Physical Chemistry

I. B. Rabinovich and P. N. Nikolaev

Isotope Effect in the Heat Capacity of Some Deuterium Compounds

(Presented by Academician A. N. Frumkin, September 2, 1961)

We have previously studied the effect of replacing hydrogen by deuterium on the density \((\rho)\), the velocity of ultrasound, and the adiabatic compressibility \((\beta_{\mathrm{ad}})\) of a number of liquids \((^{1-3})\). In the present work we measured the heat capacity at constant pressure \((c_p)\) and, using data on the magnitude of \(\beta_{\mathrm{ad}}\) and the coefficient of thermal expansion \((\alpha)\), calculated the heat capacity at constant volume \((c_v)\), the isothermal compressibility \((\beta_{\mathrm{is}})\), the ratio \((\gamma)\), and the difference \((c_p - c_v)\) of heat capacities as functions of temperature for the following liquid isotopic substances: \(C_6D_6\), \(C_6H_6\); \(C_2H_5OD\), \(C_2H_5OH\); \(CH_2OD \cdot CH_2OD\), \(CH_2OH \cdot CH_2OH\); \(CH_2OD \cdot CHOD \cdot CH_2OD\), \(CH_2OH \cdot CHOH \cdot CH_2OH\).

The aim was to study the influence of isotopy on the heat capacity \(c_v\), which until now had been done experimentally only for heavy water \((^4)\). Values of \(\beta_{\mathrm{is}}\) were also necessary for judging the influence of replacing hydrogen by deuterium on intermolecular interaction. In addition, comparison of identical thermodynamic properties of ordinary ethyl alcohol, ethylene glycol, and glycerol was of independent interest.

The synthesis of the deuterium compounds is described in papers \((^{1-3})\). The hydroxyl groups of the alcohols contained 97–98 at.% deuterium, and benzene 80%. All substances used were thoroughly purified, in particular dehydrated. Their densities and refractive indices corresponded to literature data \((^{5,6})\). For heat-capacity measurements an adiabatic calorimeter of S. M. Skuratov’s design \((^7)\) was used. Some improvements introduced by us and the procedure are described in \((^8)\). The error of an individual measurement of \(c_p\) was 0.3%. Table 1 gives graphically averaged values of \(c_p\), whose error is 0.1%. These data were used to calculate other properties. The isothermal compressibility was calculated from the formula

\[ \beta_{\mathrm{is}} = \beta_{\mathrm{ad}} + \frac{\alpha^2 T M}{c_p \rho}, \tag{1} \]

with an accuracy of 0.3–0.5%. The values of \(\rho\) and \(\beta_{\mathrm{ad}}\) for all substances except ethylene glycol were taken from work \((^1)\). For the latter these quantities were determined by one of us and L. S. Zhilkin.* The value of \(\alpha\) was calculated graphically from the density, with an accuracy of about 0.5%. Within this error the values of \(\alpha\) for isotopic substances are identical. The values of \(c_v\) given in Table 1 were calculated from the formula

\[ c_v = c_p \beta_{\mathrm{ad}} / \beta_{\mathrm{is}}, \tag{2} \]

with an accuracy of 0.6–0.8%; for calculating the isotope effect in the value of \(c_v\), graphically averaged values of it were taken. For the quantity \(\gamma\) the error is about 0.5%; for \((c_D / c_H)_v\) and \(\gamma_D / \gamma_H\), about 1%. For benzene, Table 1 gives data referring to a content of 100 at.% deuterium. The corresponding extrapolation was made on the basis of additivity of the isotope effect. Our values of \(c_p\) for ordinary benzene agree within 0.3% with the results of the averaging of several works carried out in \((^{10})\). Therefore, and since the purity of the pri—

* The values of \(\beta_{\mathrm{ad}}\) for ethylene glycol, determined from the velocity of ultrasound, are not given here, since they can be found by inverse calculation from the corresponding values of \(c_p\), \(c_v\), and \(\beta_{\mathrm{is}}\) (Table 1). Our density values for the same alcohol agree, to an accuracy of \(1 \cdot 10^{-4}\ \mathrm{g/cm^3}\), with the data of \((^9)\).

