Page 227 - Elements of Chemical Reaction Engineering 3rd Edition

Sec. 4.7 Unsteady-State Operation of Reactors 199

We now need to determine the volume as a function of either conversion or
time. An overall mass balance on all species gives

(4-78)

where MWD is the molecular weight of D. For a constant-density system,,

(4-79)

This equation must now be solved numerically and simultaneously with equa-
tions (4-74) through (4-77). However. in order to solve the set of equations
above we need to specify the rate of evaporation of D, FD.

Case 1 Immediate Evaporation
For the case where D evaporates immediately after being formed, we: can
obtain an analytical solution. For no accumulation of D in the liquid phase,

F, -T rDV = - rAV (4.-80)
dX
FD = NAO-;if (4-81)
Combining Equations (4-79) and (4-81), we have

(4-82)
Assuming that
product D
vaporizes Integrating yields
immediately after
forming V = Vo - cxNAoX

Rearranging, we have

v = V0( 1 + ELX) (4-83)
where

Combining Equation (4-77) for the case of CD = 0 with (4-83), we obtain

(4-84)

Using ithe list of integrals in Appendix A.2, we can determine the true t to
achieve a conversion X in the reactor:

Second-order
reactive (4- 85)
distillation
1 I