OPTIMIZATION OF THE SYNTHESIS OF p-IODONITROBENZENE BY THE SIMPLEX-PLANNING METHOD

A. M. SEDOV

(Submitted by the scientific seminar of the departments and laboratories of organic synthesis, CTF)

At the Department of Organic Chemistry of Tomsk Polytechnic Institute, a one-stage method has been proposed for the synthesis of p-iodonitrobenzene, based on the combined action of iodine and a nitrating mixture on benzene. As shown in [1], p-iodonitrobenzene may find application in obtaining biologically active compounds, dyes, and other practically important substances. In this connection, it seemed expedient to work out the conditions for its synthesis using one of the methods of mathematical planning of experiment, for example, the simplex method [2, 3].

The influence was studied of the following factors, on which the yield of p-iodonitrobenzene (the optimization criterion) substantially depends: $\alpha$, $\beta$—the numbers of milliliters of $\mathrm{HNO_3}$ and $\mathrm{H_2SO_4}$, respectively; $\gamma$—reaction temperature, °C; $\lambda$—amount of solvent ($\mathrm{CH_3COOH}$), ml; $\tau$—reaction duration, min.

The aim of the work was to find the values of the factors $\alpha$, $\beta$, $\gamma$, $\lambda$, $\tau$ corresponding to the maximum value of the optimization criterion.

Experimental Part

The experiments were carried out according to the following procedure: into a round-bottom flask equipped with a dropping funnel, reflux condenser, and mechanical stirrer were introduced glacial acetic acid, finely ground iodine (0.1 g-atom), 0.1 g-mol of benzene, and 5 ml of $\mathrm{CCl_4}$. Then, at a strictly controlled temperature, a mixture of nitric acid of sp. gr. 1.4 and sulfuric acid of sp. gr. 1.83 was added dropwise with constant stirring. After the reaction time had elapsed, the acid layer was separated from the solid precipitate; the latter was washed with water and sodium sulfite and purified from benzene. M.p. of p-iodonitrobenzene: 169–170°C.

On the basis of preliminary investigations, the initial point—the center of the initial simplex—and the scales along the axes of the variables—the factors—were chosen (Table 1).

We perform a coordinate transformation reducing the “natural” variables to dimensionless ones:

$$ x_1=\frac{\alpha-11}{1},\quad x_2=\frac{\beta-35}{1},\quad x_3=\frac{\gamma-110}{5},\quad x_4=\frac{\lambda-20}{10},\quad x_5=\frac{\tau-103}{20} \tag{1} $$

Table 1

Basic level and variation intervals

Using the selected part of the simplex numerical matrix (Table 2) [2], containing five columns (the number of varied factors), six rows, and formula (1), we obtain the simplex matrix in natural variables.

Table 2

Numerical simplex matrix

Table 3 gives the experimental values of the optimization criterion at the simplex points. As can be seen from Table 3, experiment No. 2 is the worst. In accordance with the ascent rule, the reflection method was used to replace

Table 3

Results of experiments
at the simplex points

point No. 2 with point No. 7. The coordinates of this point were found from formulas (2) and (3):

\[ x_i^{n+2}=2\cdot x_i^c-x_i^j,\qquad i=1,2,\ldots,n, \tag{2} \]

where $x_i^j$ is the $i$-th coordinate of the worst point;

$x_i^c$ is the $i$-th coordinate of the center of the opposite face;

$x_i^{n+2}$ is the $i$-th coordinate of the new point obtained as a result of “reflection.”

\[ X_i^c=\frac{\displaystyle\sum_{r=1}^{n+1} x_i^r}{n}\quad R\ne j \tag{3} \]

First, the coordinates of the center of the face formed by points numbered 1, 3, 4, 5, 6 were calculated:

\[ \alpha^{c}=\frac{4\times 11.0+11.5}{5}=11.1; \]

\[ \beta^{c}=\frac{3\times 35.0+35.3+34.4}{5}=34.9; \]

\[ \nu^{c}=\frac{2\times 111.0+2.110+106.9}{5}=111.2; \]

\[ \lambda^{c}=\frac{3\times 21.6+13.7+20.0}{5}=19.7; \]

\[ \tau^{c}=\frac{4\times 105.6+90.1}{5}=102.5. \]

Then the coordinates of the seventh point are expressed as:

\[ \begin{aligned} \alpha^{(7)}&=2\times 11.1-10.5=11.7;\\ \beta^{(7)}&=2\times 34.9-35.3=34.5;\\ \nu^{(7)}&=2\times 111.2-111.0=111.4;\\ \lambda^{(7)}&=2\times 19.7-21.6=17.8;\\ \tau^{(7)}&=2\times 102.5-105.6=99.4. \end{aligned} \]

After experiment No. 7 was carried out, point No. 3 turned out to be the worst point of simplex 173456. Its reflection with respect to face 17456 gives the conditions of point No. 8, whose coordinates were calculated by the method described above. Performing the experiment at point No. 8 does not lead to an increase in the yield of p-iodonitrobenzene; therefore the stepwise ascent was completed by the reflection method. As a result of the study, an “almost stationary” region was reached.

Conclusions

Using the simplex method for planning extremal experiments, the optimal conditions were found for the reaction of benzene with iodine and a nitrating mixture in glacial acetic acid; in this case the yield of p-iodonitrobenzene was increased to 46.7%, which is 20% higher than that obtained previously.

Considering that, under the action of iodine and a nitrating mixture on benzene, many different substituted benzenes are formed, the achieved yield of p-iodonitrobenzene may be regarded as sufficiently high.

Literature

1. Sedov A. M. Candidate dissertation. Tomsk, 1970.
2. Gorskii V. G., Brodskii V. V. “Zavodskaya laboratoriya,” vol. 31, No. 7, 831, 1965.
3. Nalimov V. V., Chernova N. A. Statistical Methods for Planning Extremal Experiments. Moscow, “Nauka,” 1965, p. 178.