PHYSICAL CHEMISTRY

S. G. ENTELIS, R. P. TIGER, G. V. EPPLE, and N. M. CHIRKOV

KINETICS OF THE REDUCTION REACTION OF DIPHENYL-m-TOLYLCARBINOL BY ISOPROPYL ALCOHOL VIA HYDRIDE TRANSFER IN THE SYSTEM H₂SO₄—H₂O

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

In recent years it has been established that a number of organic oxidation–reduction reactions include a stage involving the transfer of negatively charged hydrogen. Only a few works have been devoted to the study of the mechanism and kinetics of these reactions (^{(1-4)}). More thoroughly than others, the reaction of reduction of triphenylcarbinol (TPC) by aliphatic alcohols in aqueous (\mathrm{H_2SO_4}) has been studied. In order to establish how the reactivity of triarylcarbinols changes with structure, we have investigated the kinetics of reduction by isopropyl alcohol of the following representative of the series of triarylcarbinols—diphenyl-m-tolylcarbinol (DPTC).

The reaction was carried out in an (\mathrm{H_2SO_4}) medium at acid concentrations from 44 to 64%, in the temperature range (40—60^\circ). The concentration of DPTC in the reaction mixture was about (10^{-4}) mole/liter, and that of iso-(\mathrm{C_3H_7OH}) from 0.1 to 1.5 mole/liter. The progress of the transformation was followed by the decrease in optical density with time at a wavelength of 410 m(\mu), corresponding to the absorption maximum of the ionized form of DPTC, according to the previously described procedure (^{(6)}).

By analogy with triphenylcarbinol (^{(1,4)}), we assumed that the carbonium ion (\mathrm{Ph_2TolC^+}), formed as a result of ionization of DPTC, in the rate-limiting stage accepts a hydride ion from iso-(\mathrm{C_3H_7OH}) according to the following scheme:

[
\mathrm{Ph_2TolC^+ + H!:!C(CH_3)2OH}
\ \xrightarrow{k\}}'
\mathrm{Ph_2TolCH + C(CH_3)_2OH^+}
\tag{1}
]

It is not difficult to show (^{(4)}) that the expression for the observed effective rate constant of the reaction has the form

[
k_{\mathrm{ef}} =
k_{\mathrm{ist}}
\left(
\frac{K_{\mathrm{Ar_3COH}}c_0}{1+K_{\mathrm{Ar_3COH}}c_0}
\right)
\left(
\frac{1}{1+K_{\mathrm{ROH}}h_0}
\right)
[\mathrm{ROH}],
\tag{2}
]

where (k_{\mathrm{ef}}) is the observed first-order rate constant; (k_{\mathrm{ist}}) is the rate constant of the elementary act of hydride transfer; (k_{\mathrm{Ar_3COH}}), (K_{\mathrm{ROH}}) are equilibrium constants of the protonation reactions of the carbinol and the alcohol

[
\left(
K_{\mathrm{Ar_3COH}}=
\frac{[\mathrm{Ar_3C^+}]}{[\mathrm{Ar_3COH}]\,c_0};
\qquad
K_{\mathrm{ROH}}=
\frac{[\mathrm{ROH_2^+}]}{[\mathrm{ROH}]\,h_0}
\right);
]

(c_0, h_0) are the negative antilogarithms of the Denõ and Hammett acidity functions (^{(5)}), respectively.

Since the experiments were carried out in an excess of alcohol and the concentration of iso-(\mathrm{C_3H_7OH}) practically did not change during the experiment, the observed kinetics simulated first order. The values of the effective constants were found from the tangent of the angle of inclination of semilogarithmic anamorphoses of the kinetic curves.

We have studied in detail the dependence of (k_{\mathrm{ef}}) on the concentration of (\mathrm{H_2SO_4}) at different alcohol concentrations. Table 1 gives the obtained values of the effective rate constants of the reaction at different concentrations of alcohol and acid in the indicated temperature range.

As is seen from Table 1, the magnitude of the observed bimolecular con-

stant (k_0=k_{\mathrm{eff}}/C_{\mathrm{sp}}) does not remain constant as the concentration of iso-(\mathrm{C_3H_7OH}) changes. For example, in the region of low (\mathrm{H_2SO_4}) concentrations and low temperatures, the value of (k_0) decreases with increasing alcohol concentration, which is connected with the influence of the alcohol on the acidity of the medium ((^5)). This phenomenon complicates the observed regularities; therefore the obtained values of (k_{\mathrm{eff}}) were interpolated to (C_{\mathrm{sp}}=0.1) mole/liter, at which the influence of the alcohol on the acidity of the medium may be neglected ((^6)).

