3.4 The observed reaction rate constant
Most
aromatic nitration processes in mixed acids are liquid-liquid
heterogeneous processes. Because decoupling the reaction from mass
transfer is very difficult, these reactions are usually regarded as
pseudo-homogeneous in kinetic studies.30 In this work,
solution 1 is a solution formed by the addition of a small amount of CB
to sulfuric acid, and the nitration of CB can be regarded as
quasi-homogeneous.18,31 The reaction follows
second-order kinetics, which has been widely accepted with respect to
aromatic nitration, with CB and nitric acid following first-order
kinetics.3,21 Therefore, the rate of nitration can be
expressed in terms of the concentration of the reactants as follows:
where k obs is the observed second-order rate
constant and and are the concentrations of CB and nitric acid in
solution, respectively. Equation (7) can be described as follows by
considering the initial concentration and conversion of CB:
where and are the initial concentrations of CB and nitric acid,
respectively. . Under homogeneous conditions, the reaction rate of CB
nitration can be described by the following
equation:27
By integrating Equations (8) and (9), we obtain:
Therefore, a plot of vs. residence time (t ) should be a straight
line passing through the origin with a slope equal to . The observed
second-order rate constants can be calculated from the slope. The
observed reaction rate constants at four temperatures (0, 5, 10 and 15
°C) and three sulfuric acid mass fractions (85, 90 and 95 wt%) were
investigated. As shown in Figure 5 , the fitting curve exhibited
good linearity, which is in accordance with the hypothesis that the
reaction is a second-order reaction. Plots ofk obs versus temperature and sulfuric acid
concentration are shown in Figure 6 . The observed rate constant
increases with increasing temperature and sulfuric acid concentration,
which is consistent with the trends observed for CB conversion discussed
in Section 3.3. The values of k obs at different
temperature and sulfuric acid concentration are shown in Table
1 .