S. G. Entelis, G. V. Korovina, and N. M. Chirkov

Thermodynamics of the Absorption of Propylene by the System $\mathrm{H_2SO_4-H_2O}$

(Presented by Academician V. N. Kondrat’ev, April 4, 1960)

The absorption of olefins by sulfuric acid has long been studied; however, because of the complexity of the olefin–water–acid system, works devoted to the thermodynamics of this process are few in number ($^{1-3}$).

The present work is devoted to a study of the thermodynamics of the complex process of absorption of propylene by aqueous sulfuric acid, during which, as we showed earlier ($^4$), alkylsulfuric acid and alcohol are formed, which entails a sharp change in the properties of the initial solution.

Table 1

Dependence of the equilibrium constant of the alkylation reaction on the concentration of the initial acid; $t = 70^\circ\mathrm{C}$, $K_{\Gamma}^{70^\circ} = 3.27 \cdot 10^{-6}$ mole/l · mm

We have studied in detail the equilibrium of the absorption of propylene by sulfuric acid in the concentration range 62.25–74.03% at temperatures of 70–95° and initial gas pressures of 300–600 mm Hg, with determination of the concentrations of alkylsulfuric acid and alcohol in the reaction mixture. The experiments were carried out in the circulating glass apparatus described by us earlier ($^4$). The amount of acid in the experiments was about 8 g. The volume of the system in which absorption was carried out was 2000 cm$^3$. The course of absorption was followed from the fall in the pressure of propylene in the system; attainment of equilibrium was noted by the cessation of pressure change. After saturation, the reaction mixture was rapidly diluted with a large volume of cold water and analyzed for alkylsulfuric acid and alcohol.

The alkylsulfuric acid was determined acidimetrically, and the alcohol by the method of oxidative titration ($^5$). Knowledge of the equilibrium concentrations of alkylsulfuric acid and alcohol makes it possible to determine the equilibrium constants, not available in the literature, for the reactions of alkylation of sulfuric acid and hydration of propylene.

The equilibrium of the alkylation reaction

[
\mathrm{C_3H_6 + H_2SO_4 = iso\text{-}C_3H_7SO_4H}
\tag{I}
]

is conveniently characterized by the constant $K'_{\text{alk}}$, expressed through quantities determined in the experiment:

[
K'{\text{alk}} =
\frac{C}C_3H_7SO_4H}}
{K_{\Gamma} P_{\mathrm{C_3H_6}} C_{\mathrm{H_2SO_4}}}
= K_{\text{alk}}F,
\tag{1}
]

where $F = f_{\mathrm{H_2SO_4}} f_{\mathrm{C_3H_6}} / f_{\mathrm{iso\text{-}C_3H_7SO_4H}}$; $K_{\text{alk}}$ is the thermodynamic constant; $f_i$ are activity coefficients; $C_i$ are concentrations in moles per liter. The Henry constant $K_{\Gamma}$ was found by extrapolating literature data on the solubility of propylene in water ($^{12}$) to the temperature of the experiment.

It follows from Table 1 that $K'_{\text{alk}}$ is related to $H_0$ in the following way:

[
\lg K'_{\text{alk}} = -0.732\,H_0 - 1.76.
\tag{2}
]

The temperature dependence of (K'_{\mathrm{alk}}) is presented in Table 2 (67.7% (\mathrm{H_2SO_4})).

Table 2

Figure 1 gives a plot for calculating the heat of the alkylation reaction. It was found that (\Delta H_{\mathrm{alk}}=(-9.2\pm0.2)) kcal/mol and (\Delta S) is (-(17.4\pm0.2)) e.u.

Fig. 1. Plot for calculating the heat of the alkylation reaction

Of particular interest is the calculation of the equilibrium constant of the hydration reaction of propylene in the liquid phase.

