Physical Chemistry

A. I. Gel'bshtein, Yu. M. Bakshi, and M. I. Temkin

Kinetics of the Vapor-Phase Hydration of Ethylene on a Phosphoric-Acid Catalyst

(Presented by Academician V. A. Kargin, December 30, 1959)

The reaction

\[ \mathrm{C_2H_4(g) + H_2O(g) = C_2H_5OH(g)} \tag{1} \]

is widely used in industry. The process is carried out at pressures of 60–80 atm and temperatures of 280–300°; the catalyst is phosphoric acid on a porous support consisting mainly of \(\mathrm{SiO_2}\). We studied the kinetics of the reaction in a flow system under conditions close to industrial ones, with a catalyst of phosphoric acid on silica gel in the form of grains 2.5 mm in size. Experiments involving variation of the grain size and of the \(\mathrm{H_3PO_4}\) content in the catalyst showed that the reaction proceeded in the kinetic region.

It was natural to assume that the mechanism of reaction (1) should be analogous to the mechanism, previously studied in our laboratory \((^1)\), of the vapor-phase hydration of \(\mathrm{C_2H_2}\) on a phosphoric-acid catalyst, i.e., should correspond to the mechanism of olefin hydration proposed by Taft \((^2)\). Then the kinetics of reaction (1) should differ from the kinetics of hydration of \(\mathrm{C_2H_2}\) only insofar as it is necessary to take its reversibility into account. As applied to reaction (1), the scheme of the mechanism may be represented as follows:

\[ \mathrm{ C_2H_4 \ \xrightleftharpoons[-H^+]{+H^+}\ H_2C \overset{H^+}{\underset{}{\rightleftarrows}} CH_2 \ \rightleftarrows\ H_3C{-}C^+H_2 \ \xrightleftharpoons[-H_2O]{+H_2O}\ C_2H_5O^+H_2 \ \xrightleftharpoons[+H^+]{-H^+}\ C_2H_5OH . } \tag{2} \]

The rate-limiting stage is the conversion of the \(\pi\)-complex

\[ \mathrm{H_2C \overset{H^+}{\rightleftarrows} CH_2} \]

into the carbonium ion \(\mathrm{H_3C{-}C^+H_2}\). Scheme (2) leads to the following equation for the rate of the forward reaction:

\[ v_1 = k_{\pi}K_1 s \frac{f_{\pi}}{f_{\mathrm{C_2H_4}} f^{\ne}} P_{\mathrm{C_2H_4}} h_0; \tag{3} \]

here \(k_{\pi}\) is the rate constant of the rate-limiting stage; \(K_1\) is the equilibrium constant of

\[ \mathrm{C_2H_4 + H^+ \rightleftarrows H_2C \overset{H^+}{\rightleftarrows} CH_2} \]

(in terms of activities); \(s\) is the solubility coefficient of \(\mathrm{C_2H_4}\) in phosphoric acid \(\left(s = a_{\mathrm{C_2H_4}}/P_{\mathrm{C_2H_4}}\right)\); \(f_{\pi}\), \(f_{\mathrm{C_2H_4}}\), \(f^{\ne}\) are, respectively, the activity coefficients of the \(\pi\)-complex, dissolved \(\mathrm{C_2H_4}\), and the transition state of the rate-limiting stage; \(h_0\) is the acidity of phosphoric acid \(\left(h_0 = a_{\mathrm{H^+}} f_{\mathrm{B}}/f_{\mathrm{BH^+}},\right.\) where \(\mathrm{B}\) is a base); \(P_{\mathrm{C_2H_4}}\) is the partial pressure of \(\mathrm{C_2H_4}\).

