FREEZING POINT EXPERIMENTS for UNDERGRADUATES JOHN G. MILLER
AND
WALTER W. LUCASSE
University of Pennsylvania, Philadelphia, Pennsylvania
W
ITH the rapid development of physical chemistry, the teacher of this subject finds himself in somewhat of a quandary as regards the objectives of his laboratory work and how they may best be met. He may wonder whether he serves best when his experiments are selected and equipped to emphasize the high degree of accuracy that is so essential to original contribution in the field. Or again, he may question whether his mission is better fulfilled with a larger group of experiments which aim to clarify and supplement the theoretical aspects of a more representative portion of the subject. Perhaps both of these extremes represent desirable objectives, but each has its practical disadvantages. If stress is placed upon accuracy, the simple principle of the experiment may well be obscured1 by highly developed apparatus, temperature control, and indirect devices for measurement. In any case, such experimentation is inordinately time-consuming and may lead to neglect of equally important phases of the subject. It is likewise unfortunate if a large group of only semiquantitative experiments conveys an erroneous impression of the mathematical approach to the subject and the accuracy necessary for original work a t the present time. Union of these objectives in a single course is open to criticism from many angles, and perhaps the ultimate solution will be found in a general course to illustrate the simple principles, followed by one in which training in refined, measurement is paramount. C That we are in a state of doubt is well illustrated in the usual manual, where we find experiments developed to varying extents depending upon such factors, perhaps, as the length of the laboratory period, the probable institutional budget, the history of the experiment and even that of the author of the text. Freezingpoint determinations constitute a particularly suggestive case in point. The earliest equipment was undoubtedly of the most simple type. Then came the extensive work of Beckmann and the widespread use of the technic which he developed. And now, for the most part, significant measurements can be made only with extremely rapid mechanical stirring and multiplejunction thermocouples. The usual laboratory text indicates that undergraduate experimentation has followed the procession through the second stage, with here and there a compromise by introduction of difficultlypurified chemicals because of 'MILLERAND LUCASSE, J. CAEM.EDUC..13, 581-5 (Dec.. 1936).
advantages such as high mold depression. Although still extensively used, and adequate for many purposes, there is question as to the value of the use of the Beckmann thermometer by an undergraduate, particularly in view of the time required for the "setting," so essential if its use is to be of any personal significance to the student. Since it no longer represents the method of highest accuracy attainable in the field, perhaps there is advantage in turning again to the simple principle. Upon examination of a large group of recent texts, it is found that almost all undergraduate laboratory manuals in physical chemistry include freezing point measurements using the Beckmann thermometer. There is a marked tendency to use benzene solutions entirely, while if water solutions are used the experiments rather uniformly call for a single study of urea as solute. Thus there is presented to the teacher a serious difficulty when his classes are large. In addition to the time element, the expense and fragile nature of the Beckmann thermometer render i t unsuitable for such groups. The hygroscopic nature of organic solvents necessitates immediate, individual purification or, under ordinary conditions, renders the accuracy of the thermal measurement inconsistent. The writers have found i t practicable to use aqueous solutions throughout the required experiments covering the usual types. Thus, sugar serves successfullyas the solute in molecular weight determination, resorcinol for studies of association and many. common pure salts may be used for the study of electrolytic solutions. For all of these experiments a simple, rugged, and inexpensive Oo to -5' thermometer is quite satisfactory. Description of these experiments is given below. Their simple nature enables each student to perform more measurements than i~ possible with the nsual limitations of time and apparatus. More rapid workers may be allowed to work with non-aqueous solutions and with the Beckmann thermometer. To judge the success of these experiments, statistical analysis was applied to the results obtained by a large group of about equal numbers of premedical, chemistry, and chemical engineering students. The results were calculated directly from the experimental data handed in a t the end of each laboratory period. Comparison with the student calculations appearing in their final written reports revealed but few lapses of integrity or failures of comprehension. The findings of the three groups were about equal, and the statistical analysis of the whole group is reported in the description of each ex~eriment.