Formation of the alcohol in an acidic medium proceeds according to the equation

[
\mathrm{C_3H_6+H_2O+H_2SO_4 \rightleftarrows iso\text{-}C_3H_7OH_2^+ + HSO_4^-},
\tag{II}
]

which is the sum of three equations:

[
\mathrm{C_3H_6+H_2O \underset{}{\stackrel{k_{\mathrm{III}}}{\rightleftarrows}} iso\text{-}C_3H_7OH};
\tag{III}
]

[
\mathrm{H_2O+H_2SO_4 \underset{}{\stackrel{k_{\mathrm{IV}}}{\rightleftarrows}} H_3O^+ + HSO_4^-};
\tag{IV}
]

[
\mathrm{iso\text{-}C_3H_7OH+H_3O^+ \underset{}{\stackrel{k_{\mathrm{V}}}{\rightleftarrows}} iso\text{-}C_3H_7OH_2^+ + H_2O}.
\tag{V}
]

It is convenient to characterize the equilibrium of reaction (II) by the constant (K'_{\mathrm{sp}}), expressed through experimentally determined quantities:

[
K'{\mathrm{sp}}=
\frac{C}C_3H_7OH_2^+}}
{C_{\mathrm{C_3H_6}}\,a_{\mathrm{H_2O}}\,h_0}
=
K_{\mathrm{sp}}\frac{1}{k_{\mathrm{IV}}}
\frac{f_{\mathrm{C_3H_6}}}{f_{\mathrm{iso\text{-}C_3H_7OH}}},
\tag{3}
]

where (h_0) is the acidity of the medium, and (K_{\mathrm{sp}}) is the thermodynamic constant.

From the data available in the literature on the basicity of isopropyl alcohol ((^{6})), it follows that in 67.7% (\mathrm{H_2SO_4}) practically all the alcohol is in the ionized form, i.e., the value (C_{\mathrm{iso\text{-}C_3H_7OH_2^+}}) in formula (3) is equal to the concentration of all alcohol detected by analysis in the liquid phase. Indeed, analysis of the composition of the gas phase above our system shows that the fraction of alcohol in the vapors does not exceed (10^{-4}) of the total amount.

To calculate the equilibrium constant (K'{\mathrm{sp}}) by equation (3), it is necessary to use the equilibrium values (a) and (h_0^}), which differ substantially, as was shown by us earlier ((^{11})), from the corresponding values for the initial acid. In calculating the equilibrium values, we used empirical formulas ((^{11})) relating (a_{\mathrm{H_2O}}) and (h_0^) to the alcohol content in the equilibrium system:

[
h_0^* = h_0 \frac{1+0.13C_{\mathrm{sp}}}{1+0.52C_{\mathrm{sp}}},
\qquad
a_{\mathrm{H_2O}} = 55.51\,B\left(C_{\mathrm{sp}}+\frac{P_{\mathrm{H_2O}}/P_{\mathrm{SH_2O}}}{B}\right),
\tag{4}
]

where (h_0) and (h_0^*) are the acidity values of, respectively, the initial acid and the acid with concentration (C) mol/l alcohol; (P_{\mathrm{H_2O}}) and (P_{\mathrm{SH_2O}}) are the values

Table 3

Dependence of the equilibrium constant of the propylene hydration reaction in the liquid phase on the acidity function of the initial acid. (t=70^\circ), (P_{\mathrm{SH_2O}}=233.7) mm Hg.

the vapor pressures of water, respectively over the initial acid and the saturated space; for 70° an extrapolation yielded (B=16.47\cdot 10^{-2}).

It follows from Table 3 that the values of (\lg K'_{\mathrm{sp}}) are related to (H_0) by

[
\lg K'_{\mathrm{sp}}=0.319H_0-1.245 .
\tag{5}
]

The temperature dependence of (K'_{\mathrm{sp}}) is presented in Table 4.

Table 4

Dependence of the equilibrium constant of the propylene hydration reaction in the liquid phase on temperature. 67.7% (\mathrm{H_2SO_4})

Figure 2 gives a graph for calculating the heat of hydration. It was found that (\Delta H_{\mathrm{sp}}=-(3.7\pm0.3)) kcal/mol, (\Delta S=-(23.44\pm0.12)) e.u.

From Tables 1 and 3 and Fig. 3 it is seen how the fraction of propylene converted into alcohol and alkyl acid changes with the concentration of the initial (\mathrm{H_2SO_4}), which agrees with literature data ((^{2,3})).

