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Chemical Engineering 150B- Fall 2005
Problem Set #4 Solutions
Problem 1.
(15 points) Consider liquid A evaporating into initially pure gaseous B in a closed
vessel shown below:
This vessel initially has 0.4 liter of A with 75 cm
2
of surface area in a total volume of 20 liters.
After 4 minutes, B is five percent saturated with A.
(a) What is the mass transfer coefficient of A? Note that the vessel is isothermal at 298 K,
and the equilibrium vapor pressure of A at 298K is 24 torr.
Both A and B are ideal in the
gas phase.
The flux at 4 minutes can be found directly from the values given:
(
)(
)
(
)(
)
1
vapor concentration
air volume
N
liquid area
time
=
(
)
(
)
(
)
2
1
2
1
24
273
0 05
19 6
760
22 4
298
75
240
mol
.
.
.
L
N
mol / cm s
cm
sec
⎛
⎞
⎛
⎞
⎛
⎞
⎜
⎟
⎜
⎟
⎜
⎟
⎝
⎠
⎝
⎠
⎝
⎠
=
=
-8
7.0 x 10
The concentration difference is that at the interface between A and B minus that in the solution.
That at the surface is the value at saturation; that in the bulk at short times is essentially zero.
Thus,
(
)
1
A,i
A
N
k c
c
=
−
2
3
3
1
24
273
0
760
298
22 4
10
mol
mol / cm s
k
. *
cm
k
⎛
⎞
=
−
⎜
⎟
⎝
⎠
=
-8
7.0 x 10
0.054 cm/s
This value is lower than that commonly found for transfer in gases.
(b) How long will it take to reach ninety percent saturation of A in B?
The time required for 90 percent saturation can be found from a mass balance:
accumulation in gas phase =
evaporation rate
B (
g
)
A (
l
)
2 pt
2 pt
3 pt

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