PHYSICAL CHEMISTRY

I. V. BEREZIN, K. VACEK, and N. F. KAZANSKAYA

INTERACTION OF FREE METHYL RADICALS WITH THE HYDROXYL HYDROGEN ATOMS OF TERTIARY BUTYL ALCOHOL

THE ROLE OF HYDROGEN BONDS

(Presented by Academician N. N. Semenov, 26 XII 1961)

In works ($^1$, $^2$) it was shown that the hydroxyl hydrogen atoms of tertiary butyl and isopropyl alcohols practically do not react with free methyl radicals. The weak reactivity of these atoms is consistent with the high strength of the O—H bond, which for alcohols, according to data ($^3$, $^4$), is 100–104 kcal/mole. The results of the present work showed that the low reactivity of the hydroxyl hydrogen atoms of tertiary butyl alcohol is associated not with the high strength of the O—H bond, but with the formation of hydrogen bonds between alcohol molecules. In monomeric molecules, hydroxyl hydrogen atoms readily enter into reaction with free methyl radicals. The importance of taking into account the influence of hydrogen bonds on the kinetics of chemical reactions was shown earlier in the works of N. M. Emanuel and co-workers ($^5$).

In the work described here, the method of competing reactions was used to determine the rate of interaction of the hydroxyl hydrogen atoms of tertiary butyl alcohol with free methyl radicals, relative to the rate of reaction of these same radicals with the C—H bonds of n-heptane. To establish the reaction of the hydroxyl hydrogen atoms of the alcohol, the latter was labeled with tritium at the hydroxyl group. n-Heptane was used as the solvent. The source of free methyl radicals was the thermal decomposition of acetyl peroxide ($^6$, $^7$) at concentrations of 0.03–0.05 mole/l. In a number of experiments the decomposition of the peroxide was carried out in the labeled alcohol without the use of a solvent.

The following elementary reactions occurred in the system:

\[ (\mathrm{CH}_3)_3\mathrm{COT} + \mathrm{CH}_3^{\bullet} \stackrel{k_{\mathrm{OT}}}{\longrightarrow} \mathrm{CH}_3\mathrm{T} + (\mathrm{CH}_3)_3\mathrm{CO}^{\bullet}; \qquad n\text{-}\mathrm{C}_7\mathrm{H}_{16} + \mathrm{CH}_3^{\bullet} \stackrel{k_{\mathrm{CH}}}{\longrightarrow} \mathrm{CH}_4 + \mathrm{C}_7\mathrm{H}_{15}^{\bullet}. \]

From the radioactivity of the methane formed and of the initial alcohol, the ratio of the rate constants of these elementary reactions can be found ($^7$, $^8$). If the constant $k_{\mathrm{CH}}$ is referred to one secondary bond in the n-heptane molecule and the reaction of $\mathrm{CH}_3^{\bullet}$ with the hydrogen atoms of tertiary butyl alcohol is neglected, which distorts the results by no more than 4% even at the highest alcohol concentrations used by us, then the ratio of the rate constants can be represented by the following formula:

\[ k_{\mathrm{OT}} : k_{\mathrm{CH}} = \left(I_{\mathrm{m}}[\mathrm{C}_7\mathrm{H}_{16}]\cdot 10.5\right) : \left(I_{\mathrm{sp}}[\mathrm{C}_4\mathrm{H}_9\mathrm{OH}]\right) \tag{1} \]

Here $I_{\mathrm{m}}$ is the specific radioactivity of the methane formed in the reaction, and $I_{\mathrm{sp}}$ is the radioactivity of butanol, expressed as the number of pulses per minute per 1 mm pressure of substance in the volume of the internally filled counter; $[\mathrm{C}_7\mathrm{H}_{16}]$ and $[\mathrm{C}_4\mathrm{H}_9\mathrm{OH}]$ are the concentrations of heptane and alcohol; 10.5 is the stoichiometric coefficient taking into account the reaction of methyl radicals with the secondary and primary C—H bonds of n-heptane.