Figure 1 gives the dependence of (k_{\mathrm{eff}}) on the acid concentration at (C_{\mathrm{sp}}=0.1) mole/liter. As is seen from Fig. 1, this dependence, as also in the case of reduction of (\mathrm{Ph_3COH}) ((^4)), is a curve with a maximum, the position of which ((49.5\% \ \mathrm{H_2SO_4})) is practically independent of temperature. Such a form of the dependence of (k_{\mathrm{eff}}) on the concentration of (\mathrm{H_2SO_4}) is a consequence of the fact that the effective rate constant of the reaction is a complex quantity, into which, along with the true constant—

Fig. 1. Dependence of (k_{\mathrm{eff}}) on the concentration of (\mathrm{H_2SO_4}) at various temperatures. (C_{\mathrm{sp}}=0.1) mole/liter

Table 1

these include the protonation constant of isopropyl alcohol and the ionization constant of DPTC, as well as the acidity of the medium. As the concentration of H₂SO₄ increases, the factor (K_{\mathrm{Ar}3\mathrm{COH}}c_0/(1+K3\mathrm{COH}}c_0)=b), which characterizes the course of ionization of DPTC, increases, whereas the factor (1/(1+K), which includes both factors, is a function with a maximum with respect to the concentration of H₂SO₄.}}h_0)), which characterizes the fraction of the unprotonated form of the alcohol, decreases. Thus, according to equation (2), the quantity (k_{\mathrm{eff}

Table 2

(C_{\mathrm{sp}}=0.1) mol/l. Table 2 presents the temperature dependence of (K_{\mathrm{eff}}) and the values of the apparent activation energy (E_{\mathrm{eff}}) at various concentrations of H₂SO₄. (E_{\mathrm{eff}}) decreases as the acid concentration increases, which is consistent with the concept of the reaction mechanism (4).

As is evident from expression (2), in order to calculate the rate constant of the hydride-transfer step, (k_{\mathrm{true}}), it is necessary to know the quantities (K_{\mathrm{Ar}3\mathrm{COH}}) and (K}}). In the present work, by the previously described method ({}^{(5)}), the basicity constants of DPTC, (K_B^{\mathrm{Ar3\mathrm{COH}}=1/K), were measured at different temperatures.}_3\mathrm{COH}

Table 3

[
\Delta H=(2100\pm100)\ \mathrm{cal/mol};\qquad
\Delta S=-21.5\pm0.1\ \mathrm{cal/(mol\cdot deg)}
]

The value of the protonation constant of isopropyl alcohol in our case can be obtained simultaneously with the true rate constant of hydride transfer. Indeed, transforming equation (2) and replacing (k_{\mathrm{eff}}) by (k_0[\mathrm{ROH}]), it is not difficult to obtain the expression

[
\frac{k_0}{b}=k_{\mathrm{true}}-\frac{k_0}{b}h_0K_{\mathrm{ROH}}.
\tag{3}
]

Constructing graphically the dependence between (\frac{k_0}{b}) and (\frac{k_0}{b}h_0), we obtain a straight line that cuts off on the (\frac{k_0}{b}) axis a segment equal to (k_{\mathrm{true}}). From the slope of the straight line we find the value of (K_{\mathrm{ROH}}). Figure 2 gives the dependence of (\frac{k_0}{b}) on (\frac{k_0}{b}h_0) for 40, 50, 54, and 60° at (C_{\mathrm{sp}}=0.1) mol/l. Table 4 gives the values we obtained for the true rate constants of hydride transfer and the values of the basicity constants of iso-(\mathrm{C}3\mathrm{H}_7\mathrm{OH}) ((K_B^{\mathrm{ROH}}=1/K)).}

Let us compare the obtained values of the basicity constants of DPTC and TPC ({}^{(4)}) with the rate constants of the hydride-transfer step. Although introduction of one methyl group into the benzene ring of TPC only slightly changes the properties of the carbinol, it can already be said that an increase in the basicity of the carbinol, i.e., an increase in the stability of the corresponding cation, lowers its ability to add hydride ion.

