PHYSICAL CHEMISTRY

S. G. ENTELIS, G. V. EPPLE, and N. M. CHIRKOV

IONIZATION OF TRIPHENYLCARBINOL IN A SULFURIC ACID MEDIUM CONTAINING ISOPROPYL ALCOHOL

MEASUREMENT OF THE DEN0 ACIDITY FUNCTION

(Presented by Academician N. N. Semenov, 7 VIII 1959)

In connection with the growing interest in the kinetics and mechanism of acid-catalyzed reactions in nonaqueous and mixed solvents, a need has arisen for measurements of the values of acidity functions in these systems. Of especially great interest were measurements in alcohol–water media. The first quantitative studies \((^{1})\) devoted to this question showed that the dependence of the acidity function \(H_0\) on the composition of the medium is very complex and does not lend itself to a simple interpretation from the standpoint of changes in the basicity of the medium, as had been possible in other, simplest cases \((^{2})\).

As Bartlett and Tsvetkova showed, the molar decrease of the acidity function \(H_0\) in the systems \(\mathrm{H_2SO_4}—\mathrm{H_2O}\) \((^{3,4})\) and \(\mathrm{H_3PO_4}—\mathrm{H_2O}\) \((^{4})\) upon addition of isopropyl alcohol greatly exceeds the decrease caused by addition of water. An even more complex dependence of the acidity function on the composition of the medium was to be expected in the case of ionization of an indicator of the triphenylcarbinol type \((^{5})\), with elimination of a water molecule:

\[ \mathrm{Ph_3COH} + \mathrm{H^+} \ \underset{}{\stackrel{K_{\mathrm{ArOH}}}{\rightleftarrows}}\ \mathrm{Ph_3C^+} + \mathrm{H_2O}, \qquad K_{\mathrm{ArOH}} = \frac{a_{\mathrm{H^+}} a_{\mathrm{Ph_3COH}}}{a_{\mathrm{H_2O}} a_{\mathrm{Ph_3C^+}}}. \tag{1} \]

Data on the value of the acidity function \(C_0\) for mixed solvents are absent from the literature. Values of the \(J_0\) function were obtained by Gold and Hawes \((^{5})\) for the system \(\mathrm{H_2SO_4}—\mathrm{H_2O}—\mathrm{CH_3COOH}\).

In the present work the dependence of the Den0 acidity function \(C_0\) of sulfuric acid \((43—60\%\, \mathrm{H_2SO_4})\) on the concentration of added isopropyl alcohol (from 0.2 to 1.5 mole/liter) was measured at temperatures of 40, 54, and 60°. Triphenylcarbinol, which ionizes in acid according to equation (1) \((^{5})\), served as the indicator in the measurements. The acidity function of solutions containing various concentrations of alcohol was calculated from the equation

\[ C_{0i} = \mathrm{p}K_{\mathrm{ArOH}} + \lg I_i, \tag{2} \]

where \(K_{\mathrm{ArOH}}\) is the equilibrium constant of the reaction in the system \(\mathrm{H_2SO_4}—\mathrm{H_2O}\), and

\[ I_i = \frac{[\mathrm{Ph_3COH}]_i}{[\mathrm{Ph_3C^+}]_i} \]

is the indicator ratio at the \(i\)-th concentration of alcohol; the concentrations of the species are indicated in square brackets. The indicator ratio \(I_i\) was determined spectrophotometrically at \(\lambda_{\max} 432\) m\(\mu\), in the region where only the ionized form absorbs, and, according to the Lambert—Beer law, the measured optical density \(D = \varepsilon l[\mathrm{Ph_3C^+}]\). The concentration \([\mathrm{Ph_3COH}]\) was found from the material-balance equation. Measurements were carried out on a recording double-beam spectrophotometer of the SF-2M type in cuvettes 5 cm long, placed in a thermostated cuvette holder. Direct measurement of the equilibrium optical density \(D_i\) for the system \(\mathrm{H_2SO_4}—\mathrm{H_2O}— i\text{-}\mathrm{C_3H_7OH}\) is made difficult by the fact that, when isopropyl alcohol is added to a solution of triphenylcarbinol in sulfuric acid, a pseudo-first-order reaction occurs, causing—

...decrease in optical density with time. Therefore the density \(D_i\) was found by extrapolating straight lines in the coordinates \(\lg D — t\) to the initial moment of time \((t=0)\) (see Fig. 1).

