A CRYOSCOPIC STUDY OF BENZENE SOLUTIONS BY J. MERRIAM PETERSON’ WITH WORTH H. RODEBUSH
It has been common knowledge for a long time that some substances, for example acetic acid, appear to have a higher molecular weight (as estimated from vapor pressure lowering) in benzene solutions than in water solutions. Since water has a well known “ionizing” action it may also be suspected of a dissociating action on neutral polymerized molecules and is usually classed as a “dissociating” solvent. I n contradistinction benzene is often designated as an “associating” solvent. I n view of the known fact that acetic acid has an abnormally high vapor density and that it can be shown theoretically that all molecular weight results even in solution refer to the density of the vapor it may be questioned whether benzene behaves in any way except as an inert solvent. Another point which requires consideration is that high results for molecular weights obtained by the cryoscopic method might be due to deviations from ideal solution conditions and not to association a t all. These questions can best be answered by obtaining complete data for the partial pressures of solvent and solute. Since it is necessary to work in dilute solution in order to apply any of the laws of solution at all, sufficient accuracy cannot be obtained by direct measurement of partial pressures and it is necessary to use the indirect cryoscopic method, which is equivalent to measuring the vapor pressure of the solvent only. Theoretical The fundamental law of solutions for changes in composition at constant temperature and pressure is due to Gibbsz
Here ml and m2 are the masses in grams of the respective constituents of the solution and F is the total free energy of the solution. If the free energies of the pure constituents are arbitrarily taken as zero then F is the free energy change on mixing. Equation ( I ) is simply a mathematical statement of the fact that the free energy of mixing depends only on the final amount and composition of the solution. The Duhem-Margules equation is derivable from ( I ) if the vapors are perfect gases. The unit of mass is taken as the gram in order that the introduction of the concept of molecular weight may be scrutinized more carefully. This is an abstract of a thesis submitted by J. M. Peterson in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Chemistry a t the University of Illinois. * Gibbs: “Scientific Papers,” 1, 88 (1906).
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J. MERRIAM PETERSON WITH WORTH H. RODEBUSH
If the subscript I refers to the solvent we may evaluate the first coefficient of ( I ) in terms of freezing point lowering. For equilibrium between the solvent in solution and the pure solid solvent we have:
This equation
(2)
aF,
transforms into: - ATr H f am* aT (3) since aF -=
AHr - S,A& = am2 aT Tr Here AHr is the heat of fusion per gram of the solid solvent into solution. In dilute solution we may assume A H t independent of concentration and neglect the temperature coefficient of PI. Substituting in ( I ) which is strictly an’isothermal equation. AH aT aFz = o ml -Im2(4) T amp amz The appearance of d T in an isothermal equation need cause no concern since it represents the amount by which the temperature of the solution would be changed if its freezing point were measured. The best physical measurable quantity to use in expressing the second coefficient of ( I ) is the partial pressure of the solute. We have
+
Where p is the density and Vp the specific volume of the solute vapor. Substituting in (4) we have
So far nothing has been said of molecular weight. The apparent molecular weight M is defined for a gas by the equation RT 31 = P P where R is expressed in appropriate units. Combining ( 5 ) and (6) we have
M=--
(
RT2 aln p ? ) ( g ) (7) mlAHt a h m z It is necessary in order to calculate M from freezing point lowering data alone to make some assumption as to the relation of p2 and m2. We may assume that Henry’s law p? = kx2 where x2 is the mol fraction of the solute, holds for normal solutes in dilute solution. If the solution is dilute this may be written pz = k.m2 and (7) becomes M = RT2 am2 mlAHt aT It is common practice to substitute m 2 / A T for $m,/aT where AT is the freezing point lowering but this is only justified if the lowering is a linear function of m2. The equation (8) connecting freezing point lowering with molecular weight is not usually given in the exact form and it is important to rec-
A CRYOSCOPIC STUDY OF BENZLNE SOLUTIONS
gives us a hypothetical vapor density. If a solute does not give the same moleculm weight in different solutions then one of two things must be true. Either the solute has a variable molecular weight in the vapor state depending on the pressure e. g. acetic acid vapor, or the assumption of Henry’s law is not justified. If Henry’s law does hold and a solute shows different molecular weights in different solvents a t the same concentration the partial pressures
:
Q
3
e
/’
I,’
711
712
J. MERRIAM PETERSON WITH WORTH H. RODEBUSH
If ap2/ams < p?/m2 then the use of the simplified form (8) will lead to too large a value for the molecular weight. For positive deviations from ideal solutions then we may expect too large a value of the molecular weight in all except extremely dilute solutions. X negative deviation will produce the reverse effect. These theoretical considerations will be referred to later in connection with the data obtained in this work.
