Page 106 - Separation process principles 2

3.1 Steady-State, Ordinary Molecular Diffusion 71

From (3-32),
XA = 1 - 0.869 exp(0.281 z)
shown in Figure 3.2, an open beaker, 6 cm in height, is filled (1)
with liquid benzene at 25°C to within 0.5 cm of the top. A gentle Using (I), the following results are obtained:
breeze of dry air at 25OC and 1 atm is blown by a fan across the
mouth of the beaker so that evaporated benzene is carried away by
after it transfers through a stagnant air layer in the
beaker. The vapor pressure of benzene at 25OC is 0.131 atm. The
mutual diffusion coefficient for benzene in air at 25OC and 1 atm is
0.0905 cm2/s. Compute:
(a) The initial rate of evaporation of benzene as a molar flux in
moIJcm2-s
(b) The initial mole-fraction profiles in the stagnant air layer These profiles are only slightly curved.
(c) The initial fractions of the mass-transfer fluxes due to molecu- (c) From (3-27) and (3-29), we can compute the bulk flow terms,
lar diffusion xANA and xBNA, from which the molecular diffusion terms are
(d) The initial diffusion velocities, and the species velocities (rela- obtained.
tive to stationary coordinates) in the stagnant layer
(e) The time in hours for the benzene level in the beaker to drop xiN J;
2 cm from the initial level, if the specific gravity of liquid ben- Bulk-Flow Flux, Molecular-Diffusion
zene is 0.874. Neglect the accumulation of benzene and air in moYcm2-s x lo6 Flux, mol/cm2-s x lo6
the stagnant layer as it increases in height
z, cm A B A B

SOLUTZON

Let A = benzene, B = air.

(a) Take zl = 0. Then 22 - zl = Az = 0.5 cm. From Dalton's law,
assuming equilibrium at the liquid benzene-air interface, Note that the molecular-diffusion fluxes are equal but opposite,
and the bulk-flow flux of B is equal but opposite to its molecular-
diffusion flux, so that its molar flux, NB, is zero, making B (air)
stagnant.
(d) From (3-6),

From (3-35),
From (3-9), the diffusion velocities are given by

From (3-LO), the species velocities relative to stationary coordinates
are
21; = Vid f VM (4)
Air 1 atm
25°C Using (2) to (4), we obtain
____)
Vid Ji
Molecular-Diffusion Species Velocity,

' ' 1 Interface I I Velocity, cds cm/s

Beaker
Figure 3.2 Evaporation of benzene from a beaker-Example 3.2.