Electrical Conductivity and Viscosity of the Systems: Isovaleric Acid-Methyl Alcohol and Acetic Acid-Methyl Alcohol
Abstract Generated abstract
This study examines physicochemical interactions in binary liquid systems of methyl alcohol with isovaleric acid and with acetic acid. Electrical conductivity, density, and viscosity were measured at 0, 25, and 45 °C, and composition dependent curves, temperature coefficients, and viscosity corrected conductivities were used to assess deviations from additive behavior. Both systems show conductivity and viscosity maxima and density deviations consistent with acid base interaction between the acid and alcohol, with methanol acting as the probable base, while associated molecular dissociation also appears to influence the results. The interaction is reported to be more pronounced for acetic acid than for isovaleric acid, in agreement with the greater strength of acetic acid.
Full Text
Electrical Conductivity and Viscosity of the Systems: Isovaleric Acid–Methyl Alcohol and Acetic Acid–Methyl Alcohol
A. S. Naumova
In order to trace, by the method of physicochemical analysis, the relationships between alcohols and organic acids, we began our investigations with the study of systems containing methyl alcohol in mixtures with isovaleric and acetic acids. These latter differ in their strength and other properties.
From the standpoint of the theory of acids and bases of Brønsted [1], Lewis [2], and Usanovich [3], when acids are mixed with alcohols, acid–base interaction is possible, in which the amphoteric alcohol apparently manifests its basic properties.
These systems are also of interest in that, along with chemism, a process of dissociation of associated molecules of both the alcohol and the acid is possible here.
Experimental Part
Isovaleric acid was purified by fractional distillation. For the work, the fraction boiling at 173° and a pressure of 748.4 mm was taken.
Anhydrous acetic acid was subjected to repeated fractional freezing in sealed ampoules. The purified acid had a melting point of 16.5°.
Synthetic methyl alcohol was boiled for five hours over calcium oxide, after which it was subjected to double distillation. The fraction boiling at 64.5° and a pressure of 754.7 mm was collected.
For both systems, electrical conductivity, viscosity, and density were studied at 0, 25, and 45°.
Electrical conductivity was measured by Kohlrausch’s method. Viscosity was determined in a closed viscometer.
System Isovaleric Acid—Methyl Alcohol
When the components were mixed, no noticeable heating was observed. Table 1 gives the data from measurements of specific electrical conductivity, obtained 24 min after preparation of the mixtures. Figure 1 gives a graphical representation of the dependence of electrical conductivity on composition. The figure shows that the isotherms of electrical conductivity pass through a maximum (at 10 mol.% acid), which does not change its abscissa with changing temperature. We calculated the values of the absolute temperature coefficient of electrical conductivity (Table 2), the diagram of which is given in Fig. 2.
From Fig. 11) it is evident that the curve of the temperature coefficient of electrical conductivity passes through a maximum in the region of higher alcohol content.
Fig. 1. Isotherms of the specific electrical conductivity of the isovaleric acid—methyl alcohol system.
Fig. 2. Absolute temperature coefficient of electrical conductivity of the isovaleric acid—methyl alcohol system.
Table 3 gives the density values, the dependence of which on concentration is shown in Fig. 3, where it is shown that the density isotherms are concave toward the composition axis.
The results of viscosity measurements (Table 3) for various compositions are presented in Fig. 4.
Table 1
Specific electrical conductivity
| Mol. % i-C₅H₁₀O₂ | χ · 10⁶, 0° | χ · 10⁶, 25° | χ · 10⁶, 45° |
|---|---|---|---|
| 0.00 | 2.197 | 3.412 | 4.488 |
| 4.92 | 3.127 | 5.006 | 6.886 |
| 7.51 | 3.403 | 5.417 | 7.411 |
| 9.89 | 3.693 | 5.816 | 7.789 |
| 12.00 | 3.478 | 5.610 | 7.549 |
| 14.99 | 3.062 | 4.930 | 6.705 |
| 18.04 | 2.454 | 4.051 | 5.458 |
| 21.99 | 2.008 | 3.301 | 4.449 |
| 25.02 | 1.825 | 3.013 | 4.080 |
| 29.91 | 1.424 | 2.330 | 3.151 |
| 35.13 | 1.115 | 1.823 | 2.482 |
| 43.18 | 0.846 | 1.324 | 1.699 |
| 49.92 | 0.550 | 0.796 | 1.010 |
| 58.06 | 0.273 | 0.357 | 0.418 |
| 65.26 | 0.101 | 0.149 | 0.200 |
Fig. 3. Density isotherms of the isovaleric acid—methyl alcohol system.