1
W
____ FIG.2
Experimental A number of the earlier workers with the cryoscopic method obtained data on benzene solutions. Prominent among these are Raoult,' Beckman,? huw e q 3 Patern?~,~ and R0zsa.j All of this work, however, was done with mercury thermometers and comparatively crude apparatus, so that a high percentage accuracy could not be obtained in dilute solution where Henry's law may be assumed to hold. I n the work described in this paper the greatest lowering measured was 0.z57OC. Apparatus: The apparatus consisted essentially of two freezing point bulbs A and B Fig. z which were placed in Dewar tubes. In the top of the bulbs were openings for Lhe insertion of the thermocouple, air bubbling tube, pipette, etc. These openings were made tight by perforated corks which had been extracted with benzene. This part of the apparatus was enclosed in a Raoult: Ann. Chim. Phys., 2, 66 (1884). Beckman: Z. physik Chem., 2 , 715 (1888). a Auwers: Z., physik Chem., 42, 51.7(1903). Paternb: Der., 22, I 4 3 0 (1889). Roasa: Z.Electrochemie, 17, 934 (1911).
A CRYOSCOPIC STUDY O F BENZENE SOLUTIONS
713
copper can which was nearly submerged in a water thermostat. The cover of heavy sheet copper was above the water level but this has been shown to give satisfactory temperature equilibrium.' The thermostat was heavily insulated, cooled by the ice box H and heated by the lamp L. A conventional type of mercury regulator was used and no difficulty was experienced in maintaining any temperature between s" and 2s°C with variations less than 0.01'. The thermocouple was a ten-junction copper-constantan couple of resistance 54.2 ohms and a calibrated e.m.f. of 394.6 microvolts per degree a t the freezing point of benzene. The e.m.f. was read on the self-calibrating potentiometer devised by Rodebush,2with a precision of 0.02-0.03microvolt.
Experimental Procedure The apparatus was designed originally with the expectation of following the experimental procedure used by Hovorka and Rodebush on dilute water solutions. Surprising difficulties were met with however because of the peculiar waxy nature of solid benzene. It cannot be broken up into conveniently sized particles, as can ice, nor can it be handled in contact with the air because of the absorption of moisture which produces a marked change in the freezing point. I n order to get a satisfactory temperature equilibrium in freezing solutions it is necessary to have a mush of fine solid particles in contact with liquid. The ordinary laboratory method of producing this mush by supercooling did not produce enough of the solid to cover the thermocouple to a satisfactory height. This method was actually used with some success, by supercooling the benzene very markedly and it is probably the simplest and best method, but one day it suddenly became impossible to supercool benzene more than a degree in the laboratory and the method had to be abandoned. This sort of experience is of course a common occurrence in crystallization work. It became necessary therefore to devise a new procedure of obtaining a mush of solid benzene. The method finally adopted was as follows: The freezing point tubes were filled with pure benzene, stoppered, and placed in a beaker of ice water until a thin layer of solid had formed on the sides of the tube. The tube was then removed and warmed slightly with the hand whereupon, on shaking, small particles of solid benzene would break loose from the sides and settle to the bottom of the tube. By repeating this process a satisfactory amount of solid free from contamination was produced. The temperature equilibrium obtained was not as perfect as can be had with ice and water but it was usually constant within 0.001~. IVhen a sufficient amount of solid had been obtained in two tubes they were placed in the thermostat and the thermocouple and the various connecting tubes inserted. The tube B served as the standard temperature bath for the thermocouple while the benzene was withdrawn from A through the bubbling tube C. The solid benzene in A was rinsed free of pure benzene by introducing small quantities of the solution from F and withdrawing it through White: J. Am. Chem. Soc., 48, 1149(1926).