THE GENERALEXPERIMENTALPROCEDURE
The ordinary student freezing point apparatus2 was used and students worked most efficiently in groups of two, one performing the weighings, the other setting up the apparatus, while both worked together in making the measurements. The thermometersJ were one-fourth of an inch in diameter and thirteen inches in length including a one and one-half inch bulb. The graduations started one and one-half inches from the top and read downward from 0°, being marked a t each even-numbered tenth. The smallest divisions, representing two one-hundredths of a degree, were slightly more than one-fiftieth of an inch apart, the markings covering a length of five and one-half inches. Using a seven-inch pyrex test tube as the freezing point tube, the stopper carrying the thermometer and stirrer slightly obscured the lowest scale divisions which in practice were seldom used. The liquid covering but a little more than the bulb of the thermometer, obviously, there resulted a maximum exposure of stem. However, in successive determinations the stem error was thus rendered practically constant and disappeared in the difference in the readings. A warning was necessary to the effect that the stem must not be touched by hand, i t being found that an error as high as onehundredth of a degree can result in this way. With the aid of a hand lens, temperatures were estcmated to 0.005°, and each group calibrated the 0' value by several determinations with pure water. Since the serial number of the thermometer was recorded by each group, those thermometers causing consistent trouble were easily eliminated. In general, the precision of measurement was better than +O.O1° as shown by the agreement of the student calibrations and a more extensive calibration of several of the thermometers a t different points. Similar 5' to 0' thermometers served with equal success in work with beuzene solutions. Three separate deteminations were required for the freezing point of each solution studied, and the supercooling was recorded for each determination so that the correction could be made for the change in the amount of solvent due to supercooling by means of the equation
W' =
W(l
- sl80)
error acts to produce high values of the measured depression in the freezing point, the error is not serious in tindergraduate work as shown by the results given. On the other hand, use of supercooling has the advantage of marking sharply the incidence of freezing and makes the entire measurement more rapid. The addition of solid solvent followed by analysis of the solution a t equilibrium introduces an inordinate amount of additional work to obtain a degree of precision often more imaginary than actual with undergraduates. Since the freezing points were read to three significant figures, the weighings of the solute and solvent were made to four figures only. THE MOLECULAR WEIGHT OR CANE SUGAR
As might he expected in view of the possible accuracy, ordinary commercial refined sugar and Merck's Reagent Sucrose gave equally satisfactory results in these experiments. However, the latter is in very convenient form and furthermore seemed to impress the students as to the need for purity of chemicals and for general manipulative care. In either case this material is ideal for such studies due to purity, stability and high molecular weight. Two concentrations were studied, of about 1.5 and 3.5 grams in twenty-five grams of water. In case the solution was prepared too late in the period to allow measurement, standing in stoppered flasks caused no deterioration. The equation used for calculation of the molecular weight, M, was
where g is the weigbt of sugar, the' corrected weight of solvent and AT the observed depression. The arithmetic mean of the results of two hundred niuetyeight experiments was 331 with a mean error of +0.8 and the mean error of each experiment amounted to t4.4 per cent. Of these, about two-thuds, or one hundred ninety-three experiments met the usual requirement that each value be within five per cent of the true molecular weight, 342. The arithmetic mean of these accepted results was 337 with a mean error of *0.6 and the mean error of each determination was 1 2 . 4 per cent. The definitely low value of the mean (337 is 1.5 per cent low) must be scribed to the supercooling effectmentioned above.
in which W' is the corrected amount of solvent, W the amount of water weighed out for the measurement and s THE ASSOCIATION OR RESORCINOL the number of degrees of supercooling. Supercooling A study of solutions of resorcinol in water was dewas kept low by adjustment of the cooling bath since correction was not made for the fact that the true signed to replace the usual experiment with benzoic freezing point is not obtained after supercooling takes acid in benzene. I t is based on the work of Bonrion and Tnttle4 who studied the molecular association, place. Although, like the stem correction, the supercooling showing that the following equilibrium exists in the range 0.8 to 3 mold in aqueous solution Cf.,FINDLAY. "Practical physical chemistry," 5th ed., Longmans, Green and Company, New York City, 1933, pp. 119-20. a Such thermometers may he ordered to specification. Those used in the present exprrimrnrs were ubtiinrd from the I'mcicion Thermometer and Instntmenl Company. 1434 llrandyw n c Strcer. P l ~ i l l d e l ~ h i 3Pmnwlvania, . and in lots of one dozen cost about ~63.26each.