Table 1 gives the experimental results at 90° and at various concentrations of tertiary butanol in n-heptane. The ratio of the rate constants increases as the concentration of alcohol decreases, tending to a limiting value equal under these conditions to 0.144. The most satisfactory explanation for such a change in the ratio of constants may be the assumption that the hydroxyl …

Table 1

Note. The specific radioactivities of alcohol and methane are expressed as the number of pulses per minute per 1 mm pressure of substance in the counter volume.

hydrogen (tritium) atoms only of monomeric alcohol molecules. Associated molecules possess, owing to shielding, unreactive hydroxyl hydrogen atoms.

Fig. 1. Logarithmic anamorphosis of the Kemper and Mekka equation for tert-butyl alcohol (90°)

To find the true value of the ratio of constants, formula (1) should contain the concentration only of the monomeric form of the alcohol. Since the true value of the ratio of constants was obtained by us by extrapolation, the inverse problem can be solved using the same formula—finding the concentration of the monomeric form and the degree of dissociation of the alcohol \(\alpha=[\mathrm{ROH}]/[\mathrm{Alc}]\), assuming that \(k_{\mathrm{OT}}/k_{\mathrm{CH}}=0.144\) and does not depend on the alcohol concentration (\([\mathrm{ROH}]\) is the concentration of the monomeric form, \([\mathrm{Alc}]\) is the total concentration of the alcohol). Table 1 gives the values of the degree of dissociation of tert-butyl alcohol determined in this way as a function of its concentration.

It is known \((^9–^{18})\) that alcohols can form associates consisting of a considerable number of molecules. If it is assumed that in our case the following equilibria exist

\[ \mathrm{ROH}+(\mathrm{ROH})_n \ \underset{}{\overset{K_a}{\rightleftarrows}}\ (\mathrm{ROH})_{n+1}, \tag{2} \]

where \(n=1, 2, 3, 4\), etc., and \(K_a=[\mathrm{ROH}]_{n+1}/[\mathrm{ROH}]\cdot[\mathrm{ROH}]_n\) does not depend on the value of \(n\), then the following equality \((^9)\) will hold:

\[ K_a=\frac{1-\sqrt{\alpha}}{\alpha[\mathrm{Alc}]} \quad \text{or} \quad \lg\frac{1-\sqrt{\alpha}}{\alpha}=\lg K_a+\lg[\mathrm{Alc}]. \tag{3} \]

Our experimental data (Table 1) satisfy this equation well, as is seen in Fig. 1.

If tert-butanol forms linear-type associates having a free hydroxyl group at the end, then the quantity \([\mathrm{ROH}]\) obtained by us will represent the sum of the concentrations of the monomeric and polymeric forms of the alcohol. In this case \(\alpha=\alpha_1+\alpha_2+\alpha_3+\alpha_4+\) etc., where \(\alpha_n=[\mathrm{ROH}]_n/[\mathrm{Alc}]\). In work \((^9)\) it was shown that \(\alpha_n=\alpha_1(\alpha_1K_a\cdot[\mathrm{Alc}])\).

Taking this into account,

\[ \alpha=\alpha_1\sum_{1}^{\infty}(\alpha_1K_a[\mathrm{Alc}])^{\,n-1} =\alpha_1/(1-\alpha_1\cdot K_a[\mathrm{Alc}]). \]

Substituting \(K_a\) in the last expression according to formula (3), we obtain \(\alpha_1=\alpha^2\), where \(\alpha_1\) is the degree of dissociation of the alcohol only into monomeric molecules. It turns out that, with the degree of dissociation corrected in this way, dependence (3) is not at all obeyed. This indicates the absence, at least in the majority of associates, of reactive hydroxyl-

groups, which may be a consequence of their cyclic structure. The equilibrium picture considered turns out to be simplified, since the equilibrium constant for dimer formation differs from the other constants \({}^{(11)}\). In our case this difference is small. Using (3), we obtain \(K_a = 4.57\) l/mole at \(90^\circ\). A more complicated calculation according to \({}^{(11)}\) gives: \(K_{2a}=4.1\) l/mole (dimer formation) and \(K_a = 5.4\) l/mole at \(90^\circ\), i.e., very close values, which also agrees with \({}^{(11)}\), where these constants were obtained spectroscopically.

