OSMOTIC COEFFICIENTS OF CONCENTRATED AQUEOUS UREASOLUTIONS
1199
Osmotic Coefficientsof Concentrated Aqueous Urea Solutions from Freezing-Point Measurements
by R. H. Stokes' Institute for E n z p Reseurch ~ and Department of Chemistry, University o j Wisconsin, Madison, Wisconsin (Received October 86,1966)
In order to resolve an inconsistency between published freezing-point data and other thermodynamic properties, the freezing points of aqueous urea solutions have been measured in the range 1-8 M . The new results are shown to be consistent with isopiestic vapor pressure measurements and thermal properties, but show that the equations of Gucker and Pickard for the apparent molar enthalpy cannot safely be used for extrapolation outside their experimental temperature range, especially at high concentrations.
Introduction thermometer and a mercury-in-glass calorimeter thermometer, both calibrated by the National Bureau of The thermodynamic properties of aqueous urea soluStandards. The resistance thermometer was used at tions are of interest in connection with models for the an immersion of about 15 cm; tests at other immersion amide hydrogen b ~ n d and ~-~ with diffusion s t u d i e ~ . ~ , ~ depths showed that heat leakage along the stem and It is appropriate here to comment on an erroneous leads affected the reading by less than 0.001". Tests view4 that aqueous urea solutions are "nearly ideal." with various thermometer currents showed that a t The molal osmotic coefficient, at 4 M and 25" is 9 = the current used in the measurements (2.8 ma) the 0.891; the corresponding value for an ideal solution self-heating effect with this thermometer was less (ie., one with the water activity equal to the stoichiothan 0.001"; the resistance bridge was a Leeds and metric mole fraction of water) is tp = 0.965. CalcuNorthrup Model G2. When using the mercury therlations from the heat capacity and heat of dilution mometer, t,he entire apparatus and the shivering operameasurements of Gucker and PickardS have shown that tors were in a cold room held at approximately 2' in the departure from ideal behavior rapidly becomes order to minimize emergent stem corrections. The more pronounced as the temperature is lowered. mercury thermometer was not permitted to rise above Both Gucker and Scatchardg were unable to reconcile the freezing-point data of Chadwell and Politi10 with 25' isopiestic data and the thermal properties. The (1) On leave from University of New England, Armidale, N.S.W., Australia. more recent freezing-point measurements of Cavallero (2) J. A. Schellman, Compt. Rend. Trav. Lab. Carlsberg, Ser. Chim., and Indelli'' agree adequately with the other data, 29, 223 (1955). but extend only to 0.6 M . (3) G. C. Krescheck and H. A. Scheraga, J. Phys. Chem., 69, 1704 (1965). Accordingly, we report a new set- of freezing-point (4) M.Abu-Hamidiyya, (bid., 69, 2720 (1965). measurements in the region 1-8 M , ie., up to near ( 5 ) I. M. Klota and J. S. Franren, J . Am. Chem. Soc., 84, 3461 the eutectic point, from which we conclude that the (1962). work of Chadwell and Politi was in error. (6) J. G. Albright and R. Mills, J . Phys. Chem., 69, 3120 (1965). Experimental Section Since the freezing-point depressions of interest range from 1.8 to ll",ordinary thermometric methods sensitive to 0.001" are suitable. We have used an American Instrument Co. quartz sheathed platinum resistance
(7) R. H.Stokes, ibid., 69, 4012 (1965). (8) F. T. Gucker, Jr., and H. B. Pickard, J. Am. Chem. SOC.,62, 1464 (1940). (9) G. Scatchard, W. J. Hamer, and 9. E. Wood, ibid., 60, 3061 (1938). (10) H. M.Chadwell and F. W. Politi, ibid., 60, 1291 (1938). (11) L.Cavallero and Indelli, Gam. Chim. Itol., 8 5 , 993 (1955).
