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 .