Page 398 - Modelling in Transport Phenomena A Conceptual Approach

378 CHAPTER 9. STEADY MICROSCOPIC BALANCES WITH GEN.

4. The concentration of dZ3 does not interfere with the diffusion of A through
f?, i.e., A molecules, for the most part, hit molecules l? and hardly ever hit
molecules AB. This is known as the pseudo-binary behavior.

Since CA = CA(Z), Table C.8 in Appendix C indicates that the only non-zero
molar flux component is NA. and it is given by

(9.42)

For a differential volume element of thickness A2, as shown in Figure 9.14, Q.
(9.41) is expressed as

NA, 1% A - NA, lz+Az A + %A A Az = 0 (9.43)
Dividing Eq. (9.43) by AAz and taking the limit as Az + 0 gives

(9.44)

(9.45)

The use of Eq. (5.3-26) gives the rate of depletion of species A per unit volume as

%A=-kCA (9.46)
Substitution of Eqs. (9.42) and (9.4-6) into Eq. (9.45) yields

(9.47)

The boundary conditions associated with the problem are

at z = 0 CA =CA, (9.48)

at z=L -- -0 (9.49)
dCA
dz
The value of CA, in Eq. (9.48) can be determined from Henry’s law. The boundary
condition given by Eq. (9.49) indicates that since species A cannot diffuse through
the bottom of the container, i.e., impermeable wall, then, the molar flux and the
concentration gradient of species A are zero.
The physical significance and the order of magnitude of the terms in Eq. (9.47)
are given in Table 9.2. Therefore, the ratio of the rate of reaction to the rate of
diffusion is given by

Rate of reaction - IccAo - k L2
-
--
Rate of diffusion DABCAo/L2 DAB (9.410)