Page 230 - Modelling in Transport Phenomena A Conceptual Approach

210 CHAPTER 7. UNSTEADY-STATE MACROSCOPIC BALANCES

Solution
System: Contents of the reactor
The consemation statement for species A, Eq. (7.2-5), is

The number of moles of species A and B in terms of the molar extent of the
reaction, E, is given by

nA = nA, + QA & = 2000 - & (3)
ng = ngo -I- ag E = 2400 - E (4)
The molar extent of the reaction can be calculated from Eq- (5.3-12) as

E=- nAo XA
(- CYA)
- (2000) (0.8) = 1600mol
-
1 (5)
Substitution of Eqs. (3) and (4) into Eq. (2) and rearrangement gives
1600 d&
=
k (2000 - ~)(2400 - E)
Note that Eq. (6) cannot be integrated directly since the reaction rate constant, k,
is dependent on E via temperature.
The energy equation must be used to determine the variation of temperature
as a function of the molar extent of the reaction. For an adiabatic reactor, i.e.,
Qint = 0, Eq. (7.5-18) redurn to

Substitution of Eqs. (5.3-22) and (7.5-17) into Eq. (7) yields

In this problem

A@ = - 85 J/ mol. K (9)
nio Cpi = (2000) (175) + (2400) (130) = 662,000 (10)
i
AH&, - 45,000 - 85 (T - 298) (11)