Considering the values of k * at different
temperatures, the activation energy (E a)
corresponding to the electrophilic attack of on CB molecules can be
determined according to the Arrhenius equation:
where A is the pre-exponential factor
(L·mol-1·s-1),E a is the activation energy (J/mol), R is
the universal gas constant (8.314
J·mol-1·K-1), and T is the
reaction temperature (K). Taking the logarithm of Equation (18), we
obtain:
A plot of -ln k * versus 1/T is shown inFigure 9a . The data are in good agreement with the fitting
line. From the slope of the straight line, E a for
CB nitration was calculated to be 30.11 ± 1.68 kJ/mol. As mentioned in
Section 3.2, under the experimental conditions investigated, the yields
of m -NCB and DNCB were both less than 1‰. Therefore, it could be
concluded that there were only two parallel reactions that generatedo -NCB and p -NCB. The rate equation for the parallel
reactions is given by Equation (20). According to the definition of
reaction selectivity, the ratio of the rate constants for the two
parallel reactions is equal to the ratio of their respective
selectivity.
In the above equations, r i andS i are the reaction rate and selectivity,
respectively, and subscript i represents either o -NCB orp -NCB.
The selectivity of the two products at the investigated temperature is
shown in Figure 3 . The experimental results also indicated that
the selectivity of o -NCB and p -NCB did not change much
with the sulfuric acid concentration. Given the rate constant of the
overall reaction and the selectivity of the products, the rate constants
of the two parallel reactions can be calculated. The activation energies
for o -NCB and p -NCB were calculated to be 35.12 ± 1.79
kJ/mol and 29.52 ± 1.02 kJ/mol, respectively, according to the Arrhenius
equation (Figure 9b ). The greater activation energy foro -NCB indicates that the molecule needs to cross a higher energy
barrier to transform from its normal state into the active state prone
to reaction, and an increase in temperature improves the selectivity of
this reaction. It can be verified by the data in Figure 3b that
as the temperature increases, the selectivity of o -NCB increases,
while the selectivity of p -NCB decreases.