PHYSICAL CHEMISTRY

M. I. VINNIK, N. G. ZARAKHANI

KINETICS AND MECHANISM OF THE BECKMANN REARRANGEMENT OF CYCLODODECANONE OXIME IN SULFURIC ACID MEDIUM

(Presented by Academician N. N. Semenov, 27 IV 1963)

The Beckmann rearrangement of oximes is one of the important methods of organic synthesis, and an extensive literature has been devoted to elucidating its mechanism. The rearrangement is an acid-base process. The mechanisms of rearrangement proposed by various authors have been discussed in detail in review articles \((^{1-4})\).

In the present work, the kinetics of the Beckmann rearrangement in sulfuric acid medium was studied in detail, and on the basis of kinetic data the mechanism of the elementary rate-limiting step was established. Cyclododecanone oxime was chosen as the object of study

\[ (\mathrm{CH}_2)_{11}\mathrm{C}=\mathrm{NOH} \;\longrightarrow\; (\mathrm{CH}_2)_{11} \begin{matrix} \mathrm{C}=\mathrm{O}\\[-2pt] \mathrm{NH} \end{matrix} \]

The rate of rearrangement of the oxime into lactam was investigated by a spectrophotometric method. The acid concentration was determined from the electrical conductivity \((^5)\).

The process of conversion of cyclododecanone oxime into lactam is monomolecular with respect to the oxime and irreversible.

Table 1 gives the experimental values of \(K_{\mathrm{eff}}\) for various temperatures and various concentrations of sulfuric acid.

Table 1

Table 2 gives the effective constants \(K_{\mathrm{eff}}\) for \(T = 25^\circ\) as a function of the strength of sulfuric acid. The values of \(K_{\mathrm{eff}}\) in the interval 88.07%—97.67% \(\mathrm{H_2SO_4}\) were obtained by extrapolation according to the Arrhenius equation from data for higher temperatures.

Hammett \((^6)\) compared the rate constants of the rearrangement of acetophenone oxime with the acidity function and showed that in the range from 93.6% to 98.7% \(\mathrm{H_2SO_4}\) a linear dependence holds:

\[ \log K + H_0 = \mathrm{const}. \tag{1} \]

A similar relation for the case of the rearrangement of cyclododecanone oxime is obeyed for acid solutions containing from 90 to 99% \(\mathrm{H_2SO_4}\). As is seen from the data of Table 2, in stronger acids and in oleum this relation is not obeyed. In studying the hydrolysis of cyclohexanone oxime

Table 2

Note. The values of \(a_{\mathrm{H_2SO_4}}\) and \(a_{\mathrm{H_2O}}\) from 90,36% to 99% \( \mathrm{H_2SO_4}\) were taken from work (⁹).

(⁷) In aqueous solutions of hydrochloric and sulfuric acids, we came to the conclusion that in dilute acids (about \(0,05\,N\)) cyclohexanone oxime is completely ionized, while in concentrated acid solutions the ionized form associates with the acid anion into an ion pair:

\[ \mathrm{RNOH_2^+ + HSO_4^- \rightleftarrows RNOH_2^+\cdot HSO_4^-}. \tag{2} \]

The Beckmann rearrangement of oximes proceeds at a measurable rate in sulfuric acid solutions containing more than 90% \( \mathrm{H_2SO_4}\). It is precisely in such solutions that, as the acid strength increases, the concentration of \( \mathrm{HSO_4^-}\) anions (⁸) decreases, and therefore an increase in the degree of ionization of the ion pair according to equation (2) should be expected. The dependence of the rate constant on the acid strength cannot be quantitatively explained by a change in the concentration of the protonated form of the oxime \( \mathrm{RNOH_2^+}\). We therefore believe that the ions \( \mathrm{RNOH_2^+}\) are not reactive in the present process. The linear relationship between \(\lg K_{\mathrm{eff}}\) and \(H_0\) could be explained by assuming that, as the strength of sulfuric acid increases, protonation of the ion pair (the oxime salt) occurs,

\[ \mathrm{RNOH_2^+\cdot HSO_4^- + H^+ \rightleftarrows RNOH_2^+\cdot H_2SO_4}, \]

and ions \( \mathrm{RNOH_2^+\cdot H_2SO_4}\) are formed, which are the reactive species in the Beckmann rearrangement. In that case, one would expect that near 100% \( \mathrm{H_2SO_4}\), where the acidity of the medium is high, because of

