Page 591 - Bird R.B. Transport phenomena

Problems 571

18B.2. Error in neglecting the convection term in evaporation.
(a) Rework the problem in the text in §18.2 by neglecting the term x (N A + N ) in Eq. 18.0-1.
B
A
Show that this leads to
N Az = ^—_ (x -[ ~ x ) (18B.2-1)
A 2
A
This is a useful approximation if A is present only in very low concentrations.
(b) Obtain the result in (a) from Eq. 18.2-14 by making the appropriate approximation.
(c) What error is made in the determination of %b in Example 18.2-1 if the result in (a) is used?
AB
Answer: 5%
18B.3. Effect of mass transfer rate on the concentration profiles.
(a) Combine the result in Eq. 18.2-11 with that in Eq. 18.2-14 to get

(18B.3-1)

(b) Obtain the same result by integrating Eq. 18.2-1 directly, using the fact that N Az is constant.
(c) Note what happens when the mass transfer rate becomes small. Expand Eq. 18B.3-1 in a
Taylor series and keep two terms only, as is appropriate for small N . What happens to the
Az
slightly curved lines in Fig. 18.2-1 when N Az is very small?
18B.4. Absorption with chemical reaction.
(a) Rework the problem discussed in the text in §18.4, but take z = 0 to be the bottom of the
beaker and z = L at the gas-liquid interface.
(b) In solving Eq. 18.4-7, we took the solution to be of the sum of two hyperbolic functions.
Try solving the problem by using the equally valid solution Г = C } exp(b£) + C 2 exp(-fc£).
(c) In what way do the results in Eqs. 18.4-10 and 12 simplify for very large L? For very small
L? Interpret the results physically.
18B.5. Absorption of chlorine by cyclohexene. Chlorine can be absorbed from Cl 2-air mixtures by
olefins dissolved in CC1 4. It was found 5 that the reaction of Cl 2 with cyclohexene (C 6H 10) is
second order with respect to Cl 2 and zero order with respect to C 6H 10. Hence the rate of disap-
2
pearance of Cl 2 per unit volume is k 2"c A (where A designates Cl 2).
Rework the problem of §18.4 where В is a C H -CC1 mixture, assuming that the diffu-
6 1O 4
sion can be treated as pseudobinary. Assume that the air is essentially insoluble in the
C H -CC1 mixture. Let the liquid phase be sufficiently deep that L can be taken to be infinite.
6
4
1O
(a) Show that the concentration profile is given by

(b) Obtain an expression for the rate of absorption of Cl by the liquid.
2
(c) Suppose that a substance A dissolves in and reacts with substance В so that the rate of dis-
appearance of A per unit volume is some arbitrary function of the concentration, f(c ). Show
A
that the rate of absorption of A is given by

N \ = 0 = ^AB j^f(c )dc A (18B.5-2)
Az z
A
Use this result to check the result of (b).

5 G. H. Roper, Chem. Eng. Sci., 2,18-31, 247-253 (1953).