Page 191 - Modeling of Chemical Kinetics and Reactor Design

Reaction Rate Expression 161

For any product C or D, the partial pressure is expressed as:

p = C RT = p − c (π − ) π (3-209)
C
∆ n O
CO
C
For an ideal gas at both constant temperature and pressure, but with
changing number of moles during reaction, Levenspiel relates that

V = V (1 + ε X ) (3-210)
A
A
O
where
V − V V − V
ε = all A reacted no reaction = X A =1 X A =0
A
V no reaction V X A =0 (3-211)

Levenspiel considers the cases where the relationship between
concentration and conversion of reacting specie is not obvious, but
depends on a number of factors.

CASE 1: CONSTANT DENSITY SYSTEMS

This case includes most liquid reactions and also those gas reactions
that operate at both constant temperature and pressure with no change
in the number of moles during reaction. The relationship between
concentration C and fractional conversion X is as follows:
A
A
X =− C A and dX = − dC A
1
A
A
C C
AO AO
C A =− X and dC = − C dX
1
C AO A A AO A (3-212)

where ε = 0. The changes in B and C to A are
A

C − C C − C C C − C CO
AO A = BO B = (3-213)
a b c
or