CHEMICAL ENGINEERING

246 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

Then:

(a) The mass transfer coefficientD 2

√

D

t

D 2  1. 2 ð 10 ^8 /ð 5. 55

0.^5

D 5. 25 ð 10 ^5 m/s

(b) The mean rate of transfer,NAD 2 C^0 iD/t

^0.^5 D 2 ð 0. 2885  1. 2 ð 10 ^8 /ð 5. 55

0.^5

D 1. 51 ð 10 ^5 kmol/m^2 s

(c) The film thicknessLis given by:NADD/L

CN^0 i

and: LD 1. 2 ð 10 ^8 ð 0. 2885
/ 1. 51 ð 10 ^5 D 2. 29 ð 10 ^4 mD 0 .23 mm

PROBLEM 10.25

Two large reservoirs of gas are connected by a pipe of length 2Lwith a full-bore valve
at its mid-point. Initially a gasAfills one reservoir and the pipe up to the valve and gas
Bfills the other reservoir and the remainder of the pipe. The valve is opened rapidly and
the gases in the pipe mix by molecular diffusion.
Obtain an expression for the concentration of gasAin that half of the pipe in which
it is increasing, as a function of distanceyfrom the valve and timetafter opening. The
whole system is at a constant pressure and the ideal gas law is applicable to both gases. It
may be assumed that the rate of mixing in the vessels is high so that the gas concentration
at the two ends of the pipe do not change.

Solution

The system and nomenclature are shown in Fig. 10c.

y = −L

y = 0

y = +L

CA = CA 0 CA = 0

Figure 10c.

When timetD0,

For gasA:

∂CA

∂t

DD

∂^2 CA

∂y^2