Table 1

Heat capacities and isothermal compressibilities

the changing deutero-benzene and the deuterium content in it raise no doubt; we believe that the data in Table 1 for $C_p$ ($\mathrm{C_6D_6}$) are reliable to within a few tenths of a percent. Then the corresponding data of Ziegler and Andrews ($^{10}$) are low by approximately 2%.*

For the deuterium compounds studied by us, the heat capacity $c_v$ is considerably greater than for the corresponding ordinary substances (Table 1). Earlier ($^4$) it was also established that $c_v(\mathrm{D_2O}) > c_v(\mathrm{H_2O})$. Qualitatively this can be explained as follows. When a light isotope is replaced by a heavy one, the component of the heat capacity due to translational motion becomes larger as a result of the increase in molecular mass; the rotational component also increases because of the increase in the moments of inertia, while the vibrational components increase because of the decrease in the frequencies of molecular and atomic vibrations. Since, upon replacement by deuterium of hydrogen forming a hydrogen bond, the dissociation energy of the latter and the degree of association increase ($^{11}$), the associative component of the heat capacity should probably also increase in this case.

The isotopic difference in heat capacity, $100[(c_D/c_H)_v-1]$, for glycerol and ethylene glycol has similar values: 6.0—

* Our data on the value of $c_p$ of ordinary alcohols are smaller than some and larger than other corresponding data in the literature ($^{12,9,5}$) by 0.5–1.5%.

—7.5 and 5.5–8.0, respectively (Fig. 1). This corresponds to the fact that, for both substances, deuteration in the hydroxyl groups is associated with an almost identical relative increase in molecular weight (3.25%) and with approximately the same fraction of atomic bonds at which isotopic substitution occurs (in glycerol, at 3 bonds out of 13; in glycol, at 2 out of 9). For \( \mathrm{C_2H_5OD} \), relative to \( \mathrm{C_2H_5OH} \), the value of \( c_v \) is greater by 4.5–4.0%, but this is associated with an increase in molecular weight of only 2.18% and isotopic substitution at one bond out of 8. For \( \mathrm{C_6D_6} \), the heat capacity \( c_v \) is 20–18% (between 10 and 30°C) greater than the heat capacity of \( \mathrm{C_6H_6} \); however, in this case the molecular weights differ by 7.73%, and isotopic substitution occurs at 6 bonds out of 15. Judging from the data described, the component of the heat capacity due to association is probably not the determining factor for the isotopic difference in the value of \( c_v \) of the alcohols studied.

Fig. 1. Ratio of heat capacities at constant volume of isotopic compounds:
1 — \( \mathrm{C_6D_6/C_6H_6} \);
2 — \( \mathrm{CH_2OD \cdot CHOD \cdot CH_2OD/CH_2OH \cdot CHOH \cdot CH_2OH} \);
3 — \( \mathrm{CH_2OD \cdot CH_2OD/CH_2OH \cdot CH_2OH} \);
4 — \( \mathrm{C_2H_5OD/C_2H_5OH} \).

The following feature is observed in the temperature dependence of the isotopic effect (Fig. 1). With increasing temperature the ratio \((c_{\mathrm D}/c_{\mathrm H})_v\) for benzene decreases distinctly; for ethyl alcohol it decreases, but within the limits of error; for ethylene glycol and glycerol, on the contrary, it increases somewhat. Possibly this means that in the interval 10–55°C, with increasing temperature, the role of the heat-capacity component determined by the energy of rupture of hydrogen bonds increases; this component is larger in deuterated alcohols than in ordinary ones \((^{11})\). However, the same feature may also be caused by an increase in another component of the heat capacity, in particular the vibrational one \((c_E)\), or by the character of the temperature dependence of the derivative \( \partial c_E/\partial \nu \), where \( \nu \) is the frequency of vibrations. An increase in the ratio \((c_{\mathrm D}/c_{\mathrm H})_p\) with increasing temperature was established earlier for methyl alcohol \((^{13})\) in the interval 90–150°K (solid state) and 180–270°K (liquid), for ice \((^{14})\) between 60 and 200°K, and for solid benzene \((^{10})\) in the interval 100–250°K.

It is of interest to compare the isothermal compressibility of the three alcohols studied. At 25°C, for example, its values for ethyl alcohol, ethylene glycol, and glycerol are related as 4.75 : 1.5 : 1, respectively. The increase in \( \beta_{\mathrm{is}} \) between 15 and 55°C is 32.5, 15.5, and 13.5%, respectively. Such a sharp difference in the behavior of ethyl alcohol, on the one hand, and ethylene glycol and glycerol, on the other, should, of course, be attributed to differences in intermolecular interaction, as well as to structural factors of these substances, especially in the temperature range studied.

