Kinetic Study of the Mechanism of the Nitration Reaction of Aromatic Compounds with Nitric Acid

A. G. Stromberg, Kh. A. Lel’chuk

Kinetic studies of the nitration process of aromatic compounds—benzene, toluene, iodobenzene, bromobenzene, and chlorobenzene—with 100% nitric acid in a nitrobenzene solution at 20°C were carried out by one of us [1, 2]. The 100% nitric acid was obtained by us by the method developed by Mishchenko [3], by repeated distillation of a mixture of nitric acid (sp. gr. 1.40) with sulfuric acid (sp. gr. 1.84) at a residual pressure of 25–30 mm Hg and a temperature of 25–40°C.

The calculations we performed to determine the order of the nitration reaction on the basis of the experimental data indicated above led to improbably high values of the reaction order (from 6 to 10); moreover, the reaction order changed with time. These results indicate the complexity of the mechanism of the nitration process, i.e., that the process proceeds in stages.

It is known that only in rare cases is it possible to determine experimentally the composition of intermediate unstable compounds and thereby unambiguously establish the mechanism by which a reaction proceeds in stages. In most cases, one must, on the basis of theoretical considerations and indirect experimental data, propose the most probable mechanism of the process and then compare the resulting kinetic equations with the experimental data [4].

Below is given the most probable mechanism of the stepwise course of the reaction of nitration of benzene with nitric acid in a nitrobenzene solution (the letters under the formulas of the chemical compounds denote the concentrations of the reacting substances at time \(t\)):

\[ \text{I.}\quad \underset{c_1}{\mathrm{ArNO_2 \cdot HNO_3}} \rightleftharpoons \underset{c_4}{\mathrm{ArNO_2}} + \underset{s}{\mathrm{HNO_3}}, \]

\[ \text{II.}\quad \underset{s}{2\mathrm{HNO_3}} \rightleftharpoons \underset{z}{\mathrm{H_2NO_3^+}} + \underset{c_3}{\mathrm{NO_3^-}}, \]

\[ \text{III.}\quad \underset{z}{\mathrm{H_2NO_3^+}} \rightleftharpoons \underset{y}{\mathrm{H_2O}} + \underset{x}{\mathrm{NO_2^+}}, \]

\[ \text{IV.}\quad \underset{c_2}{\mathrm{ArH}} + \underset{x}{\mathrm{NO_2^+}} \rightleftharpoons \underset{p}{\mathrm{ArHNO_2^+}}, \]

\[ \text{V.}\quad \underset{p}{\mathrm{ArHNO_2^+}} + \underset{c_3}{\mathrm{NO_3^-}} \rightleftharpoons \underset{c_4}{\mathrm{ArNO_2}} + \underset{s}{\mathrm{HNO_3}}, \]

\[ \text{VI.}\quad \underset{s}{\mathrm{HNO_3}} + \underset{y}{\mathrm{H_2O}} \rightleftharpoons \underset{c_3}{\mathrm{H_3O^+}} + \underset{c_3}{\mathrm{NO_3^-}}. \]

Overall reaction

\[ \text{VII.}\quad 2\underset{c_1}{(\mathrm{ArNO_2 \cdot HNO_3})} + \underset{c_2}{\mathrm{ArH}} \rightleftharpoons 3\underset{c_4}{\mathrm{ArNO_2}} + \underset{c_3}{\mathrm{H_3O^+}} + \underset{c_3}{\mathrm{NO_3^-}}. \]

We included the first stage in the general mechanism of nitration because the data from kinetic studies of the above-mentioned systems, as well as data for the nitrobenzene—nitric acid system, for which both kinetic investigations and studies by other physicochemical methods of analysis were carried out [1, 2], show that nitrobenzene adds nitric acid in complex form and thereby deactivates it. In particular, the formation of this complex compound is indicated by the following experimental fact. The process of nitration of pure benzene or toluene with 100% nitric acid proceeds extremely vigorously at room temperature. But in a benzene—nitric acid—nitrobenzene mixture with a molar ratio of 1 : 1 : 2, respectively, the nitration process proceeds over several days and does not go to completion [2].

We included the second and third stages because numerous works carried out by both Soviet and foreign scientists have shown that the nitrating agent in the nitration of aromatic compounds with nitric acid or nitrating mixtures is the nitronium cation [5–7].

We included the fourth and fifth stages because the simple scheme of exchange decomposition

\[ \mathrm{RH} + \mathrm{HONO_2} \to \mathrm{RNO_2} + \mathrm{H_2O} \]

has long since been replaced by more complex schemes.

