Journal o f Solution Chemistry, Iiol. 1, No. 3, 1972

Apparent Molar Volumes of Urea in Several Solvents as Functions of Temperature and Concentration

Diane Hamilton 1,2 and R. H. Stokes 1,3

Received July 19, 1971

Apparent molar volumes of urea are measured over a temperature range in water, methanol, ethanol, formamide, D M F and DMSO. The limiting apparent molar volumes show a large variation in different solvents. In marked contrast to the situation in water, the temperature dependence of the limiting apparent molar volumes in the nonaqueous solvents is slight. The concentration dependence is discussed qualitatively in terms o f solute association.

K E Y W O R D S : Urea ; apparent volume ; polar solvents ; thermodynamics.

1, INTRODUCTION

One of us has reported measurements (1) of the apparent molar volume of aqueous urea at 0~ and 25-50~ The limiting apparent molar volumes (4 ~ showed a marked increase with temperature, especially at low temperatures. It was suspected that this was due to "water structure" effects. This conclusion would be strengthenedby (a) demonstration that the effect is peculiar to water, and (b) more comprehensive measurements in the range 0-25~ The present work provides these supporting data. The nonaqueous solvents used are methanol, ethanol, and formamide, which are hydrogen-bonded liquids, and dimethylformamide and dimethylsulfoxide, which are highly polar liquids probably not involving hydrogen bonds. (It is not practicable to study urea in nonpolar solvents owing to solubility restrictions.) The new measurements in water were made at 1, 3, 5, 10, 15, and 25~

i Department of Physical Chemistry, University of New England, Armidale, New South Wales, Australia.

z Now Diane Beaumont. 3 On leave (1971) at the Research School of Physical Sciences, Australian National University,

Canberra, Australia.

2 1 3

�9 1972 Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011.

214 Hamilton and Stokes

~

0

Z 0

m

T

T

?

o o o

I I • • •

oo oo

~ ~ ~ .

+,~ o

Apparent Molar Volumes of Urea in Several Solvents 215

2. M A T E R I A L S

Urea was Mann Research Laboratories ultrapure biochemical grade, dried in a vacuum desiccator to constant weight. Methanol was prepared from commercial 99.95 ~ material dried by the method of Bjerrum and Lund ~2) and distilled through an 80-cm Dixon-ring column. Ethanol was first dried from 9 5 ~ A.R. solvent with quicklime, and finally dried and distilled as for methanol. Dimethylformamide was dried first by shaking with Ca l l / f o r 2 days, then by molecular sieves, and vacuum distilled through a Vigreux column at 15 torr. Formamide was fractionally crystallized (to F.P. 2.4~ and then dried over anhydrous sodium sulfate for two days. This was followed by fractional distillation at 0.1 torr. The product was stored in a sealed flask under dry argon. Dimethylsulfoxide (Fluka analytical grade material) was dried over freshly ignited CaO for 2 days and then passed through AW 500 molecular sieve, and finally triply distilled under reduced pressure.

Some physical properties of the solvents are listed in Table I.

3. M E A S U R E M E N T S

Apparent molar volumes in dilute solutions are best obtained by dilato- metric methods, which avoid the need for direct measurement of small density differences. When the solute is a solid, it is necessary to use in the dilatometer a stock solution of concentration high enough to permit establishing the appar- ent molar volume of the solute in it with the needed accuracy by direct density measurement. This stock solution is then mixed with pure solvent in the dilatometer. In the apparatus used by Hepler, Stokes, and Stokes (3~ and later by Dunn (5) for aqueous electrolytes, dilution was a one-shot process in which 3 to 12 cm 3 of the concentrated stock was mixed with 300-1000 cm 3 of water. This method, though extremely accurate, is scarcely practical for nonaqueous solvents owing to the large volumes of pure solvents required. Accordingly we used the continuous-dilution dilatometer recently designed in this laboratory (4> for liquid mixtures. The stock solution is placed in the burette arm of the dilatometer, and the pure solvent in the bulb. In this way a series of points covering the range from about 0.05 to 0.5 of the stock solution concentration is obtained. The relationship used is (3)

