Page 257 - Introduction to chemical reaction engineering and kinetics

238 Chapter 9: Multiphase Reacting Systems

and (- RA) and (- Rn) are related by
c-w = M-R,) (9.1-8a)

we eliminate (-RA), ( -RB) and cAs (Concentration at the surface) from these four equa-
tions to obtain a differential equation involving dR/dt, which, on integration, provides the
desired relation. The equation resulting for dR/dt is

which leads to

(9.1-40)

from equation 9.1-34. For simplicity, we consider results for the two limiting cases of
equation 9.1-34 (ignoring K21R’12 or K,IR), as described in Section 9.1.2.3.3.
For small particles, integration of 9.1-40 without the term K21R’j2 results in

, (9.1-41)

or, since, for a spherical particle

fE = 1 - (R/RJ3 (9.1-42)

II (9.1-43)

The time tl for complete reaction (fn = 1) is

G=*(g+&) (9.1-44)

For large particles, the corresponding results (with the term K,IR in equation 9.1-40
dropped) are:

(9.1-45)

1 [
1 - (1 - fn)l’2 + &- 1 - (1 - fs)“3 (9.1-46)