* Hovorka and Rodebush: J. Am. Chem. Soc , 47, 1614(1925).
714
J. MERRIAY PETERSON WITH WORTH H. RODEBUSH
C. When this had been repeated several times the tube A was fded with solution and equilibrium obtained by bubbling purified air saturated with benzene vapor through both tubes. All the solutions were handled out of contact with the air or any possible source of contamination. The solutions were made up by direct weighing. The small amounts of solute were sealed in glass bulbs for weighing and the bulb broken beneath the surface of a weighed amount of benzene, to make up the solution.
FIG.3
Preparation o j Materials: Benzene. Very pure benzene may be obtained because of the possibility of freeing it from most of its impurities by fractional crystallization or freezing. Thiophene, it is true, cannot be separated in this way but this impurity can easily be removed chemically. On the other hand, paraffin hydrocarbons, olefins, acetone and most other impurities are quickly eliminated from the successive crop of crystals. Mallinckrodt’s best grade of thiophene-free, pure benzene was used. This was fractionally crystallized 5 times discarding about one-tenth of it each time. It was then fractionally distilled twice, using a tall, efficient, fractionating column, the last time from phosphorus pentoxide directly into the freezing point tubes. The distilling apparatus as well as the tubes were thoroughly dried, by a stream of dry air, immediately before use and were protected during the distillation by a phosphorus pentoxide tube. The first benzene dis-
A CRYOSCOPIC STUDY OF BENZENE SOLUTIONS
715
tilling over was never used and the last portion in the flask was never distilled. The boiling point of the benzene used varied less than .02 degree c. Further treatment appeared to have no effect upon the freezing point. Acetic acid. Kahlbaum’s acetic acid labeled “100percent” was used. This was recrystallized 5 times and fractionally distilled from a small amount of phosphorus pentoxide. Only the middle fraction was collected for use. Altho the very qonstant reading of the thermometer would not indicate any acetic anhydride in the distillate, this possibility was eliminated by a further purification by freezing. Water. “Conductivity” water was used. Methyl alcohol. A c.p. grade of methyl alcohol was used which was dried with magnesium methylate and fractionally distilled. Ethyl alcohol. Absolute ethyl alcohol was further dried with magnesium ethylate and fractioned. Benzoic acid. The purity of the benzoic acid used was certified by the Bureau of Standards. I t was recrystallized and dried in a vacuum desiccator.
TABLE I A = gms. solute in 1000grns. benzene B = freezing point lowering in centigrade degrees A B A Methyl Alcohol 0.168 0.364 0.710 I .062 I ,681
0.0268 , 0.0570
0.1078 0 .I 546 0.2342
Ethyl Alcohol 0.0364 0.803 0.0878 I . 089 0.1223 1.327 0.I459 0.322
I . 830 2.262
0.2013
0.2442
0.021
0.248 0.320 0.382 0.5 1.0
Toluene
0.610 0.658 0.981
0.0338 0.0366 0.0549
Acetic Acid 0.201
0.0156
0.399 0.895 1.611 2,894 3,923 4.452 4.897
0.0277
Water 0.074 0.I59
B
0,0539 0.0875 0.1472 0.I957 0.2199 0.2401
Benzoic Acid 0.0214 0.0450 0.0606 0.0716 0.0907 .0990 .09S6 ,0984
1,557
3.094 4.802 8.774 11.236
e0342 .0683 0.1060 0.1897 0.2402
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J. MERRIAM PETERSON WITH WORTH H. RODEBUSH
Toluene. The toluene was prepared b y the acid hydrolysis of p-tolyl sulfonic acid. The resulting product was fractionated. Results: The results are giveii in Table I and are shown graphically in Fig. 3. It will be noted that the freezing point depression appears to be a linear function of the weight of solute per 1000gms. of benzene for all of the substances except acetic acid and methyl alcohol. The results in the case of ethyl alcohol are not sufficiently consistent to determine absolutely that no curvature exists but a straight line fits the data as well as any curve that could be drawn. I n the case of the other solutes there can be no doubt, in dilute solution a t least, as to the linear relation. There appear to be no data in the literature of high accuracy for very dilute solutions of the substances we have investigated except in the case of water. Richards, Carver and Schunibl determined the freezing-point depression of benzene saturated with water to be o.ogg°C which is close to our value of 0.0987~C.R e find by