CHEMICAL ENGINEERING

MASS TRANSFER 253

or:

√

Dt

L^2

eDt/L

2

erfc

√

Dt

L^2

D

√

1



ð 0. 16 D 0. 0903

writing XD

√

Dt

L^2

thenXeX

2

erfcXD 0. 0903

Solving by trial and error:XD 0. 101
WhentD1s,DD 1. 76 ð 10 ^9 m^2 /s, and: LD 0 .42 mm.

PROBLEM 10.30

A deep pool of ethanol is suddenly exposed to an atmosphere consisting of pure carbon
dioxide and unsteady state mass transfer, governed by Fick’s Law, takes place for 100
s. What proportion of the absorbed carbon dioxide will have accumulated in the 1 mm
thick layer of ethanol closest to the surface? Diffusivity of carbon dioxide in ethanolD
4 ð 10 ^9 m^2 /s.

Solution

See Volume 1, Example 10.6.

PROBLEM 10.31

A soluble gas is absorbed into a liquid with which it undergoes a second-order irreversible
reaction. The process reaches a steady-state with the surface concentration of reacting
material remaining constant atCAs and the depth of penetration of the reactant being
small compared with the depth of liquid which can be regarded as infinite in extent.
Derive the basic differential equation for the process and from this derive an expression
for the concentration and mass transfer rate (moles per unit area and unit time) as a
function of depth below the surface. Assume that mass transfer is by molecular diffusion.
If the surface concentration is maintained at 0.04 kmol/m^3 , the second-order rate
constantk 2 is 9. 5 ð 103 m^3 /kmol s and the liquid phase diffusivityDis 1. 8 ð 10 ^9 m^2 /s,
calculate:

(a) The concentration at a depth of 0.1 mm.

(b) The molar rate of transfer at the surfacekmol/m^2 s.

(c) The molar rate of transfer at a depth of 0.1 mm.

It may be noted that if:
dCA
dy

Dq, then:

d^2 CA

dy^2

Dq

dq

dCA

Solution

Considering element of unit area and depth dy, then for a steady state process:

RATE INRATE OUTDREACTION RATE