Table 5 presents the values of the equilibrium constants for the gross absorption of propylene, (K_{\mathrm{общ}}=\Delta P_\infty/P_{\mathrm{eq}}), where (\Delta P_\infty) is the equilibrium pressure drop in the system, and (P_{\mathrm{eq}}) is the equilibrium pressure. (K_{\mathrm{общ}}) is related to the constants of alkylation (K'{\mathrm{alk}}) and alcohol formation (K') by the equation}

[
K_{\mathrm{общ}}=
\frac{K_\Gamma RT V_{\mathrm{acid}}}{2000}
\left(K'{\mathrm{sp}}ah_0+K'}{\mathrm{alk}}C\right),}
\tag{6}
]

where (V_{\mathrm{acid}}) is the volume of acid in liters. It was found that the effective heat (\Delta H_{\mathrm{общ}}=-(8.7\pm0.8)) kcal/mol, and (\Delta S=-(15.14\pm0.3)) e.u.

On the basis of the data obtained, a number of interesting quantities can be calculated. Knowledge of the heat of the alkylation reaction of sulfuric acid by propylene makes it possible to calculate the heat of formation of isopropylsulfuric acid from the elements ((\Delta H_{\mathrm{form}})_{\text{iso-}\mathrm{C_3H_7SO_4H}}) by the formula:

[
(\Delta H_{\mathrm{form}}){\text{iso-}\mathrm{C_3H_7SO_4H}}
=
\Delta H}
+
(\Delta H_{\mathrm{form}}){\mathrm{C_3H_6}(l)}
+
(\Delta H,}})_{\mathrm{H_2SO_4}(2.68)
]

where ((\Delta H_{\mathrm{form}}){\mathrm{C_3H_6}(l)}) is the heat of formation of liquid propylene; ((\Delta H) is the heat of formation of sulfuric acid at a molar соот-}})_{\mathrm{H_2SO_4}(2.68)

...of water to sulfuric acid in the solution (2.68:1 \simeq 3.1), equal to (-205.6) kcal/mole ((^8)):

[
(\Delta H_{\mathrm{form}})_{\text{iso-}\mathrm{C}_3\mathrm{H}_7\mathrm{SO}_4\mathrm{H}}
=
(-9.2 + 0.48 - 205.6)\ \text{kcal/mole}
=
-214.32\ \text{kcal/mole}.
]

Using the obtained value of the heat of formation of the protonated form of the alcohol, one can calculate by difference the heat of protonation of isopropyl alcohol:
(\Delta H_{\mathrm{V}}=\Delta H_{\mathrm{sp}}-\Delta H_{\mathrm{III}}).

The heat of reaction (III), (\Delta H_{\mathrm{III}}), is found from tabulated data

[
\Delta H_{\mathrm{III}}
=
(\Delta H_{\mathrm{form}}){\text{iso-}\mathrm{C}_3\mathrm{H}_7\mathrm{OH}(\ell)}
-
(\Delta H)}{\mathrm{H}_2\mathrm{O}(\ell)}
-
(\Delta H;}})_{\mathrm{C}_3\mathrm{H}_6(\ell)
]

[
\Delta H_{\mathrm{III}}
=
(68.4 - 0.5 - 76.6)\ \text{kcal/mole}
=
-8.7\ \text{kcal/mole},
]

Fig. 2. Plot for calculating the heat of the hydration reaction

Fig. 3. Dependence of the percentage conversion of (\mathrm{C}_3\mathrm{H}_6) into iso-(\mathrm{C}_3\mathrm{H}_7\mathrm{OH}) (1) and iso-(\mathrm{C}_3\mathrm{H}_7\mathrm{SO}_4\mathrm{H}) (2) on the acid concentration

whence the heat of protonation of isopropyl alcohol is

[
\Delta H_{\mathrm{V}}
=
(-3.7 + 8.7)\ \text{kcal/mole}
=
5\ \text{kcal/mole}.
]

The heat of protonation of isopropyl alcohol found by us is close to the heat of protonation of methyl alcohol, (\Delta H=4.6) kcal/mole, calculated from Smith’s data ((^{10})).

Table 5

Dependence of the gross-absorption equilibrium constant on temperature, (67.7\%\ \mathrm{H}_2\mathrm{SO}_4)

Institute of Chemical Physics
Academy of Sciences of the USSR

Received
29 III 1960

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