THERMOELECTRIC METHOD O F MEASURING VAPOR PRESSURE
359
T H E THERMOELECTRIC METHOD OF MEASURING VAPOR PRESSURE' RAYMOND R. ROEPKE' Division of Physics and Biophysical Research, Mayo Foundation, Rochester, Minnesota, and Department of Physiology, University of Minnesota, Minneapolis, Minnesota
Received October I, 1941
The primary purpose of this paper is to acquaint physical chemists with the sensitivity and accuracy of Baldes' (1, 2, 3) modification of the thermoelectric method of measuring vapor pressure or of comparing differences in the vapor pressure of solutions. The method is one in which the difference in temperature of a drop of a reference or known solution and a drop of the unknown solution suspended in an humidified chamber is compared, by means of a thermocouple and a sensitive galvanometer, with the difference in temperature of drops of two reference solutions. Other conditions being equal, the difference in temperature of the two drops suspended in the humidified chamber is proportional to the difference in the rate of evaporation from, or condensation on, the drops, which in 'turn is proportional to the difference in vapor pressure of the drops (3). The apparatus consists essentially of tR.0 thermocouples (permitting duplicate determinations) placed a t right angles to each other, the thermojunctions being in the form of horizontal loops. The thermocouples are mounted in a watertight chamber suspended in a water bath and are connected to a sensitive galvanometer through double-pole, double-throw switches. The procedure consists in placing a reference solution, in the form of a small drop, on one of the loops of each thermocouple and the unknown solution on the opposite loop, the filter paper on the wall and floor of the chamber being moistened also with the reference solution or a solution of approximately the same vapor pressure. The deflection of the galvanometer to which the thermocouples are connected is proportional to the difference in vapor pressures of the two solutions and is calibrated by using two reference solutions, that is, solutions of known vapor pressures. Although the thermoelectric method is a dynamic method of comparing vapor pressures, its accuracy and sensitivity have been found to be comparable to that of the sensitive static method recently described by Chandler. The dynamic method recently described by Bechtold and Xewton has a sensitivity less than one-tenth that of the thermoelectric method of Baldes. Since the thermoelectric method is a method of comparing the vapor pressures of two solutions, the accuracy with which the vapor pressure of a solution can be determined will depend on the accuracy with which the vapor pressure of the reference solution is known. However, if the vapor pressures of solutions of a suitable solute have been determined accurately by a direct method such as Presented before the Division of Physical and Inorganic Chemistry a t the 102nd Meeting of the American Chemical Society, held in Atlantic City, Kew Jersey, September 8-12, 1941. Former Fellow in Biophysics, Mayo Foundation, Rochester, Minnesota.
360
RAYMOND R. ROEPKE
that described by Fraeer and Lovelace or more recently by Chandler, the thermoelectric method may be used in conjunction with these solutions of known vapor pressures to determine the vapor pressures of other solutions with comparable accuracy. The vapor-pressure lowering versus concentration curve of the reference solute should be linear in the region in which it is used. As indicated by the work of Fraeer, Lovelace, and Rogers, mannite should prove suitable for use as the reference solute up to the limit of its solubility, Le., about 0.8 M . The thermocouple unit designed by Baldes replaces the more complicated and less accurate thermopile used in the original method devised by Hill. The modified thermoelectric method has been described in some detail by Baldes and Johnson and has been subjected to a critical study by Baldes and the author (13). This method has been used in osmotic studies on biologic fluids (6, 7, 9, 14, 16), TABLE 1 The determination of the vapor-pressure lowering or osmotic activity of solutions of sodium chloride at db'C., using 0.0208 molal sucrose as the reference solulion 0.00226 II NaCl
0.01086 Y NaCl
Vapor gessure lowering, 111 mm of HE
Osmotic activity, n mM of sucrosc kilogram of H T
Vapor pressure lowering in mm. of
k3
Ommdtic activity. n mM of sucrose kilogram of H Z
Da
0.00185 0.00190 0.00195 0.00182 0.00184 0.00190 0,00188 0.00188
4.42 4.55 4.67 4.36 4.40 4.54 4.50 4.50
0.00874 0.00885 0.00887 O.M)890 0.00872 0.00879 0.00870 0.00889
20.91 21.18 21.23 21.29 20.86 21.03 20.83 21.27
Average., . . . . . . , . Probable error.., .
