Page 569 - Elements of Chemical Reaction Engineering Ebook

Sec. 9.2 Unsteady Operation of CSTRs and Semibatch Reactors 539

4. Combining Equations (E9-l.l), (E9-1.2), and (2-6), we have

dx -- - k(l - X) (E9-1.3)
dt
From the data in Example 8-4,

k = (4.71 X IO9) exp

or

(E9-1.4)
A table similar to that used in Example 8-6 can now be constructed.
5. Energy balance. Using Equation (9-17), the relationship between X and T for
an adiabatic reaction is given by

(E9- 1.5)

6. Evaluating the parameters in the energy balance gives us the heat capacity
of the soliution:

cPs = c O, Cp, = @AZlpA + oBC,B + oCZ;C + o,C,I
= (1)(35) + (18.65)(18) + 0 + (1.670)(19.5)
= 403 Btu/lb mol A."F
From Example 8-4, AeP = -7 Btu/lb mol-"F and consequently, the second
term on the right-hand side of the expression folr the heat of reaction,
AHRx(T) = AH;;,(TR)+A6p(T-~R)
= -36,400 - 7(T - 528) (E8-4.7)
is very small compared with the first term [less than 2% at 51.5% conversion
(from Example 8-4)].
Taking the heat of reaction at the initial temperature of 535"R,
AHR~(T,) = -36,400 - (7)(535 - 528)
= -36,450 Btu/lb mol
Because terms containing Atp are very small, it can be assumed that
Aep = 0
In calculating the initial temperature, we must include the temperature rise
from the heat of mixing the two solutions:

& = (460 + 58) + 17
= 535"R

= 535 + 90.45 X (E9- 1.6)