Fig. 1

At a significant degree of protonation of the ion pair, \(K_{\mathrm{eff}}\) will increase more slowly than follows from equation (1). In fact, as was already mentioned above, with increasing sulfuric acid concentration \(\lg K_{\mathrm{eff}} + H_0\) increases. This fact cannot be explained by a change in the activity coefficient of the ion pairs \(\mathrm{RNOH_2^+ \cdot HSO_4^-}\), and therefore we consider that such a mechanism does not occur. In the range of 99–100% \(\mathrm{H_2SO_4}\), the thermodynamic activity of water \(a_{\mathrm{H_2O}}\) changes more sharply than does the acidity of the medium \(\left({}^{9}\right)\). Therefore it is reasonable to assume that the reactive oxime species are formed upon dehydration of either the ions \(\mathrm{RNOH_2^+}\) or the ion pairs \(\mathrm{RNOH_2^+ \cdot HSO_4^-}\) present in solution. The experimentally found dependence of \(K_{\mathrm{eff}}\) on the acidity function, the activity of water, and the thermodynamic activity of sulfuric acid \(a_{\mathrm{H_2SO_4}}\) is quantitatively explained on the assumption that the rate of the limiting stage is determined by the concentration of the species \(\mathrm{RN^+HSO_4^-}\), formed upon dehydration of the ion pair \(\mathrm{RNOH_2^+ \cdot HSO_4^-}\):

\[ \mathrm{RNOH_2^+ \cdot HSO_4^- \rightleftharpoons RN^+ \cdot HSO_4^- + H_2O.} \tag{3} \]

Let us denote the equilibrium constant of reaction (2) by \(K_C\), and that of reaction (3) by \(K_2\)

\[ K_C = \frac{ a_{\mathrm{RNOH_2^+}} \cdot a_{\mathrm{HSO_4^-}} }{ a_{\mathrm{RNOH_2^+ \cdot HSO_4^-}} }; \qquad K_2 = \frac{ a_{\mathrm{RNOH_2^+ \cdot HSO_4^-}} }{ a_{\mathrm{RN^+ \cdot HSO_4^-}} \cdot a_{\mathrm{H_2O}} }. \]

Expressing the concentrations \(C_{\mathrm{RNOH_2^+}}\) and \(C_{\mathrm{RNOH_2^+ \cdot HSO_4^-}}\) through the equilibrium constants and \(C_{\mathrm{RN^+ \cdot HSO_4^-}}\), after substitution into the balance equation:

\[ C_{\mathrm{RNOH_2^+}} + C_{\mathrm{RNOH_2^+ \cdot HSO_4^-}} + C_{\mathrm{RN^+ \cdot HSO_4^-}} = C_0 \]

we obtain an equation for the dependence of \(C_{\mathrm{RN^+ \cdot HSO_4^-}}\) on parameters characterizing the properties of the medium:

\[ C_{\mathrm{RN^+ \cdot HSO_4^-}} = \frac{C_0}{ 1 + K'_C \cdot K'_2 \dfrac{a_{\mathrm{H_2O}} \cdot h_0}{a_{\mathrm{H_2SO_4}}} + K'_2 a_{\mathrm{H_2O}} }. \]

\[ K'_2 = K_2 \frac{ f_{\mathrm{RN^+ \cdot HSO_4^-}} }{ f_{\mathrm{RNOH_2^+ \cdot HSO_4^-}} }; \qquad K'_C \cdot K'_2 = 4K_2 K_C K_{2A} \cdot \frac{ f_{\mathrm{RN^+ \cdot HSO_4^-}} }{ f_{\mathrm{B}} } \cdot \frac{ f_{\mathrm{BH^+}} }{ f_{\mathrm{RNOH_2^+}} }. \]

\(K_{2A}\) is the thermodynamic dissociation constant of the acid anion:

\[ \mathrm{HSO_4^- \rightleftharpoons H^+ + SO_4^{2-}.} \]

We assume that in concentrated sulfuric acid the ratios of activity coefficients

\[ \frac{ f_{\mathrm{RN^+ \cdot HSO_4^-}} }{ f_{\mathrm{RNOH_2^+ \cdot HSO_4^-}} } \quad \text{and} \quad \frac{ f_{\mathrm{RN^+ \cdot HSO_4^-}} }{ f_{\mathrm{B}} } \cdot \frac{ f_{\mathrm{BH^+}} }{ f_{\mathrm{RNOH_2^+}} } \]

are constant.

