PHYSICAL CHEMISTRY

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

ADDITIONAL DATA ON THE EQUILIBRIUM OF ETHYL ALCOHOL SYNTHESIS

(Presented by Academician S. S. Medvedev, 30 XII 1959)

Previously published data ((^1)) on the equilibrium

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

at pressures up to 81 atm show a linear dependence of (\log K_P) on the total pressure (P). This dependence, at a constant ratio (N_{\mathrm{H_2O}}/N_{\mathrm{C_2H_4}}), corresponds to the equation of state of a gas mixture with the second virial coefficient. The values of (\log K_f), obtained by linear extrapolation of (\log K_P) to (P=0), were represented by the equation ((^1))

[
\log K_f=\frac{2093}{T}-6.304.
\tag{2}
]

Additional measurements, the results of which are reported here, make it possible to judge the dependence of the ratio (\log K_\gamma/P) on the composition of the mixture and to refine the dependence of this ratio on temperature ((K_\gamma=\gamma_{\mathrm{C_2H_5OH}}/\gamma_{\mathrm{C_2H_4}}\gamma_{\mathrm{H_2O}}), where (\gamma_{\mathrm{C_2H_5OH}}) is the activity coefficient of (\mathrm{C_2H_5OH}), etc.). The measurement procedure did not differ from that described in ((^1)). Gas-mixture compositions at which condensation was excluded were used. The results are presented in Table 1, where values of (K_P) calculated with the aid of equation (2) are also given, taking, according to ((^1)), (\log K_\gamma/P=14.2\cdot10^{-4}) for (286^\circ), and (K_\gamma=1) for (332^\circ). As is seen from Table 1, the values

Table 1

* The content of (\mathrm{H_3PO_4}) in percent by weight of the catalyst is indicated in parentheses.

of (K_P) at a given (P), within the accuracy of the measurements, do not depend on the composition of the gas mixture. In addition, it is seen from the table that at (332^\circ) (K_P)

does not depend on (P), i.e., this temperature is close to the “Guldberg–Waage temperature” ((^1)). At lower temperatures (K_\gamma > 1)*. The table does not include data on the ether content, since equilibrium with respect to the ether-formation reaction was not reached.

As was shown ((^1)),

[
\frac{\ln K_\gamma}{P}=
\frac{2\sum_i \nu_i B_i - B\sum_i \nu_i}{RT}.
\tag{3}
]

The dependence of the quantities (B_i) and (B) on (T) can be represented by series of the form (a_0 + \dfrac{a_1}{T} + \dfrac{a_2}{T^2}+\cdots). Assuming that two terms of the series are sufficient, we arrive at a temperature dependence of (\log K_\gamma/P) of the form

[
\frac{\log K_\gamma}{P}=\frac{A_0}{T}+\frac{A_1}{T^2}.
\tag{4}
]

The experimental data correspond to the values (A_0=-10.47;\ A_1=6.37\cdot 10^3). Equation (2), on the basis of the equality (K_P=K_f/K_\gamma), gives

[
\log K_P=\frac{2093}{T}-6.304+
\left(\frac{10.47}{T}-\frac{6.37\cdot 10^3}{T^2}\right)P.
\tag{5}
]

Equation (5) describes the dependence of (K_P) on (T) and (P) and takes into account the independence of (K_P) from the composition of the mixture. In Table 2 the values of (K_P) according to equation (5)

Table 2

*Note. In communication ((^1)) an inaccuracy was introduced in specifying the unit of pressure. The pressures were measured in technical atmospheres (kg/cm(^2)).

are compared with the experimental values of (K_P) obtained earlier ((^1)). Tables 3 and 4 contain the equilibrium degrees of conversion of ethylene (\alpha), calculated according to equation (5) under the assumption that only reaction (1) proceeds.

Table 3

Equilibrium degrees of conversion of ethylene to alcohol, (\alpha\cdot 10^2), at (N_{\mathrm{H_2O}}/N_{\mathrm{C_2H_4}}=1)

Table 4

Equilibrium degrees of conversion of ethylene to alcohol, (\alpha\cdot 10^2), at (290^\circ)

For calculating (\alpha) it is convenient to use the series

[
\alpha=
\frac{n}{1+n}\frac{K_N}{1+K_N}
+
\frac{n^2}{(1+n)^3}
\left(\frac{K_N}{1+K_N}\right)^2
+
2\frac{n^3}{(1+n)^5}
\left(\frac{K_N}{1+K_N}\right)^3
+\cdots,
\tag{6}
]

* The corresponding formulation in ((^1)) contains misprints.

where (n) is the number of moles of (\mathrm{H_2O}) per 1 mole of (\mathrm{C_2H_4}) in the initial mixture, (K_N = P K_P). The equilibrium gas mixture at (N_{\mathrm{H_2O}}/N_{\mathrm{C_2H_4}} = 1), (250^\circ), and 100 atm (and also, possibly, some others) is unstable with respect to condensation.

The data obtained make it possible to determine the thermal effect of reaction (1). Since (K_\gamma) in the case under consideration does not depend on the composition of the gas mixture, then

[
\left(\frac{\partial \ln K_\gamma}{\partial T}\right)_P
=
\frac{\Delta H^0-\Delta H}{RT^2}.
\tag{7}
]

From the relation

[
\frac{d \ln K_f}{dT}
=
\frac{\Delta H^0}{RT^2}
\tag{8}
]

and the equality (K_P = K_f/K_\gamma), we obtain

[
\left(\frac{\partial \ln K_P}{\partial T}\right)_P
=
\frac{\Delta H}{RT^2}.
\tag{9}
]

Equation (5) gives

[
\Delta H = -9570 - \left(47.9-\frac{5.83\cdot 10^4}{T}\right)P.
\tag{10}
]

At (300^\circ) and 80 atm, (\Delta H = -5263) cal. This value differs substantially from (\Delta H^0 = -9570) cal. Consequently, in technological calculations it is necessary to take into account the dependence of (\Delta H) on (P).

Physical-Chemical Institute
named after L. Ya. Karpov

Received
30 XII 1959

CITED LITERATURE

1. Yu. M. Bakshi, A. I. Gelbshtein, M. I. Temkin, DAN, 126, 314 (1959).