Page 258 - Elements of Chemical Reaction Engineering 3rd Edition

230 Collection and Analysis of Rate Data Chap. 5

2. Rewrite the design equation in terms of the measured variable. When
there is a net increase or decrease in the total number of moles in a gas phase reac-
tion, the reaction order may be detemined from experiments performed with a con-
stant-volume batch reactor by monitoring the total pressure as a function of time.
The total pressure data should not be converted to conversion and then analyzed as
conversion-time data just because the design equations are written in terms of the
Processing data variable conversions. Rather, transform ' the design equation to the measured
in terms of the variable, which in this case is pressure. Consequently, we need to express the con-
measured centration in terms of total pressure and then substitute for the concentration of A
variable, P
in Equation (E5-1.1).
For the case of a constant-volume batch reactor, we recall Equations (3-26)
and (3-38):
CA = c*o( - X) (3-26)
1
PO T
v = VO - (1 + EX) - (3-38)
P T"
For isothermal operation and constant volume, Equation (3-38) solves to

1
x=-(P-Po) (E5-1.2)
6pA0
where

= YAOPO
Combining Equations (3-26) and (E5- 1.2) gives

(E5- 1.3)

For pure di-tert-butyl peroxide, initially yAO = 1.0 and therefore PA, = Po. Stoi-
chiometry gives 6 = 1 + 2 - 1 = 2.

(E5- 1.4)

Substitute Equation (E5-1.4) into (E5-1.1) to get

Let k' = k(ZRT)l-"; then
1 = k'(3P0- P)" (E5-1.5)

L I