Page 147 - Modeling of Chemical Kinetics and Reactor Design

Reaction Rate Expression 117

time t the concentration is C , integrating Equation 3-22 between
2
Af
these limits gives:
C Af t 2
∫
− ∫ dC A = k dt (3-23)
C AO t 1

t
−(C − C ) = ( k t − )
Af AO 2 1
C ( − C )
k = AO Af (3-24)
t − )
( 2 t 1

If t = 0, Equation 3-24 reduces to
1
C = C – kt (3-25)
Af AO 2
Plotting the concentration (C ) versus time t gives a straight line,
A
where C is the intercept and k is the slope. The velocity constant k
AO
may include arbitrary constants resulting from various limiting factors
such as diffusion constants and a fixed intensity of absorbed light.
In terms of the fractional conversion X
A
C X = kt (3-26)
AO A
Because C cannot be negative, the following is obtained
A

C − C = C X = kt for t < C AO (3-27)
AO A AO A
k
This means that the conversion is proportional to time. Figure 3-4
shows plots of the zero order rate equations. Examples of zero order
reactions are the intensity of radiation within the vat for photochemical
reactions or the surface available in certain solid catalyzed gas reactions.

FIRST ORDER REACTIONS
Consider the reaction A → B. The rate of a first order reaction
k
is proportional to the first power of the concentration of only one
component. Assuming that there is no change in volume, temperature,