If the rate of the limiting stage is determined by the concentration of dehydrated species, then:

\[ K_{\mathrm{eff}} = \frac{ K_{\mathrm{true}} }{ 1 + K'_C \cdot K'_2 \dfrac{a_{\mathrm{H_2O}} \cdot h_0}{a_{\mathrm{H_2SO_4}}} + K'_2 \cdot a_{\mathrm{H_2O}} }. \tag{4} \]

If the relative concentration of the species \(\mathrm{RN^+ \cdot HSO_4^-}\) is small, then:

\[ \frac{1}{K_{\mathrm{eff}} \cdot a_{\mathrm{H_2O}}} = \frac{K'_C K'_2}{K_{\mathrm{true}}} \cdot \frac{h_0}{a_{\mathrm{H_2SO_4}}} + \frac{K'_2}{K_{\mathrm{true}}}. \tag{5} \]

As is seen from Fig. 1, the experimental data fit this equation satisfactorily. From the slope and intercept of the straight line in the coordinates

\[ \left(\frac{1}{K_{\mathrm{eff}}a_{\mathrm{H_2O}}};\ \frac{h_0}{a_{\mathrm{H_2SO_4}}}\right) \]

the values

\[ \frac{K'_2}{K_{\mathrm{ist}}}=1.25\cdot 10^8 \]

and \(K'_C = 1\) were calculated. Judging from these values, already near 100% \(\mathrm{H_2SO_4}\), owing to the decrease in the concentration of \(\mathrm{HSO_4^-}\) anions, practically all the oxime is present in the form of \(\mathrm{RNOH_2^+}\) ions, and

\[ K'_C K'_2 \frac{a_{\mathrm{H_2O}}\cdot h_0}{a_{\mathrm{H_2SO_4}}} \gg K'_2 a_{\mathrm{H_2O}} + 1. \]

In this case the following dependence must hold:

\[ \lg K_{\mathrm{eff}}\frac{a_{\mathrm{H_2O}}\cdot h_0}{a_{\mathrm{H_2SO_4}}}=\mathrm{const}. \]

As follows from the data of Table 2, such a dependence is indeed observed for acid solutions containing more than 99.4% \(\mathrm{H_2SO_4}\), and in oleum. This dependence is also observed in solutions where \(K_{\mathrm{eff}}\) does not depend on the concentration of \(\mathrm{SO_3}\). Consequently, in such solutions all the oxime is present in the form of \(\mathrm{RNOH_2^+}\) ions. The independence of the rate constant \(K_{\mathrm{eff}}\) from the concentration of the catalyst in acid-catalyzed processes is usually regarded as the attainment of conditions under which all the reagent is present in the reactive form. In the case of the Beckmann rearrangement of cyclododecanone oxime, the constancy of \(K_{\mathrm{eff}}\) is explained not by conversion of all the reagent into the reactive form, but by the constancy of the product

\[ \frac{a_{\mathrm{H_2O}}\cdot h_0}{a_{\mathrm{H_2SO_4}}} \]

in oleum containing from 5 to 10% \(\mathrm{SO_3}\).

Below are given the equilibrium and rate-limiting stages of the Beckmann transformation of cyclododecanone oxime in an acid medium:

\[ \begin{aligned} (\mathrm{CH_2})_{11}\mathrm{C{=}NOH}+\mathrm{H_2SO_4} &\rightleftarrows (\mathrm{CH_2})_{11}\mathrm{C{=}\overset{+}{N}OH} +\mathrm{HSO_4^-} \\[-2mm] &\qquad\qquad\quad \mathrm{H} \\ (\mathrm{CH_2})_{11}\mathrm{C{=}\overset{+}{N}OH}\cdot\mathrm{HSO_4^-} &\rightleftarrows \mathrm{H_2O}+(\mathrm{CH_2})_{11}\mathrm{CN^+}\cdot\mathrm{HSO_4^-} \\ &\xrightarrow{\text{slowly}} \text{cyclic cation}\cdot\overline{\mathrm{OSO_2OH}} . \end{aligned} \]

Upon dilution of the acid with water, the rearrangement product is converted into the nonionized form of the lactam:

\[ \text{cyclic cation}\cdot\overline{\mathrm{OSO_2OH}}+2\mathrm{H_2O} \xrightarrow{\text{rapidly}} \text{lactam}+\mathrm{H_3O^+}+\mathrm{HSO_4^-}. \]

We express our gratitude to L. I. Zakharkin for kindly providing the cyclododecanone oxime preparation.

Institute of Chemical Physics
Academy of Sciences of the USSR

Received
22 IV 1963

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