0.00188 O.oooO1
A1 A1
Bi BI
c1 C2
Di
I
4.49 0.02
~
0.00881 o.oooo2
~
21 .os 0.04
in the determination of the molecular weight of inulin (19), and in the study of micelle formation in aqueous solutions of bile salts (15). In order to demonstrate the sensitivity of the modified thermoelectric method, the vapor-pressure lowerings of 0.00226 M (molal) and of 0.01086 M sodium chloride were compared with that of 0.0292 M sucrose, using four different thermocouple units (eight thermocouples). The results are given in table 1. The vapor-pressure lowerings of the solutions of sodium chloride are calculated on the basis that the vapor-pressure lowering of the 0.0292 M sucrose solution at 25OC. is 0.0122 mm. of mercury, as obtained from the data given in the International Critical Tables (18). In these determinations, the Vapor pressures of the salt solutions were compared with that of water, and the galvanometer deflection was calibrated by comparing water with the reference sucrose solution, with water on the wall of the chamber. For many purposes it is most convenient to express the results in terms of the concentration of the reference solute.
THERMOELECTRIC
METHOD OF MEASURING VAPOR PRESSURE
361
Thus a solution with an osmotic activity or equivalent vapor-pressure lowering of 10.0 mM sucrose is one which has a vapor pressure equivalent to that of a solution containing 10.0 millimoles of sucrose per kilogram of water. Although results such as those given in table 1 are obtained only under favorable conditions, they serve to illustrate the possibilities of the thermoelectric method of Baldes. In a series of experiments on solutions containing 25 per cent of egg albumin and different quantities of electrolytes, the difference in osmotic activities between two solutions of the protein was measured with three double units (six thermocouples). In fourteen different experiments in which the osmotic activity of the two solutions differed by approximately 35 mM of sucrose per kilogram of water, the “probable error” of the average of the six values in each experiment was calculated to be from 0.04 to 0.20 mM of sucrose with an average of 0.13 mM of sucrose. Even an error of 0.20 mM of sucrose would correspond to an error of only 0.00008 mm. of mercury in the vapor pressure (at 25’C.), to an error of 0.000003 in the relative activity of the water in the solution, to 3.4 mm. of mercury in the osmotic pressure, or to 0.0003’C. in the freezing-point lowering. While the sensitivity of the thermoelectric method is equal to that of the static method of Chandler, it does not necessarily follow that the method has a comparable accuracy, that is, a constant or consistent error may be involved in the determinations. However, a few simple experiments will suffice to show the accuracy which may be expected under the particular conditions under which the method is to be used, or, conversely, the conditions under which the method must be used in order to obtain the desired accuracy. Of primary importance is the effect of surface films and of differences in the non-solvent volume and in the coefficient of diffusion of water in the solutions being compared on the accuracy of the results. In other words, it is important to determine the error introduced by virtue of the dynamic nature of the method. This may be done by comparing the unknown solution with an isosmotic reference solution, first under static conditions (with the isosmotic solution also on the wall of the chamber) and then under dynamic conditions (with a hyposmotic or a hyperosmotic solution on the wall). This has been done by Baldes and the author, and it was found that even with such viscous mixtures as hemolyzed blood cells, containing 35 per cent of dry solid*, and egg yolk, containing 55 per cent of dry solids, the error involved when the determination is made under dynamic conditions amounts only to less than 2 per cent of the difference in vapor pressure between the unknown solution and the solution on the wall of the chamber. The vapor pressures of such solutions may still be determined with an accuracy comparable to the sensitivity of the method, either by making the comparison with a reference solution the vapor pressure of which does not differ greatly from that of the unknown or by determining the error and introducing a correction in the calculation, as explained by Baldes and the author (13). While it has been found that films of oleic acid or of the surface-active substances present in biologic fluids do not affect the accuracy of the thermoelectric method of Baldes significantly, it is possible that some substances may form
362
RAYMOND R. ROEPKE
such compact films that they will decrease the accuracy of the method appreciably. For example, Sklyarenko and Baranev found that while oleic, lauric, and palmitic acids do not affect the rate of evaporation of water when air is bubbled through a solution, the presence of cetyl alcohol decreases the rate of evaporation to 5 to 8 per cent of normal. It should also be noted that the error due to a high non-solvent volume, to a high viscosity, and so forth, is dependent on the total osmotic activity of the sample as well as on the difference in osmotic activity between the sample and the solution on the wall of the chamber. Balded equations (3) show that the rate of evaporation of water from, or condensation on, a drop of solution placed on a thermocouple junction varies in direct proportion to its radius. However, although an increase in the size of the drop of higher vapor pressure results in an increase in the rate of evaporation of water from the drop, this does not result in a significant, direct effect on its TABLE 2 The comparison of small drops of water with large drops of water on the thermoekctn'c units when the wall of the chamber is moistened w'th 0.164 molal sodium chloride TBEPYCCOUPLE
GALVANOYEIEP
D U ~ O N ,IN YY.