Neglecting the change in \(s\) and in the ratio \(f_{\pi}/f_{\mathrm{C_2H_4}} f^{\ne}\) with change in the composition of the acid, we arrive at the equation

\[ v_1 = k_1 h_0 P_{\mathrm{C_2H_4}} . \tag{4} \]

Analogously, for the reverse reaction we obtain

\[ v_2=k_2h_0\frac{P_{\mathrm{C_2H_5OH}}}{P_{\mathrm{H_2O}}}. \tag{5} \]

The constants \(k_1\) and \(k_2\) are related to the equilibrium constant of reaction (1) by the equality

\[ \frac{k_1}{k_2}=K_P. \tag{6} \]

Hence the observed reaction rate is given by the equation

\[ v=k\left(P_{\mathrm{C_2H_4}}-K_P^{-1}\frac{P_{\mathrm{C_2H_5OH}}}{P_{\mathrm{H_2O}}}\right); \tag{7} \]

here

\[ k=k_1h_0. \tag{8} \]

The quantity \(k\) must be constant at constant \(P_{\mathrm{H_2O}}\). Since the conversions of \(\mathrm{C_2H_4}\) and \(\mathrm{H_2O}\) are small, the change in volume during the reaction may be neglected and one may take \(v=dP_{\mathrm{C_2H_5OH}}/dt\), where \(t\) is the “reaction time,” calculated as the ratio of the volume of acid in the catalyst to the volumetric flow rate of the gas mixture \((^1)\).

Table 1

Integration of equation (7) at constant \(P_{\mathrm{C_2H_4}}\) and \(P_{\mathrm{H_2O}}\) gives

\[ k=-\frac{1}{t}K_PP_{\mathrm{H_2O}}\ln\left(1-\frac{P_{\mathrm{C_2H_5OH}}}{K_PP_{\mathrm{C_2H_4}}P_{\mathrm{H_2O}}}\right). \tag{9} \]

Table 1 gives the experimental data for \(290^\circ\) and the values of \(k\) calculated from equation (9). The values of \(K_P\) were determined from equilibrium data \((^3)\), since it was found that \(K_P\) does not depend on the ratio \(N_{\mathrm{H_2O}}/N_{\mathrm{C_2H_4}}\) at given \(P\) and \(T\) \((^*)\). The degree of attainment of equilibrium is characterized by the ratio of the conversion of ethylene \(\alpha\) to its equilibrium value \(\alpha_\infty\).

As is evident from the table, upon variation of \(P_{\mathrm{C_2H_4}}\), and also of \(t\), at constant \(P_{\mathrm{H_2O}}\), the value of \(k\) remains constant within the experimental error. With increasing \(P_{\mathrm{H_2O}}\) the alcohol yield not only does not increase, but even decreases somewhat (provided that equilibrium is not reached), in qualitative agreement with equation (8).

To verify equation (8), the composition of the acid was calculated from the partial pressure of \(\mathrm{H_2O}\) using the formula

\[ \log \frac{P_{\mathrm{H_2O}}}{P_{\mathrm{H_2O}}^{0}} = \left( \frac{1075}{T} - 1.515 \right) (72.4 - \%\, \mathrm{P_2O_5}), \tag{10} \]

where \(P_{\mathrm{H_2O}}^{0}\) is the pressure of \(\mathrm{H_2O}\) over \(\mathrm{H_3PO_4}\) (100%). Equation (10) was derived from previously published \((^{5})\) and additional data. From the acid composition, the values of \(h_0\) were determined, assuming a linear dependence of \(H_0 = -\log h_0\) on temperature \((^{6,7})\). Table 1 gives \(k_1 = k/h_0\); they are approximately constant.

It should be kept in mind that the values of \(h_0\) obtained by extrapolation are approximate. In any case, the fact that the alcohol yield changes little with significant variation of \(P_{\mathrm{H_2O}}\) indicates a zero order of the reaction with respect to \(\mathrm{H_2O}\) and confirms the basic initial assumption that \(\mathrm{H_2O}\) does not participate in the rate-limiting stage of the reaction.