1) Since the curves of the temperature coefficient of electrical conductivity, calculated for different temperature intervals, almost coincide with one another, we have given only one of them.
Table 2
Absolute temperature coefficient of electrical conductivity
| Mol.% i-C$_5$H$_{10}$O$_2$ | $\alpha \cdot 10^3$ 0–45 | $\alpha \cdot 10^3$ 0–25 | $\alpha \cdot 10^3$ 25–45 |
|---|---|---|---|
| 0,00 | 5,09 | 4,860 | 5,380 |
| 4,92 | 8,35 | 7,516 | 9,400 |
| 7,51 | 8,91 | 8,176 | 9,820 |
| 9,89 | 9,10 | 8,492 | 9,865 |
| 12,00 | 9,05 | 8,528 | 9,695 |
| 14,99 | 8,10 | 7,472 | 8,875 |
| 18,04 | 6,65 | 6,348 | 7,003 |
| 21,99 | 5,42 | 5,172 | 5,740 |
| 25,02 | 5,01 | 4,752 | 5,335 |
| 29,91 | 3,84 | 3,624 | 4,105 |
| 35,13 | 3,04 | 2,832 | 2,795 |
| 43,18 | 1,90 | 1,912 | 1,875 |
| 49,92 | 1,02 | 0,984 | 1,700 |
| 58,06 | 0,32 | 0,336 | 0,350 |
| 65,26 | 0,22 | 0,192 | 0,255 |
Table 3
| Mol.% i-C$_5$H$_{10}$O$_2$ | Density 0° | Density 25° | Density 45° | Viscosity $\eta \cdot 10^3$ 0° | Viscosity $\eta \cdot 10^3$ 25° | Viscosity $\eta \cdot 10^3$ 45° |
|---|---|---|---|---|---|---|
| 0,00 | 0,8140 | 0,7972 | 0,7805 | 7,894 | 5,582 | 4,295 |
| 5,00 | 0,8329 | 0,8169 | 0,8005 | 9,744 | 6,759 | 4,927 |
| 9,99 | 0,8469 | 0,8351 | 0,8193 | 11,51 | 7,969 | 5,711 |
| 13,00 | 0,8578 | 0,8429 | 0,8283 | — | — | — |
| 14,97 | 0,8633 | 0,8496 | 0,8326 | — | — | — |
| 15,19 | 0,8733 | 0,8587 | 0,8425 | 14,60 | 9,426 | 6,649 |
| 20,05 | 0,8785 | 0,8647 | 0,8484 | 17,07 | 10,89 | 7,581 |
| 26,73 | 0,8892 | 0,8742 | 0,8580 | 20,40 | 12,45 | 8,551 |
| 35,77 | 0,9054 | 0,8897 | 0,8735 | 25,91 | 15,07 | 10,04 |
| 43,18 | 0,9151 | 0,9011 | 0,8841 | 30,82 | 17,29 | 11,33 |
| 49,39 | 0,9219 | 0,9075 | 0,8904 | 33,83 | 18,70 | 12,11 |
| 59,80 | 0,9293 | 0,9136 | 0,8987 | 37,06 | 19,95 | 12,87 |
| 66,47 | 0,9332 | 0,9187 | 0,9033 | 38,97 | 20,88 | 13,48 |
| 75,31 | 0,9379 | 0,9239 | 0,9064 | 39,70 | 21,18 | 13,65 |
| 84,28 | 0,9412 | 0,9269 | 0,9109 | 38,73 | 21,27 | 13,86 |
| 94,89 | 0,9453 | 0,9308 | 0,9145 | 38,01 | 20,90 | 13,77 |
| 100,00 | 0,9464 | 0,9316 | 0,9163 | 37,82 | 20,79 | 13,73 |
It follows from the figure that at 0° the viscosity isotherm passes through a diffuse maximum (about 75 mol.% acid), which, with increasing temperature, becomes still flatter and at higher temperatures apparently disappears altogether.
The relative temperature coefficient of viscosity calculated by us (Table 4) is represented graphically in Fig. 5. The curves for this coefficient (Fig. 5) have a complex form and pass through a maximum and an inflection point.
