Page 72 - Modelling in Transport Phenomena A Conceptual Approach

3.3. MASS TRANSFER COEFFIClENT 53

Solution
Physical properties

p = 789 kg/ m3
For ethanol (A) at 20 "C (293 K) :
Pyt = 43.6mmHg

Assumption
1. Ideal gas behavior.

Analysis
The muss transfer coefficient can be calculated from Eq. (3.3-4), i.e.,

NA, = IC, (CA, - CA,)
The concentration difference in Eq. (1) is given a.9 the concentration of ethanol va-
por at the surface of the liquid, CA,, minus that in the bulk solution, CA, . The con-
centration at the liquid surface is the saturation concentration while the concentra-
tion in the bulk is essentially zero at relatively short times so that CA, - CA, N CA, .
Therefore Eq. (1) simplifies to

The saturation concentration of ethanol is
psat
=- A
CAW RT
- 43.6'760 = 2.39 x kmol/ m3 (3)
-
(0.08205)(20 + 273)
Since the ethanol concentration within the cylinder reaches 2% of its saturation
value in 5 minutes, the moles of ethanol evaporated during this period is

n~ = (0.02)(2.39 x 10-3)(1.5 x = 7.17 x kmol (4)
where 1.5 x m3 is the volume of the air space in the tank. Therefore, the molar
$ux at 5 minutes can be calculated as

nA
NA, = (Area) (Time)
-
- 7.17 x = 1.2 x kmol/ m2. s (5)
(2 x 10-3/1) (5 x 60)
Substitution of Eqs. (3) and (5) into Eq. (2) gives the mass transfer coeficient as
1.2 x 10-7
k- = 5 x 10-~m/s
- 2-39 x 10-3