In general form, the idea that the first stage of the substitution process is the formation of an addition product was expressed already by Kekulé. Later, many theories were proposed on this question on the basis of experimental data [5, pp. 68–80; 8], confirming the fourth and fifth stages. We included the sixth stage because, as the nitration process proceeds and the nitronium cation is formed, water accumulates; in its presence dissociation of nitric acid will occur.

It should be noted that in the ternary systems studied—benzene (or its halogen derivatives)—nitric acid—nitrobenzene, at a molar ratio of 1 : 1 : 2, dinitrobenzene is not formed in noticeable amounts. This is indicated both by literature data [9–13] and by our experimental data. When nitric acid and nitrobenzene are mixed at 20°C in a ratio of 1 : 2, the reaction of dinitrobenzene formation proceeds extremely slowly, and after 10 hours about 1–2% (molar) of the nitric acid taken has reacted.

As is known, when a reaction proceeds through stages, the overall reaction rate and its kinetic equation are determined by the limiting stage of the process. Assuming that each of the stages listed may be limiting, we derived equations for the reaction rate taking into account both the forward and the reverse reactions; in this case the other stages of the reaction are regarded as practically at equilibrium.

It is easy to see that for all limiting stages identical expressions are obtained, differing only in the form of the function \(f(c)\) and in the value of the constant (const):

\[ \lg v = \mathrm{const} + \lg p; \tag{1} \]

\[ p=f(c)\left[ K\frac{c_1^2c_2}{c_3^2c_4^3}-1\right]; \tag{2} \]

\[ K=\frac{(c_4^\infty)^3(c_3^\infty)^2}{(c_1^\infty)^2(c_2^\infty)}; \tag{3} \]

where \(c_1^\infty, c_2^\infty, c_3^\infty, c_4^\infty\) are the concentrations of the reacting substances after cessation of the reaction (as \(t\to\infty\))¹.

For the ternary mixture nitric acid–benzene–nitrobenzene, the functions \(f(c)\) for different limiting stages are given by the expressions:

\[ \begin{array}{c|cccccc} \text{stage:} & \mathrm{I} & \mathrm{II} & \mathrm{III} & \mathrm{IV} & \mathrm{V} & \mathrm{VI}\\[2mm] f(c): & \dfrac{c_4^{3/2}c_3}{c_2^{1/2}} & \dfrac{c_3^2c_4}{c_2} & \dfrac{c_4c_3}{c_2} & \dfrac{c_1}{c_3} & c_1 & c_3^2 \end{array} \]

The concentrations \(c_1, c_2, c_3,\) and \(c_4\) of the reacting substances in the equation of the overall reaction (VII) are related to the initial analytical concentrations of benzene \((\bar c_2^0)\), nitric acid \((\bar c_1^0)\), and nitrobenzene \((\bar c_4^0)\), and to the analytical concentration \((\bar c_1)\) of nitric acid at the given instant of time (determined by titration with baryta water), by the following relations:

\[ c_1=2\bar c_1-\bar c_1^0;\qquad c_2=\bar c_2^0-\bar c_1^0+\bar c_1; \]

\[ c_3=\bar c_1^0-\bar c_1;\qquad c_4=3(\bar c_1^0-\bar c_1)+0.5\,\bar c_4^0. \]

Let us explain the derivation of equations (1) and (2) for the case in which stage III is limiting; then

\[ V_{\mathrm{III}}=\vec{k}_3 z-\cev{k}_3xy. \tag{a} \]

We regard the other five stages as practically equilibrium stages and obtain for them

\[ K_{\mathrm{I}}=\frac{c_4^2s^2}{c_1^2};\qquad K_{\mathrm{II}}=\frac{c_3z}{s^2};\qquad K_{\mathrm{IV}}=\frac{p}{c_2x};\qquad K_{\mathrm{V}}=\frac{c_4s}{c_3p};\qquad K_{\mathrm{VI}}=\frac{c_3^2}{sy}. \tag{b} \]

From (a) and (b) we obtain the desired expression (1). In this case

\[ K=K_{\mathrm{I}}K_{\mathrm{II}}K_{\mathrm{III}}K_{\mathrm{IV}}K_{\mathrm{V}}K_{\mathrm{VI}}. \tag{c} \]

In an analogous way we obtain expressions for the reaction rate when the other reaction stages are assumed to be limiting.