~v = ~bv(stock) + Av/nz

where b~)(stock) is the apparent molar volume of the solute in the stock solution, and by is that in the solution in the mixing bulb, when an amount of stock containing nz moles of solute has been added. If it is desired to fill in the range between e(stock) and 0.5c(stock) another run is made with the stock solution in the bulb and the solvent in the burette arm. The dilatometer was

216 Hamilton and Stokes

Table II . a A p p a r e n t M o l a r V o l u m e s o f U r e a in V a r i o u s So l v en t s as F u n c t i o n s

o f C o n c e n t r a t i o n a n d T e m p e r a t u r e , A c c o r d i n g to t he E q u a t i o n (~o ~ ~o + ac + be z

t, ~ ~b ~ a b c range a d o

Solvent: Methanol 5 37.349 1.067 -0.125 0.05-1.65 0.011 0.80534

10 37.339 0.972 -0.073 0.09-1.77 0.014 0.80070 15 37.174 1,118 --0.124 0.08--1.89 0.005 0.79606 25 36.97O 1.193 --0.122 0.12-1.55 0.002 0.78660 35 36.89S 1.148 --0.114 0.015--1.25 0.002 0.77710

Solvent: Ethanol 20 40.75 0.470 -0.433 0.03-0.30 0.003 0.78937 25 40.75 0.396 -0.152 0.06--0.43 0.002 0.78509 35 40.75 0.136 0.095 0.04-0.56 0.002 0.77641

Solvent: Formamide 5 44.86 0.097 - - 0.07-1.5 0.022 1.14606

10 44.983 0.079 - - 0.013-1.5 0.020 1.14174 25 45.343 0.0607 - - 0.097-2.4 0.003 1.12916

Solvent: Dimethylformamide 1 39.892 1.551 -0.664 0.03-0.86 0.010 0.96688 5 39.933 1.566 -0.641 0.05-0.82 0.011 0.96309

15 39.927 1.632 -0.666 0.10-0.89 0.013 0.95630 25 39.973 1.248 -0.283 0.05-1.72 0.010 0.94407

Solvent: Dimethylsulfoxide 20 41.816 0.354 0.019 0.06-0.61 0.003 1.10031 25 41.857 0.480 -0.096 0.04-0.87 0.003 1.09538 35 41.850 0.570 -0.194 0.07-0.69 0.006 1.08531 45 41.810 0.505 -0.098 0.02-0.92 0.004 1.07525

Solvent: Water 1 41.89s 0.412 -0.032 0.02-1.9 0.02 3 42.170 0.404 -0.041 0.05-1.8 0.01 5 42.408 0.292 - - 0.03-1.8 0.01

10 42.959 0.265 - - 0.04-1.7 0.02 15 43.404 0.199 - - 0.10-2.2 0.02 20 43.852 0.166 - - 0.08-1.9 0.02 25 44.238 0.135 - - 0.02-1.9 0.003

i

a Values of c are expressed in moles urea/liter of solution. The last three columns in the table give the concentration range and the standard deviation ~ of the experimental results from the equation, and the solvent density, if, a, b, and o values are in cm3-mole -I units, and d~ ir/g-cm- 3.

Apparent Molar Volumes of Urea in Several Solvents 217

contained in a thermistor-controlled thermostat constant to +0.001~ temperatures were measured with a certified platinum resistance thermometer.

Densities of the pure solvents and the stock solutions were measured in flask-type pycnometers, giving a reproducibility of +5 x 10 -6 g-cm -3. For volatile solvents, precautions were taken against vapor loss, and corrections were made for vapor mass above the liquids. The solutions were made up by weight. Vacuum corrections were applied throughout.