3 CeHAOHh = [CJTdOHhlr
The degree of association6,x, is given by the equation: -
' B & ~ ~ O Nam TUTTLE. 1.chine. pkys., Cf., FINDLAY.106. cit., p. 127.
25, 485-96 (1928)
where (AT)o is the observed depression and (AT)' is the value that would be expected for an unassociated solute a t the same concentration. Figure 1 shows the variation of x with concentration. The curve was constructed from values calculated from the data of Bourion and Tuttle and a t the following rounded mold concentrations, leads to the corresponding values of x.
(AT)o from (AT), in the calculation of x. That the results are satisfactory for illustration of the change in the degree of association is shown by the fact that in almost every case the variation of x with the concentration was in the correct direction. THE OSMOTIC COEFFICIENTS OF STRONG ELECTROLYTES
The use of the osmotic coefficient, , in the interpretation of the behavior of solutions of stronlr ~ ~ ~ collieativc ~ . =' electrolytes has certain advantages. Understanding of the term is easier than that of the activity coefficient and its use in dealing with the colligative properties is adeq~ate.~ Since the variance of the osmotic coefficient with .change in concentration is of greatest interest to the student, the most striking results should be expected in the use of salts of higher valence type. Thus, it was found that magnesium sulfate is more satisfactory for these experiments than potassium chloride. To compare these, concentrations of 0.4 and 0.8 grams of potassium chloride in twenty-five grams of water (about 0.25 and 0.5 molal) and 0.3 and 3.0 grams of MgSOg7He0 in twenty-five grams of water (about 0.05 and 0.5 molal) were studied. The change in g for potassium chloride over this range is from 0.92 to 0.90 and for magnesium sulfate from 0.71 to 0.55. I n about two-thirds of the experiments with potassium chloride the correct trend of g was obtained, the high experimental error (about five per cent) being unfavorable to the determination of the small change in the osmotic coefficient (about two per cent). In every case, however, the correct trend in g was obtained with magnesium sulfate. : , In the case of magnesih sulfate a double correction of the solvent was needed since, like other higher valence salts, the hydrated form is the most convenient to use in preparation of solutions. Thus an addition due to the water of hydration is required and a subtraction due to the supercooling effect. as shown above. In every case the students made these corrections without error. The questionable exactness of composition of the hydrated salt caused no serious error. While the above experiments fail to emphasize the accuracy requisite for original contributions in the field of freezing point determination, they are sufficiently quantitative to permit stress of certain points. Thus the relative accuracy of a given measurement needed to achieve a final determination within stated limits of error may be indicated. An introduction to the fundamental elements of the measurement is obtained. Finally, without undue expenditure of time, emphasis upon purification and complications of refined experimentation, the simple picture of normal, associated and dissociated solutes is made more concrete. The writers wish to acknowledge many helpful suggestions made by Mr. Edgar L. EcMeldt during the preparation of this study. - . ~
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The students were directed to study two concentrations, of 2.5 and five grams of resorcinol (Mcrck's U.S.P. recrystallized) in twentyave grams of water. These concentrations are about 1 and 2 mold and should give values of x in the neighborhood of 0.3 and 0.45, respectively. The solufions were measured as soon as prepared, since standing results in noticeable oxidation of the resorcinol. c In judging the accuracy of the results, the students could calculate the molarities with the aid of density data and evaluate the equilibrium constant, the value of which is about 0.31 and constant over the range studied. In actual practice, however, it was considered that the direction of change of the degree of association with concentration was sufficient for elementary student work. To judge the usefulness of the experiment, statistical analysis was made of the results in the following manner. The per cent deviation of each determination from the true value was determined graphically from a figure similar to the one above. The arithmetic mean of these per cent deviations for two hundred fifty-two experiments was -0.29 per cent, again showing the effect of supercooling. The average per cent error of each determination was 8.29 per cent and the mean n m DANIELS,"Outlines of theoretical chemistry," per cent enor of each determination was 10.826 per 6th0 GETW ed., John Wiley & Sons. New York City, 1937, pp. 189-90; cent. These high errors result from the subtraction of 193-5.
