CHEMICAL ENGINEERING

MASS TRANSFER 233

CB 2 D 0. 0380  0. 0141

 D 0 .0239 kmol/m^3

∴ CBmD 0. 0380  0. 0239
/ln 0. 0380 / 0. 0239
D 0 .0304 kmol/m^3

Hence: DD 1540 ð 0. 0304
/ 2 ð 154 ð 0. 0141 ð 0. 0380 ð 3. 04 ð 10 ^7

D 9. 33 ð 10 ^6 m^2 /s

PROBLEM 10.15

Ammonia is absorbed in water from a mixture with air using a column operating at
atmospheric pressure and 295 K. The resistance to transfer can be regarded as lying
entirely within the gas phase. At a point in the column the partial pressure of the ammonia
is 6.6kN/m^2. The back pressure at the water interface is negligible and the resistance to
transfer can be regarded as lying in a stationary gas film 1 mm thick. If the diffusivity of
ammonia in air is 0.236 cm^2 /s, what is the transfer rate per unit area at that point in the
column? If the gas were compressed to 200 kN/m^2 pressure, how would the transfer rate
be altered?

Solution

See Volume 1, Example 10.3.

PROBLEM 10.16

What are the general principles underlying the two-film penetration and film-penetration
theories for mass transfer across a phase boundary? Give the basic differential equations
which have to be solved for these theories with the appropriate boundary conditions.
According to the penetration theory, the instantaneous rate of mass transfer per unit

areaNA (^) tat some timetafter the commencement of transfer is given by:
NA (^) tDCA

√

D

t

whereCAis the concentration driving force andDis the diffusivity.
Obtain expressions for the average rates of transfer on the basis of the Higbie and
Danckwerts assumptions.

Solution

The various theories for the mechanism of mass transfer across a phase boundary are
discussed in Section 10.5.
The basic equation for unsteady state equimolecular counter-diffusion is:

∂CA

∂t

DD

[(

∂^2 CA

∂x^2

)

yz

C

(

∂^2 CA

∂yz

)

xz

C

(

∂^2 CA

∂z^2

)

xy

]

(equation 10.67)