Table 4
Relative temperature coefficient of viscosity
| Mol. % $i\mathrm{C}_5\mathrm{H}_{10}\mathrm{O}_2$ | $\gamma \cdot 10^3$ 0–45° | $\gamma \cdot 10^3$ 0–25° | $\gamma \cdot 10^3$ 25–45° |
|---|---|---|---|
| 0.00 | 1.862 | 1.657 | 1.497 |
| 5.00 | 2.172 | 1.766 | 1.859 |
| 9.99 | 2.257 | 1.777 | 1.977 |
| 15.19 | 2.657 | 2.194 | 2.088 |
| 20.05 | 2.782 | 2.271 | 2.183 |
| 26.73 | 3.079 | 2.555 | 2.280 |
| 35.77 | 3.512 | 2.879 | 2.504 |
| 43.18 | 3.821 | 3.131 | 2.629 |
| 49.39 | 3.984 | 3.237 | 2.724 |
| 59.80 | 4.176 | 3.430 | 2.750 |
| 66.47 | 4.202 | 3.465 | 2.745 |
| 75.31 | 4.239 | 3.498 | 2.755 |
| 84.38 | 3.988 | 3.283 | 2.673 |
| 94.89 | 3.911 | 3.274 | 2.588 |
| 100.00 | 3.900 | 3.276 | 2.572 |
Fig. 4. Viscosity isotherms of the isovaleric acid—methyl alcohol system.
Fig. 5. Relative temperature coefficient of viscosity of the isovaleric acid—methyl alcohol system.
Acetic acid—methyl alcohol system
The results of measuring the specific electrical conductivity of this system are given in Table 5. The dependence of electrical conductivity on composition is given in Fig. 6. As the figure shows, the conductivity isotherms are convex toward the concentration axis throughout their entire length and pass through a maximum, which, with increasing temperature, shifts toward acetic acid and at 45° occurs at approximately 22 mol. % of it.
One of the curves of the absolute temperature coefficient that we give (the curves for the other temperature intervals almost coincide with this one) [[unclear: sentence continues on next page]]
Table 5
Specific electrical conductivity
| Mol.% C₂H₄O₂ | χ · 10⁵, 0° | χ · 10⁵, 25° | χ · 10⁵, 45° |
|---|---|---|---|
| 0,00 | 0,2197 | 0,3412 | 0,4488 |
| 3,01 | 0,7031 | 1,028 | 1,352 |
| 6,91 | 0,8221 | 1,237 | 1,628 |
| 9,60 | 0,8510 | 1,286 | 1,713 |
| 14,84 | 0,9543 | 1,460 | 1,930 |
| 19,90 | 0,9380 | 1,465 | 1,978 |
| 30,00 | 0,8773 | 1,404 | 1,901 |
| 39,62 | 0,8060 | 1,294 | 1,755 |
| 48,73 | 0,7255 | 1,126 | 1,543 |
| 55,14 | 0,6240 | 1,054 | 1,432 |
| 59,94 | 0,560 | 0,9212 | 1,259 |
| 70,00 | 0,4225 | 0,7040 | 0,957 |
| 78,52 | 0,2804 | 0,4830 | 0,6653 |
| 81,05 | 0,1797 | 0,3220 | 0,4640 |
| 88,04 | 0,1340 | 0,2480 | 0,3684 |
| 95,09 | 0,0346 | 0,0661 | 0,1242 |
| 96,85 | 0,0165 | 0,0400 | 0,0834 |
…of the conductivity coefficient (Table 6, Fig. 7) repeats the course of the specific-conductivity curves.