In calculating \(I_i\) for a system containing alcohol, it is necessary to take into account the change in the specific gravity of sulfuric acid upon addition of alcohol to it.

Fig. 1. Plot for calculating the initial optical density at \(t = 40^\circ\); 50.96% \(H_2SO_4\) and \(C_{\mathrm{sp}} = 0.5\) mol/l

Fig. 2. Plot for determining the \(pK\) of triphenylcarbinol at \(t = 40^\circ\)

Fig. 3. Dependence of the acidity function \(C_0\) on the concentration of added alcohol at \(t = 40^\circ\); 50.46% \(H_2SO_4\)

For this purpose we used the formula proposed in the work of V. I. Tsvetkova \((^4)\):

\[ d_i = d_0(1 - 0.054\, C_{\mathrm{sp}}), \]

where \(d_0\) is the specific gravity of the initial sulfuric acid; \(d_i\) is the specific gravity of the acid containing isopropyl alcohol; \(C_{\mathrm{sp}}\) is the concentration of alcohol in gram-moles per 1000 g of the initial sulfuric acid. For calculations of \(C_0\) by equation (2) we used values obtained in the \(H_2SO_4 — H_2O\) system not containing \(u\)-\(C_3H_7OH\), assuming that in the concentration interval of isopropyl alcohol studied (from 0.2 to 1.5 mol/l) the value \(pK_{\mathrm{ArOH}}\) practically does not change. The values of \(pK_{\mathrm{ArOH}}\) at elevated temperatures, which are absent from the literature, were measured by us in a special series of experiments at 30, 40, 50, and 60°. The values of \(pK_{\mathrm{ArOH}}\) were found graphically from the dependence of \(\lg I\) on \(C_0\) at \(\lg I = 0\), according to equation (2). Table 1 gives the dependence of \(\lg I\) on \(C_0\) and the values of \(pK_{\mathrm{ArOH}}\) for 30, 40, 50, and 60°. Fig. 2 presents

Table 1

Dependence of the indicator ratio on the concentration of \(H_2SO_4\)

Table 2

Temperature dependence of the acidity function of the medium \(C_0\) on the concentration of added alcohol

the graph of such a dependence for \(40^\circ\). The tangent of the angle of inclination of the straight line is close to unity.

The values of the acidity function \(C_0\) needed to find \(pK_{\mathrm{ArOH}}\) at temperatures of 30, 40, 50, and \(60^\circ\) are absent from the literature. To calculate them we used the well-known formula (3)

\[ C_0 = H_0 + \lg a_{\mathrm{H_2O}} + \lg \frac{f_{\mathrm{ArC}^{+}}}{f_{\mathrm{ArOH_2}^{+}}}, \tag{3} \]

where \(a_{\mathrm{H_2O}}\) is the thermodynamic activity of water, and \(f_{\mathrm{ArC}^{+}}/f_{\mathrm{ArOH_2}^{+}}\) is the ratio of the activity coefficients of the carbonium ion and of the protonated carbinol. In calculations by formula (3), the values of \(H_0\) at different temperatures were taken from work \((^6)\). The values of \(a_{\mathrm{H_2O}}\) for the system \(\mathrm{H_2SO_4—H_2O}\) were calculated from tabular data \((^9)\) from the vapor pressures of water over sulfuric acid \((p)\) and water \((p_S)\). The last term in equation (3) was taken as temperature-independent. Its value for different concentrations of \(\mathrm{H_2SO_4}\) at \(25^\circ\) was taken from Deno’s work \((^7)\).

Fig. 4. Dependence of the parameter \(n\) on the acidity function \(C_0\) of the initial acid at \(t=40^\circ\)

From the data of Table 1, the values of the heat and entropy of protonation of triphenylcarbinol in the \(\mathrm{H_2SO_4—H_2O}\) system were calculated; these

respectively equal to \(\Delta H = 3280 \pm 100\) kcal/mole and \(\Delta S = -18.4 \pm 0.10\) cal/mole·deg, whence

\[ 2.3 R pK_{\mathrm{ArOH}} = -\frac{3280}{T} - 18.4. \]

Table 2 presents the values of the acidity function \(C_0\) of sulfuric acid of various concentrations with additions of isopropyl alcohol, calculated from equation (2).

