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110 3. Heterogeneous Processes and Reactor Analysis

The expansion f actor R is

N
A,i 1
R
N tot,i
Then

V
1 x A
V i

and thus
1 x
C C A C
A A,i A,i
1 x
A
Example 5
Consider the gas-phase reaction

a A g) ( b B(l) C(l)
which is carried out isothermally and isobarically. The limiting reactant is B while the gas
feed is pure A. Express the concentration of A as a function of con v ersion.

Solution
actor For the expansion f, we cannot use the expression (3.88) in the form

N
B,i
R
N tot,i
This is why the limiting reactant is B and expansion factor should be based on B, b ut
this is not a gaseous species, and thus does not contribute to the volume of the gas-phase.
However, we can use the same equation in the follo wing form:
N tot,( 1) x N tot,i

R
N tot,i
In this expression, we should take into account only the gas species, i.e. reactant A. We have

N tot,i N A,i

a
N N N x
tot A,i B,i B
b
where, for x 1,
B
a
N N N
tot,( x 1) A,i B,i
b