Volume 70, Number 4 April 1966
R. H. STOKES
1200
2" at any time in order to reduce bulb hysteresis error. It was found, however, that even if the thermometer was allowed to warm up to 25" before use, the zeropoint depression resulting from hysteresis was only 0.005". The equilibration vessel was a 20 X 2.5-cm glass tube fitted inside a 21 X 3.5-cm tube, which in turn was inside a dewar vessel containing an ice-salt mixture adjusted to slightly below the freezing point of the solution. The thermometer, the vertically moving mechanical helical stirrer of plastic-coated wire, and the passage for inserting the sampling needle passed through the stopper of the inner glass tube. The solution was placed in the central tube and frozen in a separate cooling bath until a suitable amount of ice had crystallized out before setting it in the apparatus. After about 10 min stirring, with temperature readings every minute, a long hypodermic needle was inserted through the stopper and down to the bottom of the solution tube. Further temperature readings were taken over 10 min; if the rate of change exceeded 0.001"/min, the dewar temperature was adjusted. When the temperature was sufficiently steady, stirring was stopped and about 15 sec was allowed for the ice crystals to float clear of the bottom of the tube. A 25-ml portion of the solution was then drawn off by means of the hypodermic syringe. Sampling was completed within 1 min of stopping the stirrer, so that temperature uncertainty during sampling was no more than 0.001". The samples were analyzed by density measurements at 25", since the highly precise data of Gucker, et a1.,I2 make possible accurate composition determination from density in this concentration range. The syringe and contents were warmed to 30" by warm water, then the syringe outlet was closed and the plunger pulled out a few centimeters, forming a vapor bubble. Vigorous shaking then degassed the solution sufficiently to prevent the formation of bubbles in the pycnometer. (This method of degassing solutions is highly recommended as it does not permit any signiiicant loss of water vapor such as occurs if pumping is used.) The pycnometer (volume -25 ml) was then filled directly from the syringe. A reproducibility of h l X 10-6 g ml-1 was obtained in the density measurements; vacuum corrections to all weighings were, of course, made. In the case of urea solutions, this precision in the density is equivalent to &0.07% in the molality of a 1 M solution, and proportionately less at higher concentrations. The urea used was of analytical reagent quality. For some of the measurements, material recrystallized from water (not heated above 60"), washed with cold ethanol, and dried on the filter pump and then The Journal of Physical Chemistry
at 55" to constant weight was used. This material gave results indistinguishable from the analytical reagent grade product. All solutions were used within a few hours of making up. Electrical conductivities were measured on each batch of material and showed negligible amounts of ionic impurities. Biuret tests were also negative. Solutions made up by weight from dried material were used to check the density measurement technique; molalities determined from the solution densities agreed to 0.1% or better with the weight compositions. Of some interest in connection with the purification of the urea was the observation that material recrystallized from absolute ethanol (temperature not above 60") and dried to constant weight at 55" was apparently impure: solutions of this material when analyzed by density gave molalities some 0.6% lower than those based on the weights of dry solid and water, and the molal freezing point depressions (AT/m) were 0.6 to 1% higher than those of the good material. It was thought possible that some contamination with urethane had occurred through reaction with the alcohol. It would seem advisable to avoid the use of hot alcohol in the purification of urea. From the density of the samples withdrawn from the freezing-point apparatus, molarities (c) and subsequently molalities (m) were calculated from the equation12for 25' d
- do
= 1.59686 X 10-*~-
1.3958 X 10-4c2
+ 2.593 X 1 O - V
(1)
which is readily solved for c by successive approximations.
Results and Discussion Table I gives the molalities and freezing points of the solutions studied. As the molal fp depression AT/m falls rather rapidly with increasing concentration, the arbitrary deviation function 2 =
AT
+ 0.09488~- 0.005117m2 m
(2)
was used to represent the experimental results and to compare them with other work. Figure 1 shows that there are no systematic differences between the analytical reagent material and the recrystallized material, nor between the results from the platinum resistance thermometer and the mercury thermometer. The results of Cavallero and Indellill are seen to be consistent with ours except for their two highest concentra(12) F. T.Gucker, Jr., F. W. Gage, and C . E. Moser, J . Am. Chem. SOC.,60, 2582 (1938).
-
OSMOTIC COEFFICIENTS OF CONCENTRATED AQUEOUS UREASOLUTIONS
t t
L 2
0
1
A
i
m
6
4
L 8
Figure 1. The deviation function x defined by eq 2 for the freezing points of aqueous urea solutions: 0 , this work, platinum resistance thermometer, recrystallized urea; 8, this work, platinum resistance thermometer, ACS grade urea; 0,this work, mercury thermometer, ACS grade Cavallero urea; A, Chadwell and Politi (ref 10); and Indelli (ref 11).