Despite the fact that the accuracy of the data obtained does not exceed 20%, and near 60% \(\mathrm{H_2SO_4}\), where the values of \(C_{\mathrm{Ph_3COH}}\) are very small, the error sometimes reaches 100%, the following regularities can clearly be established.

The acidity function \(C_0\), like \(H_0\), decreases with increasing concentration of alcohol in the system according to a linear law (Fig. 3)

\[ \Delta C_0 = C_{0i} - C_0 = n C_{\mathrm{sp}}. \tag{4} \]

Table 3

Dependence of the parameter \(n\) on the acidity \(C_0\) of the initial acid

This dependence has a more abrupt character than the dependence for \(H_0\). The values of \(n\) decrease with increasing concentration of the initial acid and with temperature; moreover, as is seen from Fig. 4, within one temperature the relation

\[ n = a(C_0 + A), \tag{5} \]

is satisfied, where \(C_0\) refers to the initial \(\mathrm{H_2SO_4}\).

For example, at \(40^\circ\), \(a = 0.304\), \(A = 8.69\); at \(54^\circ\), \(a = 0.281\), \(A = 7.93\), and at \(60^\circ\), \(a = 0.228\), \(A = 7.60\). The dependence of \(n\) on \(C_0\) for three temperatures is presented in Table 3 and for \(t = 40^\circ\) in Fig. 4.

The change in the character of the dependence between \(C_{0i}\) and \(C_{\mathrm{sp}}\) in the investigated range of temperatures and concentrations of \(\mathrm{H_2SO_4}\) is in accord with the hypothesis that the effect of added alcohol on the acidity of the acid–water system is reduced mainly to the destruction of hydrogen bonds in the structure of water and thereby to an increase in the basicity of its molecules \((^{1,8,10})\). If this is so, then an increase in temperature, as well as an increase in acid concentration, should lead to a decrease in the degree of association of water molecules and thus contribute to a reduction of the influence of alcohol on the change in the structure of the solvent, and hence on its basicity. This consequence of the hypothesis is confirmed by the data obtained: a decrease in \(n\) with increasing concentration of \(\mathrm{H_2SO_4}\) and a decrease in the parameters \(a\) and \(A\) with temperature. The difference in the behavior of \(C_0\) and \(H_0\) \((^{3,4})\) upon addition of alcohol to the acid is associated with the influence of alcohol on the thermodynamic activity of unionized water; the alcohol added to the \(\mathrm{H_2SO_4}\)–\(\mathrm{H_2O}\) system binds part of the acid, thereby liberating water and increasing \(a_{\mathrm{H_2O}}\). An increase in \(a_{\mathrm{H_2O}}\) leads to a decrease in \(C_0\).

Institute of Chemical Physics
Academy of Sciences of the USSR

Received
4 VIII 1959

REFERENCES

1. E. A. Braude, J. Chem. Soc., 1948, 1971.
2. S. G. Entelis, N. M. Chirkov, ZhFKh, 31, 1311 (1957).
3. P. D. Bartlett, I. D. McCollum, J. Am. Chem. Soc., 78, 1441 (1956).
4. V. I. Tsvetkova, Candidate’s dissertation, Institute of Chemical Physics, Academy of Sciences of the USSR, 1956.
5. V. Gold, B. W. J. Hawes, J. Chem. Soc., 1951, 2102.
6. A. I. Gel'bshtein, G. G. Shcheglova, M. I. Temkin, ZhNKh, 1, 506 (1956).
7. N. C. Deno, J. J. Jaruzelski, A. Schriesheim, J. Am. Chem. Soc., 77, 3044 (1955).
8. G. Bates, G. Schwarzenbach, Helv. Chim. Acta, 38, 699 (1955).
9. Chemist’s Handbook, 3, 1952, p. 234.
10. A. G. Mitchell, W. F. K. Wynn-Jones, Disc. Farad. Soc., No. 15, 161 (1953).