Page 233 - Modeling of Chemical Kinetics and Reactor Design

Reaction Rate Expression 203

A B
Amount at t = 0 C C
AO BO
Amount at t = t C C
A B
Amounts that have reacted C – C = C – C
AO A BO B
In terms of the fractional conversion of B, X B

X = C BO − C B
B (3-299)
C BO

Equation 3-299 is further expressed as:

C = C (1 − X ) (3-300)
BO
B
B
Since the concentration of A and B is the same, then

C = C = C (1 − X ) (3-301)
B
BO
A
B
and
− dC B = C BO dX B (3-302)
dt dt

Substituting Equations 3-300 and 3-302 into Equation 3-298 gives

dX B 2 2
− ( r ) =C = kC − (1 X ) (3-303)
B BO BO B
dt
Rearranging Equation 3-303 and integrating between the limits t =
0, X = 0 and t = t, X = X gives
B
B
B
X B dX t
∫ X ) 2 = kC BO∫ dt (3-304)
B
0 ( 1− B 0

 1 
X B
  = kC BO t (3-305)
0  1 X− B 