Replacement of hydrogen by deuterium in the substances investigated causes an increase in isothermal compressibility by 0.5–1.5%. Since the accuracy of the values of \( \beta_{\mathrm{is}} \) is a few tenths of a percent, the direction of the isotopic effect in this quantity is beyond doubt. It has the same sign as the isotopic effect in adiabatic compressibility, but is smaller than the latter—the difference in the value of \( \beta_{\mathrm{ad}} \) at 20°C for \( \mathrm{C_6D_6} \) and \( \mathrm{C_6H_6} \) is 6%, while for the corresponding deuterated and ordinary alcohols it is 1.5–2%. According to the calculation made in \((^{1})\), at 20°C \( \beta_{\mathrm{is}}(\mathrm{D_2O}) \) is greater than \( \beta_{\mathrm{is}}(\mathrm{H_2O}) \) by 3%, and \( \beta_{\mathrm{ad}}(\mathrm{D_2O}) \) is greater than \( \beta_{\mathrm{ad}}(\mathrm{H_2O}) \) by 4%.

Owing to the identity of the composition and structure of the molecule and of the types of intermolecular forces, apparently, in the region of moderate temperatures the structure of isotopic substances in the liquid phase is the same for the heavy and ordinary versions.

water has been shown experimentally \(^{(15)}\). Therefore the isotopic difference in compressibility should be explained by the difference in intermolecular interaction. For benzene this means that replacement of hydrogen by deuterium causes a weakening of the dispersion interaction of the molecules. This agrees with the data \(^{(6,17)}\). Since the energy of association by means of a hydrogen bond increases when the hydrogen forming it is replaced by deuterium \(^{(11)}\), for ethanol the increase in compressibility as a result of the indicated isotopic substitution must be explained by a weakening of the dispersion interaction of the associates. This corresponds to the opinion of V. V. Tarasov \(^{(16)}\) concerning the compressibility of monohydric alcohols. For glycerin and ethylene glycol we explain the relation \(\beta_{\mathrm{D}} > \beta_{\mathrm{H}}\) by the fact that replacement of hydrogen by deuterium in the hydroxyl groups causes an increase in the degree of order of the spatial molecular network (a decrease in the number of broken hydrogen bonds), which corresponds to a certain decrease in the density of the distribution of molecules and an increase in the molecular volume \(^{(1)}\).

Fig. 2. Ratio of heat capacity at constant pressure to heat capacity at constant volume:
1 — \(\mathrm{C_6H_6}\); 2 — \(\mathrm{C_6D_6}\); 3 — \(\mathrm{C_2H_5OH}\); 4 — \(\mathrm{C_2H_5OD}\); 5 — \(\mathrm{CH_2OH \cdot CH_2OH}\); 6 — \(\mathrm{CH_2OD \cdot CH_2OD}\); 7 — \(\mathrm{CH_2OH \cdot CHOH \cdot CH_2OH}\); 8 — \(\mathrm{CH_2OD \cdot CHOD \cdot CH_2OD}\).

For glycerin a peculiarity is observed in the temperature dependence of \(\gamma\). For benzene this quantity decreases by approximately 4% in the interval \(10 \div 30^\circ\mathrm{C}\); for ethyl alcohol, between 15 and \(55^\circ\), it increases by 1.5%; for ethylene glycol its change is within the limits of error, while for glycerin the same quantity in the interval \(10 \div 55^\circ\) increases by 2% (Fig. 2). This is connected with the difference in the temperature dependence of the quantities \(c_v\) and \((c_p - c_v)\). For benzene the first of these increases, while the second decreases with increasing temperature; for ethylene glycol both quantities increase at approximately the same rate; for ethyl alcohol \(c_v\) increases faster than \((c_p - c_v)\), while for glycerin the opposite takes place (Table 1).

In connection with the dependences set forth above, the influence of replacing hydrogen by deuterium on the heat capacity \(c_p\) is qualitatively analogous to its influence on the quantity \(c_v\), but for \(c_p\) the isotopic effect is smaller.

Research Institute of Chemistry
at Gorky State University
named after N. I. Lobachevsky

Received
21 VII 1961

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