The values of the equilibrium constants obtained by us are higher than the values obtained spectroscopically \({}^{(11,13-16)}\) by approximately one order of magnitude. It is possible that one of the reasons for these discrepancies is connected with the use of carbon tetrachloride as solvent, whereas our measurements were carried out in an \(n\)-heptane medium. It is also possible that not all alcohol associates are sufficiently clearly manifested in the infrared spectra. Allowance for the thermodynamic isotope effect in alcohol association may also affect the magnitude of the equilibrium constant. An approximate calculation, however, shows that for the process

\[ (\mathrm{ROH})_{n+1} + \mathrm{ROT} \rightleftarrows (\mathrm{ROH})_n \cdot \mathrm{ROT} + \mathrm{ROH} \]

the equilibrium constant differs little from unity. Consequently, in treating the results no correction for the isotope effect was introduced.

The temperature dependence of the ratio \(k_{\mathrm{OT}}/k_{\mathrm{CH}}\) was studied with a butanol solution of concentration 0.0122 mole/l (see Table 2). Using the value of the equilibrium constant at \(90^\circ\) and the heat effect of association, which is equal to 4–6 kcal/mole \({}^{(14,18)}\), one can find \(\alpha\) and \([\mathrm{ROH}]\) for any temperature and then, by formula (1), the values of \(k_{\mathrm{OT}}/k_{\mathrm{CH}}\). The temperature dependence is expressed by the formula:

\[ k_{\mathrm{OT}} : k_{\mathrm{CH}} = 42 \exp [(-4100 \pm 500)/RT]. \]

The kinetic isotope effect \((k_{\mathrm{OH}}:k_{\mathrm{OT}})\) of hydroxyl tritium atoms in the reaction with \(\mathrm{CH}_3^\cdot\) is unknown. It may, however, by analogy with the isotope effect in a similar reaction of a tritium atom bound to carbon \({}^{(20)}\), be assumed that \(E_{\mathrm{OT}} - E_{\mathrm{OH}} \approx 3\) kcal/mole and \(A_{\mathrm{OT}}/A_{\mathrm{OH}} \approx 3\) (\(A\) are the preexponentials of the corresponding constants). Then we obtain:

\[ k_{\mathrm{OH}} : k_{\mathrm{CH}} \approx 14 \exp(-1100/RT). \]

If one starts from the dissociation energies of the \(\mathrm{O-H}\) (102 kcal) and \(\mathrm{C-H}\) (90 kcal) bonds, then on the basis of the Polanyi rule \({}^{(21)}\) it would be expected that at \(90^\circ\) \(k_{\mathrm{OH}}\) would be 60 times smaller than \(k_{\mathrm{CH}}\), if, as is usually assumed, \(A_{\mathrm{OH}} = A_{\mathrm{CH}}\). In fact, at this temperature \(k_{\mathrm{OH}}\) is three times larger than \(k_{\mathrm{CH}}\). This indicates an increased reactivity of hydroxyl hydrogen atoms in free-radical reactions, which should be connected with the polar character of this bond.

Allowance for the polarity of element–hydrogen bonds can apparently explain many features of the kinetics of elementary free-radical reactions. In particular, for reactions of peroxide-type free radicals with hydroxyl hydrogen atoms in carboxylic acids, both their increased reactivity and the shielding of hydrogen atoms in acid dimers formed through hydrogen bonds are also observed \({}^{(22)}\).