APPAPBI+ DIYFEPENCE IN OSUOTIC ACIIVITY, IN YM OF NaC1 PEP XILOGMU or W A ~
-0.5: -4.5 -6.4
-0.1'
-2.3 -1.0 -4.0
-0.6 -0.2
Average
-0.9 -1.6
-1.0
-0.7
* A negative value indicates that the larger drop has the lower temperature and hence an apparently lower osmotic activity or higher vapor pressure.
temperature, as is often suggested, since the rate at which heat is transferred to the drop (by radiation, conduction, and convection) is similarly dependent on its size. Such a conclusion is indicated by the results of Balded theoretical considerations (3) of the method and can be demonstrated by a simple experiment. The results of such an experiment are given in table 2. Small drops of water were compared, on the thermocouple, with large drops of water with 154 mM sodium chloride on the wall of the chamber. The drops were as large or as small as could be retained by the thermocouple loops in an approximately spherical form. The ratio of the diameters was about 1:1.5 (volumes = 1:3.4). The large variation in the results obtained with the different thermocouples in this experiment is due to the great difference in vapor pressure between the drops and the solution on the wall of the chamber. This is another reason for using on the wall of the chamber a solution which does not differ appreciably in vapor pressure from the solutions being compared on the thermocouple unit. The results given in table 2 show that even with the greatest possible differ-
THERMOELECTRIC METHOD OF MEASURING VAPOE PRESSURE
363
ence in the size of the drops on the thermocouple, the effect on the temperature of the drops is not appreciable. The diffcrence in temperature corresponds to an error of only 0.5 per cent of the difference in osmotic activity between the drops and the solution on the wall of the chamber, even though the rate of evaporation of water from the larger drop is 50 per cent greater than that from the smaller drop. Thus, one is not justified in referring to the modified thermoelectric method as a method of comparing vapor pressures by comparing rates of evaporation from, or condensation on, drops of the solutions placed on the thermocouple units. The difference in temperature of the drops is essentially a measure of their diffcrence in vapor pressure or osmotic activity and is a measure of the difference in the rate of evaporation from, or condensation on, the drops only if the drops are of a uniform size. Since the comparison of osmotic activities is made with solutions differing in osmotic activity by 20 mM sodium chloride or less, it is not necessary under ordinary conditions, with dilute solutions, that the drops be of exactly the same size. The thermoelectric method is not applicable, of course, to the study of solutions of volatile solutes. However, the presence of a small amount of a volatile solute in the solution will not interfere with the determination of osmotic activity if the osmotic activity contributed by the volatile solute is negligible, since a volatile solute rapidly evaporates from the drop. For example, if one of two portions of an aqueous solution is saturated with ether and drops of the two portions are compared on the thermocouple, the galvanometer deflection will become constant and will indicate zero difference in osmotic activity within 25 or 30 min. The same is true of aqueous solutions containing an excess of heavy water. If a drop of ordinary water is compared on the thermocouple with a drop of 5 per cent solution of deuterium oxide in water, the galvanometer deflection within 5 min. will indicate a lower vapor pressure of the solution of deuterium oxide, corresponding to a difference in osmotic activity of about 100 mM sodium chloride. However, the deflection will decrease gradually until, in approximately 40 or 45 min., it will indicate zero difference in vapor pressure. Thus, while the net movement of water between the drop and its surroundings is small, there is a relatively rapid interchange of water molecules. In the study of solutions in which a high degree of accuracy is desired, the drops may take up sufficient carbon dioxide from the atmosphere to introduce a significant error unless the solutions are sufficiently acid or the activity of the carbon dioxide taken up by the unknown solution is equal to the activity of that taken up by the reference solution. However, the carbon dioxide may be removed from the air in the chamber by wetting the filter paper lining the wall of the chamber with a slightly alkaline solution which has a vapor pressure equal to that of the reference solution. In cases in which a high degree of accuracy is desired and in which the vapoi pressure of the unknown solution differs appreciably from that of the reference solution, it is necessary to correct for any change in the sensitivity of the galvanometer which might occur between the time the apparatus is calibrated and the time the unknown solutions are compared. Although this may be done by
364
RAYMOND R . ROEPKE
frequently checking the galvanometer sensitivity, using the auxiliary circuit described by Baldes and Johnson (4),a more convenient procedure is to use an even number of thermocouple units and reverse the order in which the solutions are compared on each of the units. For example, if two units are used, on the first unit the unknown solution is compared with the reference solution, followed by the calibration with the two reference solutions. On the second unit, the galvahometer deflection is first calibrated by comparing the two reference solutions, and this calibration is followed by the comparison of the unknown with the reference solution. Thus if the sensitivity of the galvanometer decreases during the course of the determination, the value for the difference in vapor pressure between the unknown and reference solution obtained with the first thermocouple unit will be