+,
Table I : Freezing-Point Depressions for Aqueous Urea Solutions ma
AT^
ZC
Notea
1.0425 1.0603 1.594 1.746 1.761 2.338 2.905 3.063 3.182 3.774 3.849 3.862 4.396 4.418 5.011 5.766 6.439 7.047 7.167 7.523 8.053
1.830 1.860 2.736 2.983 3.000 3.894 4.730 4.954 5.122 5.977 6.069 6.097 6.814 6.843 7.613 8.581 9.431 10.162 10.308 10.775 11.375
1.849 1.849 I . 855 1.859 1.855 1.859 1.861 1.860 1.860 1.869 1.866 1.869 1.868 1.868 1.866 1.865 1,864 1.857 I . 861 1.857 1.847
d e
f
e
tions. With the sole exception of their eutectic point results, the data of Chadwell and Politi'O disagree with both ours and those of Cavallero and Indelli.' It is difficult at this distance in time to seek an explanation of the discrepancy; we are, however, satisfied that our results are more correct. As a check on the performance of our apparatus, we made a measurement on potassium chloride, obtaining m = 0.9759, A T = 3.189". From Scatchard'sl3 very precise measurements on potassium chloride, the value of AT for this molality is 3.186". From the internal consistency of our results we believe that osmotic coefficients derived from them should be reliable to j=O.OOl. Table I1 gives osmotic coefficients at round molalities, calculated from the equations14 55.51 #J=-In aw
e
d d d d
f e
d d d d
f d e
(3)
m
-log aw = 0.004207AT
+ 2.1 X 10-'jAT2
(4) These osmotic coefficients refer to solutions at their respective freezing points. Conversion to 0" or to 25' presents some difficulty in spite of the fact that thermal data are available down to 2". Gucker and Pickard* give equations for the relative apparent molar enthalpy of aqueous urea at temperatures from 2 to 40', based on their measurements of heats of dilution (aL2)at 25" and the heat capacity measurements of Gucker and Ayres. l5 While the equation for 25" reproduces their heat of dilution measurements very well, we find that the equation for the relative partial molar heat capacity of the solute, obtained by differentiation of their expressions for GLP with respect to temperature, is
d d
~~~
~
Table 11: Freezing Points and Osmotic Coefficients a t the Freezing Point for Aqueous Urea Solutions a t Round Molalities m
FP, 'C
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
-0.9035 -1.760 -2.583 -3.375 -4.137 -4.871 -5.588 -6.282
0.972 0.947 0.927 0.909 0.892 0.875 0.861 0.847
m
Fp, "C
"FP
4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0
-6.951 -7.605 -8.247 -8.882 -9.510 - 10.126 - 10.742 - 11.332
0.8335 0.821 0.810 0.800 0.790 0.782 0.774 0.766
f
'
AT is the freezing-point a m = moles of urea/kg of water. depression. x = AT/m 0.09488m - 0.005117me. Mercury thermometer; Mallinckrodt ACS grade urea. e Platinum Platinum resistance thermometer; recrystallized urea. resistance thermometer; Mallinckrodt ACS grade urea.
+
1201
'
(13) G. Scatchard and S. 5. Prentiss, J. Am. Chem. SOC.,5 5 , 4355 (1933). (14) R. A. Robinson and R. H. Stokes, "Electrolyte Solutions," 2nd ed, Butterworth and Co. Ltd., London, 1959, Chapter 8. (15) F. T. Gucker, Jr., and F. D. Ayres, J. Am. Chem. SOC.,59, 2152 (1937).
Volume YO, Number 4 April 1966
R. H. STOKES
1202
less satisfactory in reproducing the heat capacity data, especially at low temperatures and high concentrations. In the extreme case, at 2" and 8 m, the equation gives A@cpp = 6.9 cal mole-' deg-l in contrast with the experimental value of 12.2 cal mole-' deg-1. Furthermore, the equations yield values which with increasing molality reach a maximum and turn down again, in contrast to the monotone rise of the experimental values. Since the quantity required in converting the osmotic coefficient from 25" to other temperatures involves the slope of the curve of aL2us. m, the use of these equations is clearly not acceptable at high concentrations. Any extrapolation below the lowest experimental temperature of the heat capacity data is even less desirable. Accordingly, we have preferred to compare the 25" isopiestic data with our freezingpoint values in the followingway. The temperature dependence of the osmotic coefficient 4 is given by (5)
where &, the relative partial molar enthalpy of the solvent in the solution at temperature T, is given by
Using standard thermodynamic relations (6) transforms to &(T)
=
-q(-) +
- 55.51 ahaL, In m
298O
and hence (5) in terms of experimentally available thermal quantities becomes RT2-d4 = dT
(-)
- aaLI a In m 2980
sT (-)
b@CP*
2980
a In m
dT
(8)
T
The first term on the right of (8) is evaluated from the equation of Gucker and Pickard18which fits these data very well. The second we have evaluated by graphical differentiation. Normally, this method is not as good as analytical procedures, but in this case it happens becomes almost linear that at high concentrations aCpr in In m, so that the slope is readily determined. As a check, the slopes were also determined from graphs of aCp,us. m followed by multiplication by m, with good agreement with the first method. The integration in (8) was then made by graphical-tabular methods. Finally, eq 5 wm integrated similarly to give $(=) in terms of &gBo. The recent extremely careThe Journal of Phyedcal Chmistry
I
I
I
I
I
I
I
1
1
I
Figure 2. Osmotic coefficients of urea a t various temperatures: 0, 25' isopiestic values; 0, calculated from 25' isopiestic data and thermal properties of solutions as in text; e, freezing-point data from Table 11.