The results are given in Table II. Because some hundreds of individual re- sults are involved, the results for each system and temperature are given as the coefficients of quadratic equations in the concentration c(moles/liter), with the range of concentration covered and the standard deviations cr from the equa- tions. Since only a short extrapolation to zero concentration is involved, the uncertainty in 6o is comparable to the standard deviation quoted. The solvent densities are given in the last column in g-cm -3. The 6, a, b, and tr values are for cm3-mole -~ units.

4. D ISCUSSION

4.1. Limiting Apparent Molar Volumes

The limiting apparent molar volumes are plotted against temperature in Fig. 1. (The restricted temperature ranges for ethanol and DMSO are due respectively to the limited solubility in ethanol and to the freezing point of DMSO.) One noteworthy feature, is the large variation with solvent, from 37 cm3-mole -~ in methanol to 45 cm3-mole -~ in formamide, the latter figure being close to the molar volume of solid urea. Properties which might be expected to bear some relation to ~0 are the cohesive energy density AE,,/~', the dielectric constant E, the molar volume V, and the compressibility ft. These are listed in Table III along with the limiting apparent molar volume of urea at 25~ which temperature is common to all the solvents. The only clear correlation that emerges from Table III is that ~~ o increases as the compress- ibility of the solvent decreases: if the compressibility is regarded as a measure of the void space in the liquid, one could argue that this means that the solute molecule does not have to create a hole for itself of the full dimensions de- manded by its intrinsic size. (We have been unable to find a compressibility value for DMF, and venture the prediction that it should lie between 1.15 and 1:25 • 1 0 - 4 bar-1.)

4.2. Temperature Dependence of ~0

In all the solvents except water, ~o shows only a small temperature dependence. The results for methanol solutions are surprising in having a

218 Hamilton and Stokes

' e

D M S O o o o o

EfOH o o o

o 0 0 DMF

- - O - ' - - - - - - - - - - ~ e ~ M e OH

I I I I I I I ] 10 20 V~ 30 40 50

Fig. 1. Temperature dependence of the limiting apparent molar volume of urea in several solvents. | This work; �9 ref. 1 ; . . . . . solid urea.

Solvent

Table III. Solvent Properties and ff~ at 25~

F AEo/~ fl (footnote f ) (footnote g) E (footnote h)

~o (urea) (footnote f )

H 2 0 18.07 2297 e 78.30 0.457 44.24 MeOH 40.74 858 e 32.63 1.265 36.97 E tOH 58.68 678 ~ 24.30 1.145 40.75 Formamide 39.89 17304 109.03 b 0.4110 45.34 D M F 77.44 485 a 36.7 - - 39.97 D M S O 71.33 710 d 46.6 0.65 c 41.86

a Using latent heat of vaporization at bp., ref. 8. b F rom ref. 9.

F r o m Rayleigh light-scattering data, ref. 10. d F r o m ref. 11. e F r o m ref. 12.

In cma-mole -1 units. g In J-cm -3 units. h In bar -1 • 10 -4 units.

Apparent Molar Volumes of Urea in Several Solvents 219

negative slope; this .was carefully checked and appears to be genuine. The possibility that it might be connected with absorption of water by the anhydrous methanol was examined by repeating the 25~ measurements in methanol to which 0.1 ~ by weight of water had been added; the results were slightly higher than for the anhydrous methanol, and as might be expected diverged increas- ingly as dilution increased, so that the extrapolated value was N0.1 cm3-mole - higher in the presence of this small amount of added water. The observed change in q~0 between 5 and 35~ is, however, -0 .5 cm3-mole -1, so that one would have to postulate an unlikely and, moreover, smoothly temperature- dependent, water contamination to explain the observed negative slope.

