A SIMPLE METHOD FOR ACCURATE DETERMINATIONS OF VAPOR PRESSURES O F SOLUTIONS D. A. SINCLAIR University College, Auekland, NEWZealand Received January 12, 1033 INTRODUCTION
The importance of vapor pressure in the study of solutions warrants a far more extensive exploitation of this property than has yet been made. Many attempts have been made to evolve practical and accurate means of determination, but the amount of reliable data so far accumulated is very scanty indeed. Hitherto facility and accuracy appear t o have been incompatible. Undoubtedly the most accurate determinations of vapor pressure lowering, to date, are those of Lovelace, Frsser and coworkers (l), who by rigorous care in the removal of air and using a reliable sensitive manometer seem to have attained an accuracy to the order of less than 0.001 mm. The method is too elaborate for general application, but for standard determinations it has, as yet, no equal. Reviews of the older methods are available in the literature. Recent determinations may be mentioned briefly. Bousfield and Bousfield (2) used an apparatus which was very neat and compact, but these authors appear not to have appreciated fully the errors arising from residual air, and errors to the extent of nearly 10 per cent of the lowering are evident in the region of lower concentration. The pressure of residual air may be much greater than that indicated by the volume of the bubble of air remaining when the solutions have been brought to atmospheric pressure. The most advanced development of the dynamical method has been made by Pearce and Snow (3). The accuracy attainable is of the order of 0.01 mm., but by taking a mean of several observations, values reliable to within a few thousandths of a millimeter may be obtained. The dew-point method used recently by Hepburn (4)seems to be capable of useful application. An accuracy of 0.03 mm. is estimated. A method described by Hill (5), depending on the principle of the wet and dry bulb thermometer, may prove useful for some purposes. With moderately concentrated solutions the estimated accuracy is 2 per cent. The limited accuracy of the various methods may be gauged from the 495
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fact that at 25°C. the molecular lowering for solutions of such salts as potassium chloride is only about 0.75 mm. BOUSFIELD’S ISOPIESTIC METHOD
I n the paper referred to above, Bousfield makes mention of a method for comparing the vapor pressures of solutions, called the “isopiestic” method and described in earlier papers. This method is apparently so simple that the absence of further mention of its application would appear to indicate that it did not fulfil expectations. According to Bousfield, four open cylindrical glass vessels containing different solutions are placed in a desiccator vessel, which is evacuated and placed in a thermostat for two or three days. By this time the solutions will have come into equilibrium by distillation of water, so that each will have the same vapor pressure. The concentrations are determined by weight and hence, if accurate data are available for one solution, equally accurate values may be assigned to the others. Results, apparently confirmatory, are quoted. I n order to test Bousfield’s method, the author placed two crystallizing dishes containing respectively approximately 1 M potassium chloride solution and water in a vessel which was evacuated to 15 mm. and left for several days. The amount of distillation occurring was barely noticeable even when the dishes were floated on mercury, to aid temperature equalization. Presumably, the rate of distillation between two solutions differing in concentration by only 1per cent would be 100 times as slow! As pointed out by Bousfield, the attainment of equilibrium is dependent on the equalization of temperatures. When the air is removed the vapor pressures of all surfaces in the vessel must be the same, but the temperatures are different. However, the order of the magnitudes involved was apparently not realized. From data in the International Critical Tables the following calculations were made.