too high, whereas the value obtained with the second unit will be too low by an equal amount. Thus the error may be eliminated by averaging the values obtained with the two units. Owing to the effect of pressure on the thermal conductivity of air and on the coefficient of diffusion of water vapor through air, a decrease in atmospheric pressure or in the pressure within the chamber will result in an increase in the difference in temperature of the drops on the thermocouple. Calculations by means of equation G of Baldes (3) indicate that a decrease in pressure of 10 mm. of mercury (from 745 to 735 mm.) w-ould result in an increase of 0.38 per cent in the galvanometer deflection at 20OC. Thus if a high degree of accuracy is desired, it is necessary that due consideration be given to possible changes in atmospheric pressure between the time the apparatus is calibrated and the time the unknown solutions are compared. The procedure just described to eliminate errors due to changes in the sensitivitv of the galvanometer will also eliminate errors due to sudden changes in atmospheric pressure. The effect of pressure on the difference in temperature of the tx-0 drops on the thermocouple decreases 11-ith increase in temperature. For example, at 0°C. the galvanometer deflection obtained by comparing two salt solutions on the thermocouple is increased approximately 150 per cent by evacuation of the chamber, whereas at 29.4OC. the deflection is increased only 27 per cent by evacuation to approximately the same extent. Where a high degree of accuracy is not essential or where the unknown solutions are compared with reference solutions of approximately the same vapor pressure, it is not likely that changes in atmospheric pressure will introduce a significant error. In such cases, a single calibration of a thermocouple unit may serve for a number of determinations if corrections are introduced to take care of significant rhanges in the sensitivity of the galvanometer. The sensitivity of the thermoelectric method is dependent to a certain estent on the temperature. For esample, two salt solutions, when placed on opposite loops of a thermocouple, result in a galvanometer deflection at 0°C. which is about four-tenths of the deflertion at 25OC. Thus a given difference in concentration or osmotic activity of the two solutions will result in a greater deflection of the galvanometer as the temperature is increased, whereas a given difference in vapor pressure will result in a smaller deflertion as the temperature is increased.
THERMOELECTRIC METHOD O F MEASURING VAPOR PRESSURE
365
In comparing the vapor pressures of two solutions a t 2kioC., a change in the temperature of the water bath of 0.1'C. will result in a change in the deflection of the galvanometer of only 0.2 per rent. From this fact one might be led to conclude that it iq not necessary to rontrol carefully the temperature of the water bath. However, in attempting to measure or compare the vapor pressures of solutions with a high degree of precision, one must take into account the fact that it is necessary to measure very small differences in temperature of the two drops and hence very small electromotive forces in the thermoelectric circuit. A difference in osmotic activity of 1.0 mM of sucrose per kilogram of water will result in a differencein temperature of the two drops of approximately 0.00025°C. (at 25OC.), which would produce an electromotive force in the thermocouple of approximately 0 01 microvolt (with a constantan-manganin couple). Since one may be interested in measuring differences in temperature of the two drops to within 0.OO0loC. or less, it is important that the water bath be well stirred in order that any variation in the temperature of the water bath will take place uniformly or symmetrically with respect to opposite junctions of the thermocouple. In order to reduce extraneous electromotive forces to a minimum, it is advisable to use switches and lead wires constructed of copper only. However, any error due to extraneous electromotive forces can he eliminated by reversing the order of the solutions on the thermojunctions and averaging the two readings, providing the extraneous electromotive forces remain constant during the time necessary to replace the drops and take a second reading (4). In addition to having a high sensitivity and accuracy, the modified thermoelectric method of Baldes is a relatively rapid method and requires only a small volume of sample. If one thermocouple unit is used, a complete determination of vapor pressure, including the calibration with the reference solution, requires about 2 hr.; if four units (eight thermocouples) are used, eight determinations may be made in 3 hr. or less, only a fraction of a cubic centimeter of sample being required. The method may be used over a relatively wide range of temperatures and with solutions of volatile organic solvents as well aa aqueous solutions. The method may be used also in the case of solutions which have a very high viscosity. Since the thermoelectric method may be employed essentially aa a static method, by using as the reference solution one which differs only slightly in vapor pressure from the unknown solution, the chief limitations on the accuracy of the method which have been noted are the presence of volatile solutes and the occurrence of thermochemical reactions in the sample (13). SUMMARY
Data are presented to show the sensitivity which may be obtained with Baldes' modification of the thermoelectric method of measuring vapor pressures. Attention is called to a number of factors which must be taken into consideration in order to obtain an accuracy comparable to the sensitivity of the method. Evidence is presented to show that the temperature of a drop of solution placed on a thermocouple loop is, for practical purposes, independent of its size.