The temperature dependence of the equilibrium constant was studied with an alcohol solution of concentration 0.1215 mole/l, and also with pure alcohol. The experimental data are given in Table 2. In the case of the solution, from the activity of methane, using formulas (4) and (1), the values of \([\mathrm{ROH}]\) and \(\alpha\) were found at different temperatures. The values \(K_a\), determined with the aid of (3), are given in Table 2. The temperature dependence has the form:

\[ K_a = 10^{-3.9} \exp [(7500 \pm 1000)/RT]\ \text{l/mole} \tag{5} \]

In pure butanol, nonradioactive methane is formed in the interaction of \(\mathrm{CH}_3^\cdot\) with the methyl groups of the alcohol molecule. Therefore formula (1) for this case is somewhat changed:

\[ \frac{k_{\mathrm{OT}}}{k_{\mathrm{CH}}^{\mathrm{M}}} = \frac{I_{\mathrm{M}}[\mathrm{Cn}] \cdot 9}{I_{\mathrm{sp}}[\mathrm{ROH}]} . \tag{6} \]

Table 2

| \(T\), °C | \multicolumn{3}{c}{\([\mathrm{Sp}]=0.0122\) mol/l; \(I_{\mathrm{Sp}}=(325\pm1)\cdot10^5\)} | \multicolumn{3}{c}{\([\mathrm{Sp}]=0.1215\) mol/l; \(I_{\mathrm{Sp}}=(1367\pm3)\cdot10^3\)} | \(T\), °C | \multicolumn{3}{c}{\([\mathrm{Sp}]=10.62\) mol/l (pure); \(I_{\mathrm{Sp}}=(238\pm1)\cdot10^3\)} |
|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|
| | \(I_M\) | \(\alpha,\%\) | \(\dfrac{k_{OT}}{k_{CH}^{M}}\cdot10^2\) | \(I_M\) | \(\alpha,\%\) | \(K_a\) | | \(I_M\) | \(\alpha,\%\) | \(K_a\) |
| 60.0 | \(378\pm10\) | 83.0 | 8.3 | \(52.5\pm0.5\) | 26.1 | 15.3 | 55.0 | \(186\pm7\) | 0.67 | 12.9 |
| 70.0 | \(491\pm1\) | 85.5 | 10.4 | \(79\pm3\) | 32.7 | 10.7 | 70.0 | \(330\pm15\) | 1.00 | 8.4 |
| 80.0 | \(638\pm4\) | 88.0 | 12.9 | \(107.3\pm0.5\) | 37.3 | 8.6 | 80.0 | \(469\pm10\) | 1.29 | 6.4 |
| 90.0 | \(726\pm2\) | 91.0 | 14.4 | \(159.5\pm1.5\) | 47.2 | 5.4 | 85.0 | \(572\pm10\) | 1.50 | 5.5 |

Here \(k_{CH}^{M}\) is the rate constant of the reaction of \(\mathrm{CH}_3^{\bullet}\) with the C—H bonds of the alcohol, calculated per one bond; 9 is the number of C—H bonds; the remaining notation is the same as in (1). If the ratio \(k_{OT}/k_{CH}^{M}\) is known, the degree of dissociation of the alcohol at different temperatures can be determined. It may be assumed that \(k_{CH}^{M}\) has the same value as the rate constant of the reaction of \(\mathrm{CH}_3^{\bullet}\) with the primary bond of n-heptane \((k_{CH}^{p})\), for which, according to the data of (7), we have:

\[ \frac{k_{CH}}{k_{CH}^{p}}=\frac{k_{CH}}{k_{CH}^{M}}=\exp(1700/RT). \tag{7} \]

From (4) and (7) we obtain:

\[ \frac{k_{OT}}{k_{CH}^{M}}=42\exp(-2400/RT). \tag{8} \]

Table 2 gives the experimental data and the values of the degree of dissociation of the undiluted alcohol at different temperatures, obtained with the aid of (8) and (6). The form of the temperature dependence of the constant is as follows: \(K_a=10^{-3.28}\exp[(6600\pm500)/RT]\) l/mol.

The values of the equilibrium constant and its temperature dependence, found in two different experiments, are close (see (5)).

The thermal effect of association (6.6–7.5 kcal) is somewhat higher than could have been expected for tertiary butanol on the basis of spectroscopic measurements. The entropy change is from 15 to 19 e.u. This is close to the average value \(\Delta S_0\) for reactions involving the disappearance of 1 mole, which for the gas phase, according to the data of (19), is 23 e.u.

Moscow State University
named after M. V. Lomonosov

Received
26 XII 1961

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