recognize that

1
K L =

1
k L +

1
k G K aw

, (6.54)

where each term represents a resistance to mass transfer

R T = R L + R G . (6.55)

The rate can also be expressed as follows:

K G C G i − K aw C L i ,

r 1 = (6.56)