366
CECIL C. LYNCH
REFERENCES
(1) BALDES,E. J.: J. Sci. Instruments 11, 223 (1934). (2) BALDES,E. J.: Thesis, University of London, June, 1936. (3) BALDES,E. J.: Biodynamioa, No. 46 (1939). A. F.: Biodynamica, No. 47 (1939). (4) BALDES,E.J., AND JOHNSON, M. F.,AND NEWTON, R. F.: J. Am. Chem. SOC.82,1390 (1940). (5) BECHTOLD, H . , AND DUKE-ELDER, W. 9.: J. Physiol. 89, 61 (1937). (6) BENHAN,G. H., DAVSON, (7) BENHAM, G.H., DUKE-ELDER, W. S., AND HODQSON, T. H.: J. Physiol. 92, 355 (1938). R. C.: J. Phys. Chem. 44,574 (1940). (8) CHANDLER, (9) Fox, H . M.,AND BALDES,E. J.: J. Exptl. Biol. 12, 174 (1935). J. C., AND LOVELACE, B. F.: J. Am. Chem. Soo. 38, 2439 (1914). (10) FRAZER, (11) FRAZER, J. C., LOVELACE, B. F., AND ROGERS,T. H.: J. Am. Chem. SOC.43, 1793 (1920). (12) HILL,A. V.: Proc. Roy. SOC.(London) Al27, 9 (1930). E. J.: J. Biol. Chem. 128,349 (1938). (13) ROEPKE,R. R., AND BALDES, W. A.: Am. J. Physiol. 130, 340 (1940). (14) ROEPKE,R. R., AND HETHERINGTON, (15) ROEPKE,R. R., AND MASON,H . L.: J. Biol. Chem. 133, 103 (1940). (16) ROEPKE,R. R., AND VISSCHER,M. B.: Proo. SOC.Exptl. Biol. Med. 41, 500 (1939). S. I., AND BARANEV, M. K.: J. Phys. Chem. (U. S. S. R.) 12, 271 (1938); (17) SKLYARENKO, Chem. Abstracts 33, 4846 (1939). E. W.:International Critical Tables of Numerical Data, Physics, Chemistry (18) WASHBURN, and Technology, Vol. 3,p. 292. McGraw-Hill Book Company, Inc., New York (1928). (19) WESTFALL, B. B., AND LANDIS, E. M.: J. Biol. Chem. 118, 727 (1936).
T H E TERNARY SYSTEM LITHIUM CHLORIDE-DIOXANE-WATER CECIL C. LYNCH
Department of Chemistry, Univeraty of Delaware, Newark, Delaware Received October 10, 1941
In connection with a study of potentiometric titration in dioxane-water mixtures (4), a preliminary investigation on the solubility of lithium chloride in such mixtures indicated that this system offered an interesting problem. In view of such observations, a study of the phase relations of the 25OC. isotherm in the lithium chloride-dioxane-water system has been made and is here presented. PREPARATION OF MATERIALS
Dioxane: Technical 1,4-dioxane from the Eastman Kodak Company was purified by the method described by Eigenberger (2). The product was kept over metallic sodium, from which it was distilled when needed. Lithium chloride: Baker's C.P. lithium chloride was treated in the following manner: A saturated aqueous solution of lithium chloride was prepared and to this was added, a t room temperature, excess dioxane. This caused the separation of about half of the lithium chloride as the compoundLiC1. HzO-(C*Ha)&. This compound will be discussed later. On filtering and washing with pure