For the ternary mixture nitric acid–chlorobenzene (or bromobenzene)–nitrobenzene, the constants \(K\) and the functions \(f(c)\) for different limiting stages are given by the expressions

\[ K=\frac{(c_5^\infty)(c_3^\infty)^2(c_4^\infty)^2}{(c_1^\infty)^2(c_2^\infty)}; \tag{4} \]

\[ p=f(c)\left[K^{1/2}\frac{c_1c_2^{1/2}}{c_3c_4^{1/2}}-1\right], \]

\[ p=f(c)\left[K^{1/2}\frac{c_1c_2^{1/2}}{c_3c_4c_5^{1/2}}-1\right]. \]

(\(c_4^0\) is the concentration of free nitrobenzene not bound in a complex with nitric acid after cessation of the reaction).

\[ \begin{array}{c|cccccc} \text{Stage:} & \mathrm{I} & \mathrm{II} & \mathrm{III} & \mathrm{IV} & \mathrm{V} & \mathrm{VI} \\ \hline f(c): & \dfrac{c_1 c_4 c_5^{1/2}}{c_2^{1/2}} & \dfrac{c_3^2 c_5}{c_2} & \dfrac{c_3 c_5}{c_4} & \dfrac{c_1 c_5}{c_3 c_4} & \dfrac{c_1 c_5}{c_4} & c_3^2 . \end{array} \]

The difference between the expressions for the constants \(K\) and the functions \(f(c)\) in ternary systems involving benzene and those involving halogen derivatives of benzene is due to the fact that in the former case the nitration product (nitrobenzene) is identical with the solvent (nitrobenzene).

The concentrations of the reacting substances \(c_1, c_2, c_3, c_4\), and \(c_5\) are in this case related to the analytical concentrations by the following relations:

\[ c_1 = 2\bar c_1-\bar c_1^0;\qquad c_2=\bar c_2^0-\bar c_1^0+\bar c_1; \]

\[ c_3=c_5=\bar c_1^0-\bar c_1;\qquad c_4=2(\bar c_1^0-\bar c_1)+0.5\,\bar c_4^0 . \]

(\(\bar c_1^0\), \(\bar c_2^0\), \(\bar c_4^0\) are the initial analytical concentrations, respectively, of nitric acid, chloro- or bromobenzene, and nitrobenzene.)

It follows from equation (1) that, if the adopted limiting stage corresponds to reality, then in the coordinates \(\lg v\) and \(\lg p\) a straight line with a slope equal to unity should be obtained. If, however, the adopted reaction mechanism does not correspond to reality, then, generally speaking, either a curved line or a straight line with a slope different from unity may be obtained.

To determine the values of the reaction rate \(v\) for different time intervals, a graph was constructed in the coordinates: amount of analytically determined nitric acid consumed, in moles per liter, and time; the values of the slopes of tangents to different points of the curve were determined graphically. Next, a graph was constructed in the coordinates reaction rate and time, and the average rate values for different time intervals were determined graphically.

To calculate the values of the functions \(p\) in formula (2), we computed, from the experimental data, the concentrations \(c_1, c_2, c_3, c_4\) and the values of the constant \(K\) (see formulas (3) and (4)).

Table 1 gives the values of the reaction rate and the concentration of nitric acid at different time intervals for all the systems studied at \(20^\circ\)C. The molar ratio at the initial moment of time in the ternary systems benzene (chlorobenzene, bromobenzene), nitric acid, and nitrobenzene is equal to \(1:1:2\).

Using the obtained values of \(\lg v\) and \(\lg p\), graphs were constructed. As an example we give the graph (Fig. 1) for the system bromobenzene—nitric acid—nitrobenzene. Straight lines I–VI were constructed from the experimental data on the assumption that, respectively, stages I–VI are limiting. For the other systems studied, the graphs are analogous and differ only in the values of the slopes.

The values of the slopes of the straight lines for all the systems studied are given in Table 2.

From the data presented it is evident that, for all systems, straight lines with a slope equal to unity were obtained for the third stage. For the sixth stage in all the systems studied the slopes are also equal or close to unity. For the remaining stages the straight lines pass at different angles, and the values of the slopes differ greatly from unity. On the basis of these experimental data and

formulas (1) we conclude that the limiting stage of the nitration reaction in all the systems studied is the third stage, i.e., the stage of formation of the nitronium cation. The sixth stage cannot

Table 1

Rate of the nitration reaction \(v\), mol/liter·hour, and concentration \(\bar c_1\), mol/liter, of nitric acid at different time intervals at 20°C for three ternary systems (1 : 1 : 2)

be limiting, since the processes of dissociation of molecules of mineral acids in water proceed very rapidly.

