Page 188 - Modeling of Chemical Kinetics and Reactor Design

158 Modeling of Chemical Kinetics and Reactor Design

where Const. is a proportionality constant related to the absorption
coefficients of the reactants and products at 325 nm.
Substituting Equation 3-197 into the integrated first order reaction
Equation 3-33 gives the corresponding equations expressed in terms
of the solution absorbance:

ln (D – D) = –kt + ln (D –D ) (3-198)
∞
∞
O
or
D – D = (D – D )e –kt (3-199)
∞
∞
O
Equation 3-199 infers that the absorbance approaches the value at
the end of the reaction (infinity value) with the same rate constant k
as that for the reaction expressed in terms of the reactant concentration.
The required rate constant can be determined from the slope of a plot
of ln (D – D ) versus time. The same equations can be written for
∞
O
reactions monitored in terms of optical rotation or conductance.
In the case of a second order reaction, an example is the alkaline
hydrolysis of an ester as represented by the following equation:

−

CH COOC H + OH  → CH COOH + C H OH (3-200)
k 2
2
5
2
3
5
3
The rate equation for a constant volume batch system is
dC
− CH COOC H 5 = kC C − (3-201)
2
3
2
3
2
dt CH COOC H 5 OH
Substituting Equation 3-197 into Equation 3-53 gives the following
equation for the change in absorbance at the selected wavelength.
1 − 1 =
.
( D − D) ( D − D ) Const k t (3-202)
2
∞
∞
O
A plot of 1/(D – D) versus time t is linear with the slope =
∞
Const.k . The rate constant k is determined if the proportionality
2
2
constant Const. is known, between the absorbance change and the
extent of the reaction. The proportionality constant can either be
determined by calibrating the system or, more accurately, by studying
the reaction under pseudo-first order conditions.