Page 192 - Modelling in Transport Phenomena A Conceptual Approach

172 CHAPTER 6. STEADY-STATE MACROSCOPIC BALANCES

where CA,,, and cB,, represent the molar concentrations of species d and t3 in
the reactor, respectively. Dropping the subscript “sys” and dividing Eq. (1) by the
volumetric flow rate, Q, gives

(CA)in - CA
7= (2)
k CACB
Using Eq. (5.3-17), the extent of reaction can be calculated m

- (2000) (0.8) = 1600 mol/ m3
-
1 (3)
Therefore, the concentrations of species d, t3, and C in the reactor are
+
CA = (cA)~~ QA < = 2000 - 1600 = 400 mol/ m3 (4)
CB = (c~)in + (YB = 2400 - 1600 = 800 mol/ m3 (5)
cc = (%)in + ac [ = (2)(1600) = 3200 mol/ m3 (6)

If kl and kz represent the rate constants at temperatures of TI and T2, respectively,
then

Therefore, the reaction rate constant at 65°C (338K) is

- -
-
k = 8.4 x 10-6exp - -
[ ?E (3&? 2k)]
= 9.15 x m3/ mol. min
Substitution of numerical values into Eq. (2) gives
2000 - 400
7= = 54.6min
(9.15 x (400)(800)

b) The reactor volume, V, is given by

The volumetric pow rate can be determined from the production rate of species C,
a.e..
820
ccQ=820 + &=-- - 0.256 m3/ min
3200
Hence, the reactor volume is

V = (54.6)(0.256) = 14m3