extrapolation that the solubility of water a t the freezing point is 0.3 j gm. per 1000 gms. of benzene. The toluene solutions were studied with the special purpose of determining the so called “molal freezing point” constant for benzene. Since even in the case of Henry’s law can not be assumed except as a limiting law results were obtained only in very dilute solutions. The value obtained in this way is 5. I I but the experimental error makes the last figure uncertain. The value calculated by equation (8) from the heat of fusion of benzene is j.0; but the most probable heat of fusion 30.4 cal/gm as estimated from numerous determinations in the literature must be uncertain by f percent.? The value which we shall adopt 5.10 appears to give satisfactory values for the apparent molecular weights at inflnite dilution for the various solutes and is probably not in error by more than one percent. In Fig. 4 the values of dm,!dT for the various solutes are plotted against the freezing point lowering. The values of dm/dT are obtained by graphical methods from the curves of Fig. I1 and are of course not of high accuracy except in the cases where the curve is linear. Since, assunling Henry’s law, the apparent molecular weight is j . I X dm, aT this quantity is also shown on the left side of Fig. 3. It should be noted in advance that an apparent molecular weight greater than the formula weight is easily accounted for as due, either to association or positive deviation from the ideal solution law, while a value less than the formula weight probably means error in the value estimated for am,’dT since negative deviations from the ideal solution law are not probable. I n the case of water and ethyl alcohol the apparent molecular weights are independent of concentration and equal respectively to 18.1 and 46.4 indicating no appreciable association of the vapors. Some association is indicated in the case of methy1 alcohol and the limiting value of 31.1 may be due to error or to one of the causes noted above. The case of acetic acid is that of a typical associated vapor. The value of 59 at infinite dilution is probably too low because of error in extrapolation. Undoubtedly acetic acid vapor is completely depolymerized a t low pressures and approaches the double forRichards, Carver and Schurnb: J. Am. Chem. SOC.,41, 2019 (1919). See Landolt-Bomstein-Roth: “Tabellen.”
A CRYOSCOPIC STUDY O F BENZENE SOLUTIONS
717
mula a t high pressures. Our measurements cover practically the entire range from complete dissociation to complete association but it is only a t the lower limit of concentrated that Henry’s law may be assumed to be anything more than a rough approximation. Molecular weights calculated over the rest of
-40.0
zoo
IO.0
2.0
F r e e z i n g Point L o w e r i n g
O
c
FIG.4
the range measurements must be regarded as approximations only. The case of benzoic acid is somewhat different. At the higher concentrations the vapor density corresponds to the double formula or even a greater degree of association, while the measurements have not been carried to sufficiently low concentrations to show the complete dissociation as in the case of acetic acid. The extrapolation to zero concentration is without significance. Henry’s law cannot be assumed to hold in any part of the measured range except as a rough approximation. I n view of the small vapor pressure of benzoic acid it is seen that the polymerized molecule of benzoic acid is a far more stable aff airkhan the polymerized acetic acid molecule.
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J. MERRIAM PETERSON WITH WORTH H. RODEBUSH
From the foregoing considerations one may draw the conclusion that for all of the solutes investigated, except benzoic acid, Henry’s law holds at least in the more dilute solutions; and that where the freezing point depression indicates polymerization an abnormal vapor density actually exists. The latter conclusion is, as shown in the beginning of this paper by thermodynamic reasoning, a necessary consequence if the first is true.
sAn exact equation has been derived from thermodynamics, which relates the freezing point depression of a dilute solution to the vapor density of the solute. Data are given for the freezing point lowerings of dilute benzene solutions for a number of solutes. The vapor densities of the solutes are calculated from the freezing point data. Urbana, Illinois.