Table 6
Absolute temperature coefficient of electrical conductivity (C) and viscosity (γ)
| Mol.% C₂H₄O₂ | C · 10⁷, 0—25 | C · 10⁷, 25—45 | C · 10⁷, 0—45 | Mol.% C₂H₄O₂ | γ · 10³, 0—25 | γ · 10³, 25—45 | γ · 10³, 0—45 |
|---|---|---|---|---|---|---|---|
| 0,00 | 0,486 | 0,538 | 0,5091 | 0,00 | 6,25 | 6,43 | 8,00 |
| 3,01 | 1,299 | 1,620 | 1,443 | 10,00 | 11,17 | 8,04 | 9,78 |
| 6,91 | 1,652 | 1,955 | 1,791 | 20,02 | 13,43 | 9,47 | 11,70 |
| 9,60 | 1,740 | 2,135 | 1,916 | 30,10 | 16,62 | 11,17 | 14,20 |
| 14,84 | 2,202 | 2,350 | 2,168 | 42,03 | 20,57 | 13,74 | 17,53 |
| 19,90 | 2,108 | 2,565 | 2,311 | 49,15 | 24,04 | 15,44 | 20,22 |
| 30,00 | 2,106 | 2,485 | 2,275 | 60,06 | 30,44 | 17,88 | 24,86 |
| 39,62 | 1,952 | 2,305 | 2,109 | 69,56 | 31,68 | 18,27 | 25,72 |
| 48,73 | 1,602 | 1,668 | 1,817 | 74,94 | 31,40 | 19,06 | 26,00 |
| 55,14 | 1,720 | 1,890 | 1,790 | 78,93 | 31,40 | 18,73 | 25,77 |
| 59,94 | 1,400 | 1,689 | 1,562 | 88,04 | 30,08 | 17,53 | 24,50 |
| 70,00 | 1,126 | 1,265 | 1,187 | 95,09 | 27,88 | 16,66 | 22,84 |
| 78,52 | 0,801 | 0,9115 | 0,8553 | 100,00 | 21,48 | 14,04 | 18,18 |
| 81,05 | 0,569 | 0,710 | 0,6317 | ||||
| 88,04 | 0,456 | 0,602 | 0,5209 | ||||
| 95,09 | 0,086 | 0,290 | 0,1991 | ||||
| 96,85 | 0,094 | 0,217 | 0,1487 |
* The data obtained in measuring density and viscosity are given in Table 7. Figure 8 shows the viscosity isotherms. It follows from the figure that the dependence of viscosity on composition is represented by curves passing through a maximum, which, with increasing temperature, becomes flatter and shifts toward the more viscous component. At 0° the maximum of the isotherm corresponds to approximately 75 mol.% acid.
Table 7
| Mol. % C₂H₄O₂ | Density, 0° | Density, 25° | Density, 45° | Viscosity, 0° | Viscosity, 25° | Viscosity, 45° |
|---|---|---|---|---|---|---|
| 0.00 | 0.8140 | 0.7972 | 0.7805 | 0.007894 | 0.005582 | 0.004295 |
| 10.00 | 0.8536 | 0.8321 | 0.8205 | 0.009117 | 0.006325 | 0.004717 |
| 20.02 | 0.8893 | 0.8671 | 0.8553 | 0.01157 | 0.007200 | 0.005306 |
| 30.10 | 0.9240 | 0.9007 | 0.8892 | 0.01238 | 0.008226 | 0.005992 |
| 42.03 | 0.9503 | 0.9379 | 0.9247 | 0.01471 | 0.009568 | 0.006821 |
| 49.15 | 0.9787 | 0.9547 | 0.9428 | 0.01660 | 0.01059 | 0.007502 |
| 60.06 | 1.006 | 0.9801 | 0.9634 | 0.01914 | 0.01153 | 0.007955 |
| 69.56 | 1.025 | 1.001 | 0.9881 | 0.02008 | 0.01216 | 0.008505 |
| 74.94 | 1.035 | 1.011 | 0.9967 | 0.02020 | 0.01235 | 0.008538 |
| 78.93 | 1.042 | 1.017 | 1.004 | 0.02037 | 0.01252 | 0.008774 |
| 88.04 | 1.057 | 1.032 | 1.019 | 0.01963 | 0.01211 | 0.008604 |
| 95.09 | 1.067 | 1.041 | 1.028 | 0.01885 | 0.01188 | 0.008548 |
| 100.00 | 1.072 | 1.048 | 1.035 | 0.01605 | 0.01068 | 0.007871 |
The maximum on the curves of the absolute temperature coefficient of viscosity (Table 6, Fig. 9) is expressed more sharply than on the viscosity isotherms.
Fig. 6. Isotherms of the specific electrical conductivity of the acetic acid—methyl alcohol system.
Fig. 7. Absolute temperature coefficient of electrical conductivity of the acetic acid—methyl alcohol system.
Discussion of the Results
From a number of diagrams of the properties studied by us, both systems must be assigned to the irrational type.