P for water is 1.4 mm. per degree. Hence a pressure difference At 25°C. ddt of 0.001 mm. a t the same temperature corresponds to a temperature difference of 0.0007”C. a t the same pressure. The latent heat of vaporization of water a t 25°C. is 2436 joules per gram. Therefore, if we have two surfaces differing in temperature by 0.0007”C. and separated by a medium of thermal conductance equivalent to one centimeter cube of the undermentioned materials, the times required for 1 gram of water to distil, or 2436 joules to flow, from one to the other may be calculated from the thermal conductivities (without convection) to be for (a) glass-10 years, (b) water-17 years, (c) gases-500 years, (d) mercury-15 months, (e) copper-10 days. Considering these astonishing figures, it is surprising that the results quoted by Bousfield are as good as they are. Earlier papers show, how-
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ever, that these figures were taken from series of experiments extending over several months, in which solutions were built up by distillation of water from the trough of the desiccator, weighings being made every two or three days. Apparently, no experiment was made to see if two solutions of the same salt came to the same concentration after two or three days and assumptions were made which were not sustained by later trials. APPLICATION O F T H E ISOPIESTIC METHOD
From the above considerations it would appear that the method as described by Bousfield is too.slow to be suitable for practical application. However, by incorporating the following principles in the design of apparatus, it seemed probable that the method could be rendered practicable. By providing good metallic conduction between the solutions, the retardation due to thermal resistance between them may be reduced t80 quite a small value. The factors limiting the rate of athinment of equilibrium would then be diffusion of solute and conduction of heat through the solutions. These could be accelerated by stirring and by making the solutions shallow. Too violent agitation is to be avoided, however, since minute heating effects would cause appreciable errors. Quantities of solutions as small as compatible with accuracy in weighing are also desirable, to minimize the amounts which have to distil. T H E , METHOD ADOPTED BY T H E AUTHOR
Preliminary experiments Solutions of potassium chloride placed in silver-plated copper dishes fitting neatly together and mounted on a copper base were found to approach identity of concentration a t quite a feasible rate, when rocked in an evacuated desiccator vessel in a thermostat. It was discovered that the rate was greatly increased by placing some solution in the crevices between the dishes. Evidently the temperature gradient here was reduced appreciably by the substitution of solution for vapor in the gaps. Using about 2-cc. quantities of approximately 1 M potassium chloride, it was found that a 25 per cent difference could be reduced to 1 per cent in twenty-four hours. During a series of experiments in which potassium chloride and cane sugar solutions were compared the following procedure was evolved. Apparatus The dishes were 1+inches square by 2 inch deep, a set of four being placed in square formation on a silver-plated block 1 inch thick. The block acted as a steadying heat reservoir as well as a conducting medium. The thermostat was believed to keep constant to about 0.01"C. at 25'C.
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The variations need not necessarily be reduced to a very small amount, as the temperature waves are damped down considerably by the thick walls of the desiccator, and the massive copper block ensures that any small disturbance is equitably distributed. The heating lamp was blackened since the radiation, which had an appreciable effect on the regulator, would also be liable to affect the dishes and possibly maintain a permanent temperature gradient therein. The period and angle of oscillation were about 1 second and 20" respectively.
Procedure The solutions were weighed into the dishes by pipetting in 2 cc. and weighing quickly to the nearest milligram. I n the case of concentrated solutions the amount of solid in 2 cc. was sufficient to be weighed in directly with accuracy. I n all determinations made, potassium chloride solutions were used as standard. Duplicates of each solution were inserted, being placed in diagonal opposition in the set, so as not to be in direct contact, and therefore to provide a more reliable mean. Caustic soda of about the same concentration as the potassium chloride in the dishes was used as intermediate conducting solution, being preferred since it spread more easily over greasy surfaces. The evacuation was effected by means of a water pump, the pressures being reduced to 15-20 mm. Complete removal of air is not requiredmerely sufficient to remove the diffusion retardation. The dishes, on being removed from the desiccator, were kept covered while they were cooled rapidly in a stream of cold water and dried on the outsides with filter paper. An approximate weight was estimated, while still covered, and final weighing completed in a few seconds after removing the cover. Errors due to evaporation may amount to several milligrams and this is the largest error with the more concentrated solutions. A better plan would be to provide the dishes with permanent lids, but this refinement was not introduced at this stage. The same set of solutions may be used to make as many as five or six determinations over a range of concentrations varying by about 40 per cent. The most convenient method of varying the concentrations, and that which gave the best results, was by distillation of water from the bottom of the desiccator. This distillation is chiefly indirect. The thermal conduction between the block and the walls of the vessel being poor, the block is heated from room temperature t o 25°C. by distillation of water onto the block, from the water in the bottom which is heated more quickly. This water then distils into the dishes. Finally the block attains a slightly higher temperature than the thermostat and further distillation takes place into the solutions, a t a rate depending on the flow of heat from the block to the thermostat. This is negligibly slow with dilute solutions, but is appreciable with concentrated solutions.