The increase of 4 ~ with temperature in water is large by contrast. The present results (open circles) confirm the earlier conclusion (~) that the slope becomes more marked at low temperatures. This behavior seems characteristic of aqueous solutions in general rather than a peculiarity of urea solutions. It is shown, for example, by aqueous electrolytes (5) and sucrose (6) solutions. For potassium iodide, an electrolyte having a similar molar volume to urea, the increase wit h temperature is about twice as steep in the range 0-25~ Since the nonaqueous solvents are all highly polar and in some cases are known to be quite strongly associated, we must conclude that this feature of aqueous solutions is a consequence of the elusive phenomenon of "water structure." Indeed, one of our reasons for undertaking the present study was to seek a quantitative indicator of water structure, but this aim was defeated by the wide variation of q~0 in different solvents; this makes it difficult to guess where the q~o curve for "unstructured water" would lie.

Of fifteen nonelectrolytes in aqueous solution studied by Neal and Goring ~7~ only t-butanol shows a negative slope of q~v against temperature at 4~ In terms of the apparent specific volume (q~/mol.wt.) urea has the greatest positive slope of all those solutes with the exception of formamide.

4.3. Concent ra t ion Dependence of r Figure 2 shows, for 25~ only, the dependence of the apparent molar

volume on concentration in the six solvents, on the same scale as Fig. 1. The data for other temperatures can be obtained from the coefficients of Table II, where it will be seen that the slopes in the nonaqueous solvents show only minor changes with temperature. The water results show a systematic trend to smaller slopes as the temperature rises. The positive slopes of all the curves indicate positive excess volumes for all the mixtures; if the increase of apparent volume with temperature is attributed to a solute association reaction, (1) the associated species is required to have a larger apparent volume (per stoichiometric mole) than the unassociated form present at infinite dilution. This could come about through a solute dimer, for example, interacting more weakly w,_'th solvent

220 Hamilton and Stokes

c c c Formamlde x ~-

45

e ~ Water - - ~ •

' e

4 o

MeOH /

35 I _ I I 0"5 c//moledm "3 I '0 1"5 2"0

Fig. 2. Concentration dependence of the apparent molar volume of urea in several solvents at 25~ | Pycnometer; • dilatometer.

d ipoles than the monomer . More quant i ta t ive conclusions canno t be d rawn f rom the volumet r ic da t a alone. In a fol lowing pape r it is shown tha t the heats o f d i lu t ion o f u rea in these solvents assist in the in terpre ta t ion .

A C K N O W L E D G M E N T S

This work was assisted by a g ran t f rom the Aus t ra l i an Research G r a n t s Commiss ion . The senior au tho r thanks the Di rec to r o f the Research School o f Physics, Professor Sir Ernest Ti t te r ton , and the Head of the Diffusion Research Uni t , Dr. R. Mills, for their hospi ta l i ty at the Aus t ra l i an N a t i o n a l Univers i ty dur ing the p repa ra t ion o f the paper .

REFERENCES

1. R. H. Stokes, Australian J. Chem. 20, 2087 (1967). 2. J. Bjerrum and H. Lund, Bet. Deut. Chem. Ges. 64, 210 (1931). 3. L. Hepler, J. M. Stokes, and R, H. Stokes, Trans. Faraday Soc. 61, 20 (1965). 4. R. H. Stokes, B. J. Levien, and K. N. Marsh, J. Chem. Thermodyn. 2, 43 (1970). 5. L. A. Dunn, Trans. Faraday Soc. 64, 2951 (1968). 6. J. E. Garrod and T. M. Herrington, J. Phys. Chem. 74, 363 (1970). 7. J. L. Neal and D. A. I. Goring, J. Phys. Chem. 74, 658 (1970).

Apparent Molar Volumes of Urea in Several Solvents 221

8. A. J. Parker, Chem. Rev. 61, 1 (1969). 9. L. A. Dunn and R. H. Stokes, Trans. Faraday Soc. 65, 2906 (1969).

10. L. L. Haynes, R. L. Schmidt, and H. L. Clever, J. Chem. Eng. Data 15, 534 (1970). 11. T. B. Douglas, J. Am. Chem. Soc. 70, 2001 (1948). 12. J. Polak and G. C. Benson, J. Chem. Thermodyn. 3, 235 (1971).