CHEMICAL ENGINEERING

MASS TRANSFER 243

X eX

2

erfX erfcXX

p

erfcX Right hand side

1 0.368 0.843 0.157 0.278 0.0897

0.9 0.445 0.797 0.203 0.324 0.121

0.97 0.390 0.830 0.170 0.292 0.098

0.96 0.398 0.825 0.175 0.297 0.101

∴ XD 0. 96 Dy^2 / 4 Dt

∴ yD 0. 96 ð 4 ð 10 ^9 ð 60
0.^5 D 4. 8 ð 10 ^4 mor 0.48 mm

PROBLEM 10.23

A chamber, of volume 1 m^3 , contains air at a temperature of 293 K and a pressure of
101 .3kN/m^2 , with a partial pressure of water vapour of 0.8kN/m^2. A bowl of liquid
with a free surface of 0.01 m^2 and maintained at a temperature of 303 K is introduced
into the chamber. How long will it take for the air to become 90% saturated at 293 K
and how much water must be evaporated?
The diffusivity of water vapour in air is 2. 4 ð 10 ^5 m^2 /s and the mass transfer resis-
tance is equivalent to that of a stagnant gas film of thickness 0.25 mm. Neglect the effects
of bulk flow. Saturation vapour pressure of waterD 4 .3kN/m^2 at 303 K and 2.3kN/m^2
at 293 K.

Solution

Moles transferred,

nDDA/L

CAsCA

whereCADconcentration (kmol/m^3 ),CAsis the saturation value ofCAat the surfaceD
is the diffusivity andLis the thickness of the stagnant gas film.
If the saturated vapour pressure at the interface is 4.3kN/m^2 and if at any time the
partial pressure in the air isPAkN/m^2 , then the rate of evaporation is given by:

dn

dt

D

0. 01 ð 2. 4 ð 10 ^5

 0. 25 / 1000

[

1

22. 4

ð

273

303

(

4. 3

101. 3



PA

101. 3

)]

D 3. 81 ð 10 ^7  4. 3 PA kmol/s

1m^3 of air at 303 K and 101.3kN/m^2 is equivalent to 1 / 22. 4
 273 / 293
D 0 .0416 kmol

Initial moisture contentD 0. 8 / 101. 3
ð 0. 0416 D 3. 29 ð 10 ^4 kmol

Final moisture contentD 0. 9 ð 2. 3 / 101. 3
ð 0. 0416 D 8. 50 ð 10 ^4 kmol

∴ Water evaporatedD 8. 50  3. 29
ð 10 ^4 D 5. 21 ð 10 ^4 kmol
D 5. 21 ð 10 ^4 ð 18
D 9. 38 ð 10 ^3 kg water