Comparing the data obtained in the study of the isovaleric acid—methyl alcohol system, one may come to the conclusion that, upon mixing the acid and the alcohol, an acid–base interaction takes place.
The chemical interaction of the components of the system is indicated by the form of the curves for all the properties studied by us. Thus, the isotherms of electrical conduct-
Fig. 8. Viscosity isotherms of the system acetic acid—methyl alcohol.
Fig. 9. Absolute temperature coefficient of viscosity of the system acetic acid—methyl alcohol.
... of conductivity (Fig. 1) pass through a maximum [4], which is also retained on the curves of corrected electrical conductivity1) (Table 8, Fig. 10), i.e., when the influence of viscosity on electrical conductivity is excluded. This means that the appearance—
Fig. 10. Isotherm of corrected electrical conductivity of the system isovaleric acid—methyl alcohol.
Table 8
Corrected specific electrical conductivity
| Mol.% \(i\)-\(C_5H_{10}O_2\) | \(\chi \cdot \eta \cdot 10^8\), 0° | \(\chi \cdot \eta \cdot 10^8\), 25° | \(\chi \cdot \eta \cdot 10^8\), 45° |
|---|---|---|---|
| 0.00 | 1.734 | 1.904 | 1.925 |
| 4.92 | 3.047 | 3.384 | 3.393 |
| 7.51 | 3.573 | 3.949 | 3.928 |
| 9.89 | 4.210 | 4.420 | 4.352 |
| 12.00 | 4.347 | 4.656 | 4.605 |
| 14.99 | 4.287 | 4.634 | 4.425 |
| 18.09 | 3.758 | 4.011 | 3.930 |
| 21.99 | 3.514 | 3.631 | 3.515 |
| 25.02 | 3.513 | 3.616 | 3.468 |
| 29.91 | 3.168 | 3.145 | 2.930 |
| 35.13 | 2.871 | 2.734 | 2.482 |
| 43.18 | 2.607 | 2.289 | 1.926 |
| 49.92 | 1.897 | 1.489 | 1.242 |
| 58.06 | 1.007 | 0.710 | 0.543 |
| 65.26 | 0.3878 | 0.305 | 0.270 |
—the maximum on the isotherms of electrical conductivity is due to the presence of an electrolyte formed as a result of the interaction of the components
1) In the diagrams of Figs. 10 and 11 only one curve is given, for reasons stated below.
systems [5]. Since the electrical conductivity in the system increases comparatively little, the compound formed is a weak electrolyte.
The character of the density curves, convex with respect to the composition axis, i.e., the considerable positive deviation from its additive values (Fig. 3), indicates that mixing of the components of the system is accompanied by compression, which usually occurs in chemical interaction of substances.
The course of the viscosity isotherms also testifies to the presence of chemical behavior in the system [6]. The maximum in the viscosity diagrams is not very sharply expressed, evidently because the difference in viscosity of the individual components is rather large [6, 8]. The diffuseness of the maximum of the viscosity curves may also be explained by insufficient strength of the compound formed and by the influence, on the behavior of the system, of the process of dissociation of the associated molecules of the components.
It is possible that the complex form of the diagrams of the temperature coefficient of viscosity (Fig. 5), and especially of the corrected electrical conductivity (Fig. 10), is explained not only by the fact that, when the acid and alcohol are mixed, chemical interaction occurs, but also by the fact that, as a result of this interaction, not one but several compounds are formed.
Carboxylic acids, including isovaleric acid, in mixtures with alcohols and other organic substances were studied by L. P. Kulev, B. V. Tronov, and others by the method of electromotive forces [9]. The authors note that isovaleric acid is more capable of complex formation than the other acids they took. They also showed that with certain substances it gives several molecular compounds. It may be that in the present case, too, not one compound is formed, which also causes complication in the course of the curves of the indicated properties.
On the basis of the results obtained by us, one may thus come to the conclusion that the formation of solutions from methyl alcohol and isovaleric acid is accompanied by two simultaneously occurring processes: weak chemical interaction of the components and the dissociation of their associated molecules.
The data obtained for the system acetic acid—methyl alcohol also indicate that acetic acid and methyl alcohol, when mixed, enter into an acid–base interaction in which, as in the first system, the role of the base is in all probability performed by the alcohol.
Here this interaction is expressed more sharply, since acetic acid is stronger than isovaleric acid, and therefore the acidic and basic functions in the present case are expressed to a greater degree.