Table 2

Values of the slopes of straight lines on plots in the coordinates \(\lg v\) and \(\lg p\) (1) and (2) for the nitration reaction of benzene and its derivatives at 20°C

Bonner, Bowyer, and Williams [14] determined the rate of nitration of nitrobenzene and pentadeuteronitrobenzene in the presence of sulfuric acid. They showed that cleavage of the C–H bond is not the step determining the rate of nitration of an aromatic compound. Hence, in agreement with our data, it follows that the fourth stage cannot be limiting.

We compiled another possible variant of the mechanism of the process of nitration of benzene in nitrobenzene solution. The formation of a complex of nitrobenzene with nitric acid (the first stage) was excluded. The principal kinetic equations were derived in the same way as indicated above, and plots were constructed in the coordinates \(\lg v\) and \(\lg p\); the values of the slopes are given in Table 2, column 5.

In this case the limiting stage also proved to be the stage of formation of the nitronium cation.

It should be noted that the nitro derivative obtained in the course of nitration, under the experimental conditions, does not give back the original aromatic compound and nitric acid, i.e., the reaction as a whole—and consequently one or several stages of the nitration process—is irreversible.

In the mathematical analysis of the limiting stage, all six stages considered were, for simplicity, taken to be reversible. However, the calculations show that the rate of the reverse process on the portion of the kinetic curve used for constructing the graph may be practically neglected, since the data for the first ten hours of the reaction were used for the calculations, when the rate of the reverse reaction is insignificant.

Fig. 1. Dependence of the logarithm of the reaction rate (\(v\)) on the logarithm of the concentration function (\(p\)) of the reacting substances (see formula 2) for the ternary system: nitric acid (100%)-bromobenzene-nitrobenzene. The straight lines are shifted, respectively, to the right along the abscissa: II by 0.5, III by 1.0, IV by 1.0, V by 2.5, VI by 4 units of \(\lg p\). The slope of the dashed line in the graph corresponds to the theoretical value of unity in accordance with formula (1).

The calculations carried out for each stage showed that the process is limited by the stage of formation of the nitronium cation (stage 3). This ionic reaction is, of course, reversible. Consequently, the irreversibility of the process as a whole can be explained by the fact that one of the stages involving organic compounds (stage IV or V) proceeds sufficiently rapidly but is irreversible.

Conclusions

1. For the most substantiated mechanism of the nitration reaction proceeding by stages, kinetic equations have been derived for the possible limiting stages of the process. These equations have been brought to such a form that a graph plotted from experimental kinetic data in the chosen coordinates should be represented by a straight line with a slope equal to unity.

2. On the basis of the experimental kinetic data, numerical calculations have been made, using the derived equations, for various possible

limiting stages for three ternary systems. It has been shown that in all cases, under conditions where there is no excess of nitric acid, the most probable limiting stage of the process is the reaction of formation of the nitronium cation, which is consistent with the views most widely accepted in the modern literature.

REFERENCES

1. B. V. Tronov, Kh. A. Lel’chuk. Izv. Tomskogo politekhnicheskogo in-ta, III, 6, 1961.

2. Kh. A. Lel’chuk, B. V. Tronov. Izv. Tomskogo politekhnicheskogo in-ta, III, 12, 1961.

3. K. P. Mishchenko. Zh. Prikladnoi khimii, II, 5, 521, 1929.

4. G. M. Panchenkov, V. P. Lebedev. Chemical Kinetics and Catalysis. Moscow University Press, 235, 1961.

5. A. V. Topchiev. Nitration of Hydrocarbons and Other Organic Compounds. Academy of Sciences of the USSR Press, 122, 1949.

6. A. I. Titov. Uspekhi khimii, 27, 845, 1958.

7. K. K. Ingold. Reaction Mechanism and Structure of Organic Compounds. Foreign Literature Publishing House, 227, 1959.

8. H. Zollinger. Experientia, 12, 165, 1956.

9. Deville, Ann. chim. et phys., 3, 187.

10. Beilstein, Kurbatov, Ann., 155, 1.

11. Witt, Noelting. Ber., 18, 1337.

12. A. Hollemann. J. Chem. Soc., Abstr., 17, 1909.

13. A. Hollemann. Chem. Rev., 1, 187, 1925.

14. T. Bonner, F. Bowyer, G. Williams. J. Chem. Soc., 2650, 1953.

1. Equation (2) for the first stage for the system with benzene has the following form:

   and with halogen derivatives of benzene: ↩