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The removal of water by pumping off was difficult to accomplish satisfactorily. The best method was found to be to use high concentrations of intermediate solution. The times required for the solutions t o come sufficiently close t o equilibrium vary according to viscosities, but other things being equal, rates of distillation should be proportional to the temperature difference. For the same percentage difference in concentration this is proportional to the concentration. For any one concentration the difference should be reduced equal fractions in equal times. With 0.5 M potassium chloride solutions the rate is greater than one-tenth in one day and so, if the solutions do not differ originally by more than 2 or 3 per cent, one day should be sufficient for a n accuracy of 0.3 per cent. I n general, one day was allowed for all solutions above 0.5 M and below this the times were increased, until at 0.1 M three days were allowed. This time gave uniform results.
Calculation of results The actual calculations are simple, the molality being inversely proportional to the weight of water in the dish. Potassium chloride was always taken as standard, the values obtained by Lovelace, Fraser and Sease (6) being taken as correct and assuming that the relative lowering is the same a t 25°C. as at 20°C. The International Critical Tables state that the variation with temperature is inappreciable for this salt. The vapor pressure of water at 20°C. was taken as 17.535 mm. Results are expressed in terms of molecular relative lowering, in conformity with the practice in the tables. The clearest method of exhibiting the results is by means of a graph, plotting molecular relative lowering against molality. Tables of values taken from the author’s curves are provided to enable the curves to be reconstructed. RESULTS
Cane sugar solutions The choice of cane sugar as a solute for preliminary experiments was perhaps not the best, on account of the high viscosity of the solutions. Nevertheless, the results obtained were gratifyingly good. The materials used were A.R. potassium chloride and a specimen of sugar prepared some years ago for research work in this College. Determinations were made over a range of concentration from 0.2 M to 1.5 M , corresponding to 0.1 to 0.9 M potassium chloride. The results are shown in figure 1 and table 1. A better uniformity is desirable in the higher concentration region, but below 0.8 M the deviations from the
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smooth curve are less than 0.3 per cent, or less than 0.0007 mm. expressed as pressure. With three obvious exceptions the deviations in the higher region are of the order of 0.2 per cent., which a t 1.4 M corresponds to about 0.0014 mm. Errors of 0.2 per cent are quite possibly introduced by losses by evaporation before weighing, and a better uniformity was not to be expected.
FIQ.1
TABLE 1 Values of R = - f o r sucrose solutions, M PO M
at 15°C.
(moles per 1000 grams of water)
R X 106
0.2 0.4 0.6 0.8 0.9 1 .o 1.1 1.2 1.3 1.4
1796 1821 1848 1881 1906 1936 1951 1959 1967 1985
The curve obtained from the few points given in the International Critical Tables is also shown in figure 1. The original paper was not available to the author, but the determinations were probably made with the Lovelace and Fraser apparatus. The difference is not great and, except for the elevation between 0.8 and 1.3 M , is less than 0.002 mm. Although the difference in the molal lowering becomes greater in the dilute region, the
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actual difference in pressure becomes smaller and at 0.2 M is only about 0.001 mm. The elevation between 0.8 M and 1.3 M corresponds to the elevation in the standard curve for potassium chloride (see figure 3). It may be eliminated by allowing deviations of 0.002 mm. in the measurements of Lovelace, Fraser and Sease, but this would be altogether too revolting to these authors. The real existence of this irregularity is supported by the independent measurements on lithium chloride solutions made by Lovelace, Bahlke and Fraser (l),which show a similar irregularity. It has also been observed recently by Burrage (7) that there is a parallelism in the curve for the solubility of lead chloride in potassium chloride solutions.
FIG.2
The significance is uncertain, but it would appear that the irregularity is due to a property of water in this activity range which is independent of the type of solute. Further direct measurement in this region is highly desirable.
Sodium chloride solutions
A few determinations on sodium chloride solutions serve to show that the irregularity appears also in the curve for this salt. The author’s determinations tend to confirm the values given in the International Critical Tables (original paper unavailable). Bousfield and Bousfield obtained values about 8 to 9 per cent higher. The author’s results are inserted as dots in figure 3.