The electrical conductivity of this system is higher than that of the first (Tables 1 and 5), and with change in concentration it changes comparatively slowly.
The appearance of a maximum on the electrical-conductivity curves can also be explained by the formation in the system of a new electrolyte [4], since this maximum does not disappear when the influence of viscosity on electrical conductivity is excluded (Table 9, Fig. 11). The maximum on the isotherms of corrected electrical conductivity (Fig. 11) has a different abscissa and is still broader.
The form of the viscosity curves obtained for the system acetic acid—methyl alcohol also confirms the presence of chemical interaction in the system [6].
The maximum on the viscosity isotherms is expressed more sharply here. With change in temperature it shifts and is also diffuse. It is possible that in this system, as in the first, several compounds are formed, the appearance of which also accounts for the rather broad maximum both on the isotherms of specific electrical conductivity and of viscosity.
Along with chemical interaction, here, apparently, there also occurs a process of decomposition of the associated molecules of the individual components.
It is possible that, in a different arrangement of the experiment—namely, upon introducing an indifferent solvent into both the first and the second systems—the influence on their behavior of the process of decomposition of associated molecules will be excluded to some extent, and the chemical interaction will be more clearly reflected in the composition–property diagrams [7].
Fig. 11. Isotherm of the corrected electrical conductivity of the acetic acid–methyl alcohol system.
Table 9
Corrected electrical conductivity
| Mol.% C₂H₄O₂ | $\chi \cdot \eta \cdot 10^6$ at 0° | $\chi \cdot \eta \cdot 10^6$ at 25° | $\chi \cdot \eta \cdot 10^6$ at 45° |
|---|---|---|---|
| 0.00 | 0.01734 | 0.01905 | 0.01928 |
| 3.01 | 0.05772 | 0.05963 | 0.05949 |
| 6.91 | 0.07103 | 0.07546 | 0.07489 |
| 9.60 | 0.07735 | 0.08102 | 0.08137 |
| 14.84 | 0.09333 | 0.09811 | 0.09650 |
| 19.90 | 0.09886 | 0.1055 | 0.1048 |
| 30.30 | 0.1086 | 0.1155 | 0.1139 |
| 39.62 | 0.1153 | 0.1210 | 0.1185 |
| 48.73 | 0.1197 | 0.1176 | 0.1142 |
| 55.14 | 0.1129 | 0.1180 | 0.1117 |
| 59.94 | 0.1064 | 0.1062 | 0.1002 |
| 70.00 | 0.08492 | 0.08694 | 0.0823 |
| 78.52 | 0.0572 | 0.06086 | 0.05855 |
| 84.05 | 0.03612 | 0.04015 | 0.04083 |
| 88.04 | 0.0263 | 0.03004 | 0.0317 |
| 95.09 | 0.006523 | 0.007855 | 0.01062 |
| 96.85 | 0.002937 | 0.00460 | 0.006847 |
Conclusions
-
At 0, 25, and 45° the electrical conductivity, density, and viscosity of systems containing methyl alcohol mixed with isovaleric and acetic acids were studied.
-
On the basis of the data obtained, the presence of acid–base interaction between the components of both systems was established.
-
The chemical interaction in the acetic acid–methyl alcohol system is more vigorous than in the system containing the same alcohol but the weaker isovaleric acid.
LITERATURE
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- G. N. Lewis, I. Franke, Inst., 226, 293, 1938.
- Usanovich M. Zhurn. obshchei khimii, 9, 182, 1939.
- I. Kendall and R. M. Gross, I. Am. Soc. 43, 1426, 1921.
- Usanovich M. Zhurn. obshchei khimii, 11, 959, 1940.
- Kurnakov N. S. Introduction to Physicochemical Analysis, Moscow–Leningrad, p. 326, 1940.
- Udovenko V. V. and Airapetova R. P. Zhurn. obshchei khimii, 9, 1796, 1939; Kurnakov and Kvyat. ZhRKhO, 46, 1372, 1914; Kremann, Mechanische Eigenschaften flüssiger Stoffe, S. 298, Leipzig, 1928.
- Sakhanov A. N. and Ryakhovskii N. A. ZhRKhO, 47, 113, 1915.
- Tronov B. V. and Kulev L. P. Izv. Tomsk. politekhnich. in-ta im. S. M. Kirova, 64, 3, 1948.