Page 199 - Modeling of Chemical Kinetics and Reactor Design

Reaction Rate Expression 169

data. The following procedures are used to determine the rate constant
k and the concentration dependence of the rate equation f(C ).
i

1. Set a hypothesis as to the form of the concentration dependent
of the rate function f(C ). This can be of the form
i

− ( r A ) =− dC A = kf C (3-224)
( ) i
dt
2. From the experimental data of concentration versus time, deter-
mine the reaction rate at various times.
3. Draw a smooth curve through these data.
4. Determine the slope of this curve at selected values of the
concentration. The slopes are the rates of reaction at these
compositions.
5. Calculate f(C ) for each composition.
i
6. Prepare a plot of reaction rate (–dC /dt) versus f(C ). If the plot
i
A
is linear and passes through the origin, the rate equation is
consistent with the data, otherwise another equation should be
tested. Figure 3-17 shows a schematic of the differential method.

Integral Method

This method estimates the reaction order based on the reaction
stoichiometry and assumptions concerning its mechanism. The assumed
rate equation is then integrated to obtain a relation between the
composition and time. The following procedures are used for deter-
mining the rate equations:

1. Set a hypothesis as to the mathematical form of the reaction rate
function. In a constant volume system, the rate equation for the
disappearance of reactant A is

− ( r A )=− dC A = ( ) (3-225)
kf C
A
dt
2. Separate the variables and integrate Equation 3-225 to give

C A t
∫
− ∫ dC A = kdt
( )
fC A (3-226)
C AO 0