CHEMICAL ENGINEERING

MASS TRANSFER 231

maintained at a constant temperature, and an air stream is passed over the top of the tube
sufficiently rapidly to ensure the partial pressure of the vapour there remains approximately
zero. On the assumption that the vapour is transferred from the surface of the liquid to the
air stream by molecular diffusion, calculate the diffusivity of carbon tetrachloride vapour
in air at 321 K and atmospheric pressure from the following experimentally obtained data:

Time from commencement Liquid level

of experiment (ks) (cm)

00.00

1.6 0.25

11.1 1.29

27.4 2.32

80.2 4.39

117.5 5.47

168.6 6.70

199.7 7.38

289.3 9.03

383.1 10.48

The vapour pressure of carbon tetrachloride at 321 K is 37.6kN/m^2 , and the density
of the liquid is 1540 kg/m^3. The kilogram molecular volume is 22.4m^3.

Solution

Equations 10.37 and 10.38 state that:

NADD

CA 2 CA 1

y 2 y 1

CT

CBm

In this problem, the distance through which the gas is diffusing will be taken ashand
CA 2 D0.

∴ NADDCA/h
CT/CBm kmol/m^2 s

whereCAis the concentration at the interface.
If the liquid level falls by a distance dhin time dt, the rate of evaporation is:

NAD+L/M

dh/dtkmol/m^2 s

Hence: +L/M
dh/dtDDCA/h
CT/CBm

If this equation is integrated, noting that whentD0,hDh 0 , then:

h^2 h^20 D 2 MD/+L

CACT/CBm

t

or:

t/hh 0

 D+L/ 2 MD

CBm/CACT

hh 0

 C+LCBm/MDCACT

h 0