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Potassium toluene-p-suljonate solutions An extensive series of determinations was executed with solutions of this salt over a range of concentration from 0.1 M to saturation. The specimen used was some of a preparation used in previous research work in this College, and was taken as sufficiently pure without further test, other than that for water content. The salt crystallizes with one molecule of water of crystallization. This is, however, easily driven off. A sample of a batch dried a t 130OC. in an air-oven for two hours did not lose weight further on being subjected to two hours' treatment with a stream of air under 20 mm. pressure a t 130°C., dried over phosphorus pentoxide. The results are exhibited in figure 2 and table 2. Satisfactory general uniformity was obtained. The distribution of points in the region of the irregularity unfortunately does not allow the exact shape of the curve to be determined here. The small irregularity, although quite evident, seems to TABLE 2 Valuesof R foor potassium toluenesulfonate solutions, at 86°C. M
R X 106
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
3274 3192 3128 3072 3040 3005 2960 2907 2864
II
M
1 .o 1.2 1.4 1.6 1.8 2.0 2.5 3.0 3.5
R
x
105
2820 2727 2641 2572 2508 2450 2316 2210 2118
be masked by a longer irregularity extending to 1.3 M , which may or may not be due to experimental error, since the five points from 0.79 M to 1.3 M were all obtained from one set only. Circumstances did not allow confirmation to be made. The solubility of the salt does not appear to have been determined previously. From the vapor pressure of the saturated solution it was estimated by the author, by a short extrapolation, that the molality of the saturated solution was about 3.87. COMFARISON OF MOLECULAR LOWERING CURVES
Figure 3 gives a comparison of the curves for five salts. The values for potassium nitrate and sodium chloride were taken from the International Critical Tables, while those for potassium and lithium chlorides are from the original papers previously referred to.
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The comparison shows what wide variations exist among these simple salts with common anions and cations. A close parallelism between potassium nitrate and potassium toluenesulfonate is evident. Whether this is fortuitous or due directly to common properties of the sulfonic and nitrate ions must be decided by further investigations.
... 0.
0.
VIG.
3
CONCLUSION
The method described for determining vapor pressures of solutions appears to be capable of yielding results of a high degree of accuracy. The sensitivity is demonstrated by the clear discernment of irregularities, which are detected only by the most accurate direct measurements which have been made and are very close to the experimental error thereof. With greater refinement and care, even more accurate result8sshould be obtainable, but for the present sufficiently good results are obtainable by the simple procedure described above. The method should prove very useful in extending vapor pressure data, which are highly desirable and will become more and more important as the theory of solutions progresses into the more concentrated regions. SUMMARY
Solutions may be brought rapidly into equilibrium as regards vapor pressure, and by taking one as a standard, values for the vapor pressure TEE J O U R N A L O P P H Y S I C A L C H E M I S T R Y , Vola. S X Y V I I , N O .
4
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1). A. SINCLAIR
lowering may be obtained with an accuracy of 0.3 per cent or less for solutions of concentration above 0.1 M . Determinations have been made on solutions of sucrose, sodium chloride, and potassium toluene-p-sulfonate, using potassium chloride as standard. The author desires to thank Professor 17, P. Worley, under whose supervision this work was carried out, for his sustained interest, and for his assistance in preparing the paper for publication. REFERENCES
(1) LOVELACE, BAHLKE, A N D FRASER: J. Am. Chem. SOC.46,2930 (1923), and earlier papers. (2) BOUSFIELD AND BOUSFIELD: Proc. Roy. Soc. London A103, 429 (1923). AND SNOW:J. Phys. Chem. 31,231 (1927). (3) PEARCE (4) HEPBURN: J. Chem. SOC.1932, 550. (5) HILL:Proc. Roy. SOC.London Al27, 9 (1930). (6) LOVELACE, FRASER,AND SEASE:J. Am. Chem. SOC.43, 102 (1921). (7) BURRAQE: Trans. Faraday SOC.28, 529 (1932).