Table 4

For example, at 60° for TPC (\mathrm{p}K_B=-6.17), (k_{\mathrm{true}}=5.39\cdot10^{-2}\ \mathrm{l/(mol\cdot sec)}) ({}^{(4)}), whereas for DPTC (\mathrm{p}K_B=-6.05), (k_{\mathrm{true}}=3.72\cdot10^{-2}\ \mathrm{l/(mol\cdot sec)}); i.e., an increase in (\mathrm{p}K_B) by (+0.12) unit causes a decrease in the logarithm of the reaction rate constant: (\Delta\lg k_{\mathrm{true}}=-0.16).

According to the data of Table 4, the value of the true activation energy was calculated as
(E_{\text{true}} = 20300 \pm 600) cal/mole, and the pre-exponential factor as
(A = 9.6 \cdot 10^{11}) l/mole·sec.

It is interesting to note that here, as in the case of TPC, the value of the pre-exponential factor is close to the collision number (Z_0 = 1.1 \cdot 10^{11}) l/mole·sec, calculated from the formula for an ideal solution, taking
(r_{\mathrm{RHO}} = 3.1) Å and (r_{\mathrm{Ar_3C^+}} \simeq r_{\mathrm{Ar_3COH}} = 4.5) Å.

Facts contradicting the theory of absolute reaction rates—namely the appearance of “normal” pre-exponential factors in reactions of polyatomic polar molecules in the liquid phase—have long been known(^7), but have still not received a proper explanation. Two possible reasons may be indicated for the increase of the pre-exponential factor in the cases mentioned above. First, the presence of electrostatic ion–dipole or dipole–dipole interaction can considerably increase the probability of collision of the reacting particles. Second, the interaction of reacting molecules with the solvent can lead to a decrease in rotational degrees of freedom, the presence of which accounts for small values of pre-exponential factors in the case of reactions of polyatomic molecules*. The expression for the true rate constant has the form

[
k_{\text{true}} = 9.6 \cdot 10^{11} e^{-20300/RT}.
\tag{4}
]

Fig. 2. Graphical determination of the values of (k_{\text{true}}) and (pK_{\mathrm{ROH}})

From the temperature dependence of the basicity constant, the heat of the alcohol protonation reaction was found to be
(\Delta H = 8100 \pm 1000) cal/mole and the value
(\Delta S = +11.4 \pm 0.1) cal/mole·deg. The obtained value of (\Delta H) for protonation of iso-(\mathrm{C_3H_7OH}) agrees satisfactorily with our previously obtained data(^4). Substituting the obtained values of (k_{\text{true}}), (K_{\mathrm{Ar_3COH}}), and (K_{\mathrm{ROH}}) into equation (2), we obtain the formula for calculating the observed bimolecular constant

[
k_0 =
9.6 \cdot 10^{11} e^{-20300/RT}
\left[
\frac{2.08 \cdot 10^{-5} e^{-2100/RT} c_0}
{1 + 2.08 \cdot 10^{-5} e^{-2100/RT} c_0}
\right]
\left[
\frac{1}
{1 + 3.09 \cdot 10^2 e^{-8100/RT} h_0}
\right].
\tag{5}
]

The values of (k_0) for 40° C, calculated by equation (5) and obtained experimentally, are presented in Table 5. As can be seen from the table, the experimental and calculated values practically coincide.

Table 5

Thus, the assumption underlying the work—that the rate-limiting stage is the interaction of the ionic form of diphenyl-m-tolylcarbinol with a molecule of iso-(\mathrm{C_3H_7OH})—is correct.

Institute of Chemical Physics
Academy of Sciences of the USSR

Received
31 X 1960

REFERENCES

1. P. D. Bartlett, J. D. McCollum, J. Am. Chem. Soc., 78, 1441 (1956).
2. R. Stewart, Canad. J. Chem., 35, 766 (1957).
3. R. Stewart, J. Am. Chem. Soc., 79, 3057 (1957).
4. S. G. Entelis, G. V. Epple, N. M. Chirkov, DAN, 136, No. 3 (1961).
5. N. C. Deno, J. J. Jaruzelski, A. Schriesheim, J. Am. Chem. Soc., 77, 3044 (1955).
6. S. G. Entelis, G. V. Epple, N. M. Chirkov, DAN, 130, 826 (1960).
7. Melvin-Hughes, Kinetics of Reactions in Solutions, 1937.

* The latter consideration was put forward by Prof. N. D. Sokolov in a presentation at the conference on heterolytic reactions in May 1960 in Kiev.