Table 2

For technological calculations it is convenient to represent the reaction rate as an explicit function of \(P_{\mathrm{H_2O}}\). This can be done as follows. Since the catalyst consists of solutions of \(\mathrm{H_3PO_4}\) containing little \(\mathrm{H_2O}\), then, by analogy with Brand’s result \((^{8})\) for concentrated solutions of \(\mathrm{H_2SO_4}\), it may be assumed that

\[ H_0 = \mathrm{const} - \log \frac{X_{\mathrm{H_3PO_4}}}{X_{\mathrm{H_2PO_4^-}}}, \tag{11} \]

where \(X_{\mathrm{H_3PO_4}}\) is the mole fraction of \(\mathrm{H_3PO_4}\), etc. Considering \(\mathrm{H_2O}\) as a base, we obtain

\[ H_0 = pK - \log \frac{X_{\mathrm{H_3O^+}}}{X_{\mathrm{H_2O}}}. \tag{12} \]

Taking into account that \(X_{\mathrm{H_2PO_4^-}} = X_{\mathrm{H_3O^+}}\), regarding \(X_{\mathrm{H_2O}}\) as proportional to \(P_{\mathrm{H_2O}}\) and \(X_{\mathrm{H_3PO_4}}\) as practically constant, we arrive at the approximate equality

\[ h_0 = \frac{C}{P_{\mathrm{H_2O}}^{1/2}}, \tag{13} \]

where \(C\) is a constant depending on temperature.

Equations (7), (8), and (13) give

\[ v = \frac{k'}{P_{\mathrm{H_2O}}^{1/2}} \left( P_{\mathrm{C_2H_4}} - K_{P}^{-1} \frac{P_{\mathrm{C_2H_5OH}}}{P_{\mathrm{H_2O}}} \right), \tag{14} \]

where \(k' = k_1 C\). To calculate \(k'\), equation (9) and the equality

\[ k' = k P_{\mathrm{H_2O}}^{1/2}. \tag{15} \]

were used. The values of \(k'\) given in Table 1 are approximately constant. Data analogous to those presented in Table 1 were obtained in experiments at 270, 310, and 330°, covering the same values of \(P_{\mathrm{C_2H_4}}\), \(P_{\mathrm{H_2O}}\), and \(t\). Average values of \(k_1\) and \(k'\) at different temperatures and \(P_{\mathrm{H_2O}} = 30\) atm are given in Table 2 (\(t\) in seconds).

The temperature dependence of \(k_1\) and \(k'\) is given by the equations

\[ \log k_1 = 12.18 - \frac{35\,150}{4.57T}, \tag{16} \]

\[ \log k' = 5.39 - \frac{14\,860}{4.57T}. \tag{17} \]

The ethylene used in the experiments contained small amounts of \((\mathrm{C_2H_5})_2\mathrm{O}\). The amount of ether in the reaction products differed little from its amount in the initial ethylene. Thus, under the experimental conditions, the ether-formation reaction practically did not occur. This was confirmed by special experiments with ethylene almost free of ether.

In studying the absorption of \(\mathrm{C_2H_4}\) and \(\mathrm{C_3H_6}\) by solutions of sulfuric acid \({}^{9}\) and the acid hydration of \(\mathrm{C_2H_2}\) \({}^{1}\), the conclusion was drawn that the rate-limiting stage is the conversion of the \(\pi\)-complex into a carbonium ion. The results of the present work make it possible to extend this conclusion to the acid hydration of \(\mathrm{C_2H_4}\).

Physicochemical Institute
named after L. Ya. Karpov

Received
21 XII 1959

CITED LITERATURE

\({}^{1}\) E. N. Tsybina, A. I. Gel’bshtein et al., ZhFKh, 32, 856 (1958).
\({}^{2}\) R. W. Taft, J. Am. Chem. Soc., 74, 5372 (1952).
\({}^{3}\) Yu. M. Bakshi, A. I. Gel’bshtein, M. I. Temkin, DAN, 126, 314 (1959).
\({}^{4}\) Yu. M. Bakshi, A. I. Gel’bshtein, M. I. Temkin, DAN, 132, No. 1 (1960).
\({}^{5}\) A. I. Gel’bshtein, M. I. Temkin, ZhOKh, 23, 1278 (1953).
\({}^{6}\) A. I. Gel’bshtein, G. G. Shcheglova, M. I. Temkin, DAN, 107, 108 (1956).
\({}^{7}\) A. I. Gel’bshtein, G. G. Shcheglova, M. I. Temkin, ZhNKh, 1, 282 (1956).
\({}^{8}\) J. C. D. Brand, J. Chem. Soc., 1950, 997.
\({}^{9}\) A. I. Gel’bshtein, M. I. Temkin, ZhFKh, 31, 2697 (1957).