ful isopiestic vapor pressure measurements of Ellerton1s were used as the source of the 42980 values. By ) temperatures this method we have calculated t # ~ ( ~for down to 2", the lowest temperature at which the thermal data are available. The variation of aCp2 with temperature becomes increasingly rapid as the temperature is lowered, so that no great reliance can be placed on even short extrapolations. Hence, rather than below 2" and thus estiattempt to guess values of aCp, mate corrections to 4 from the freezing points to 25", we prefer to present the data as the temperature dependence of the osmotic coefficient (Figure 2). The lines extending below 2" in the figure seem to us to be reasonable extrapolations from the 25-2" data, and agree quite satisfactorily with the freezing-point data. There are possibly discrepancies of up to 0.003 in the osmotic coefficient at 2, 3, and 4 M . It is clear however, that there is no serious inconsistency between our freezing-point results, the 25" isopiestic data, and the thermal measurements. It must be concluded that the freezing-point data of Chadwell and Politilo were erroneous. Some of the discrepancy found by earlier investigators in the region above 4 M also seems to have arisen from the unsatisfactory fit of the equations of ref 8 to the heat capacity data of ref 4. Acdnowledgment. The author is indebted to the University of Wisconsin for its hospitality, and to the (16) H. J. Ellerton and P. J. Dunlop, to be published (private communication from P. J. Dunlop) : see also ref 9.
NMRSTUDY OF MOLECULAR COMPLEXES OF DMF
U. S. National Science Foundation for the award of a Senior Foreign Scientist Fellowship during the tenure of which this work was done. This work was supported in part by Public Health Service Research Grant No. AM-05177 from the National Institute of Arthritis
1203
and Metabolic Diseases. Thanks are also due to Dr. R. A. Robinson of the National Bureau of Standards for the loan of a calibrated thermometer, and to Mrs. J. M. Stokes for extensive assistance with the experimental work.
Nuclear Magnetic Resonance Study of Molecular Complexes of Dimethylformamide with Aromatic Donors1
by Antonio A. SandovaP Department of Chemistry, University of Missouri at Kansas City, Kansas City, Missouri
64110
and Melvin W. Hanna* Department of Chemistry, University of Colorado, Boulder, Colorado 80804 (Received October $1, 1966)
The complexes of dimethylformamide (DMF) with benzene, toluene, p-xylene, mesitylene, and durene have been studied by nmr spectroscopy. Equilibrium quotients for association and the chemical shifts of the two methyl groups in DMF in the pure complex have been determined. Contrary to an earlier suggestion, the complexes become stronger as the number of methyl substituents on the donor increases. The upfield shifts of the methyl protons in DMF in the pure complex become smaller, however, as the number of methyl groups on the donor is increased. This effect is very likely a measure of the decreased ring currents in the donor molecules as they become more substituted.
Introduction It is now well established that, in certain cases, nmr spectroscopy can be used to study molecular complex eq~ilibria.~The nmr method is especially valuable when it is applicable because it can give specific information about the geometry of the complex in solut i ~ n . ~ - ’Hatton and Richards, in studying solvent effects on the shifts of the two methyl proton resonances in dimethylformamide (DMF), have concluded that the DMF molecule must lie above the plane of the benzene ring with one methyl group approximately above the six-field axis of the benzene ring and the other methyl group off to one side.s Their postulated structure for the complex is
(1) Supported in part by the Directorate of Chemical Sciences, Air Force Oflice of Scientific Research, under Grant AF-AFOSR21&65. (2) NSF Summer Research Institute Participant. (3) Alfred P. Sloan Fellow. (4) M. W. Hanna and A. L. Ashbaugh, J . Phys. Chem., 68, 811 (1984). (5) J. V. Hatton and R. E. Richards, Mol. Phys., 5 , 139, 153 (1962). (6) J. V. Hatton and W. G. Schneider, Can. J . C h a . , 40, 1285 (1962).
Volume 70, Number 4 April 1966
