J. Phys. Chem. 1981, 85, 3480-3493
3480
extent of conversion obtained very small because of masking of the porphyrin absorbance by that of 13-.51 A more interesting reaction in terms of overall quantum efficiency involves the use of iodide in conjunction with molecular oxygen to intercept selectively oxidized porphyrin and reduced viologen, respectively, as outlined in eq 7-14. The net reaction occurring here is given by eq MV+ + 0 02-
2
MV2++ 0 2 -
(10)
HOy
(11)
-+
-+
+ H+
+ I- I. HOzHO2- + H+ HzOz HzO2 + 2HI 2Hz0 + 1 2 HO2.
-
(12) (13)
-.+ (14) 15; although this reaction is clearly energeticallydownhill, (15) 4HI + 0 2 --+ 212 + 2Hz0 it does not occur rapidly in the dark or in the absence of the porphyrin photocatalyst. The reaction is mechanistically interesting in that the protonation of superoxide (eq 11) generates an oxidant from what was initially a reducing radical (MV); in this way the photoreaction can provide a limiting quantum yield of 2 for iodide oxidation;
however, subsequent reaction of H20zwith HI (eq 14) (which is spontaneous!) indicates that the true limiting quantum yield is 4 . The reaction up to formation of H202 (eq 7-13) is an oxidiative counterpart to the tertiary amine mediated photoreduction of polypyridyl ruthenium(I1) complexes where deprotonation of an oxidized fragment provides the net generation of two reduced species per photon.52In the present experiments with [MV2+]= 0.005 M, [NaI] = 0.05 M, [SDS] = 0.02 M, and 1% PVA, we obtain 4+-(405nm) = 0.30 f 0.05; since each 1, comes from two oxidized iodide ions, the net efficiency of iodide oxidation is 0.60 or -15% of the theoretical reaction quantum efficiency. Here again, the reaction cannot be driven to large conversions because of competitive absorption by the product 1, complex. However, the moderately high overall initial efficiency for a reaction initiated by an excited-state electron transfer process in which both substrate and quencher may be recycled can be regarded as noteworthy and suggests that other useful applications in similar reactions can be forthcoming. Acknowledgment. We are grateful to the National Institutes of Health (Grant GM 15,238) for support of this research. We thank Professor M. S. Wrighton for helpful discussions concerning the applications with iodide ion.
Isotope Effects in Aqueous Systems. 12. Thermodynamics of Urea-h,/H,O and Urea-d4/D,0 Solutions Gy. Jaklit and W. Alexander Van Hook* Chemistry Depaftment, University of Tennessee, Knoxville, Tennessee 379 16 (Received: April 30, 1980; In Final Form: Ju/y 7, I98 1)
Differential vapor pressure measurements yielding osmotic coefficients and osmotic coefficient isotope effects for urea-h4/Hz0and urea-d4/D20solutions (4,8,12, 16,18, and 20 m, and saturated) are reported over the temperature range 15-60 "C. Solubilities and apparent molar volumes and their isotope effects (IE's) have also been measured. From these various data as supplemented by information from published sources, we have calculated standard-state (infinite-dilution)and excess partial molar free energies, volumes, enthalpies, and expansivities (and their isotope effects) as appropriate. Raman spectra in the librational and OH and OD stretching regions are reported. The various data are discussed in terms of solution models of the urea/water system in the context of the theory of isotope effects in condensed phases.
Introduction The thermodynamic properties of aqueous urea solutions are of interest in part because of the importance of this solute as a denaturing agent in protein chemistry.l This has stimulated a good deal of work focusing on the thermodynamic properties of transfer from water (or other solvents) to aqueous solutions of urea.2 For urea solutions themselves a critical analysis of data available through 1967 has been provided by stoke^,^ who also presents a rationalization of the solution thermodynamics of the urea-h4/H20system in terms of an association model. An alternative analysis of the excess thermodynamic properties of urea/HzO solutions was given by Frank and Franks.ls4 These authors assumed that addition of urea as solute shifted the equilibrium between solvent species in an assumed two-state model for water. The data availablel~~v~ included osmotic and activity coefficients gathered isopiestically at 25 "C5-' and at the freezing point,8 and extending to 20 m-(25 "C)and 8 m (fp), re'Central Research Institute for Physics, Budapest.
spectively. Additionally, integral heat of solution (25 "C, 0.3-18 m)? heat of dilution (5, 25, and 45 "C; 0.1-12 m),1° and heat capacity data (2-40 "C, 0.1-17 m)9*11were considered, as was information on the solubilities across the entire phase diagram12and the densities (0,25,30,40, and 50 "C to 10 m; 25 "C to 17 m; 1,3,5, and 10 "C to 2 m)?8J3 (1)Franks, F. In "Water; A Comprehensive Treatise"; Franks, F., Ed.; Plenum Press: New York, 1973;Vol. 2,pp 355,370. (2)Wetlaufer, D. B.;Malik, S. K.; Stoller, L.; Coffin, R. J. J. Am. Chem. SOC. 1964,86,509. (3) Stokes, R. H. Aust. J. Chem. 1967,20, 2087. (4)Frank, H. S.;Franks, F. J. Chem. Phys. 1968,48,4746. (5) Ellerton, H. D.; Dunlop, P. D. J. Phys. Chem. 1964, 70, 1831. 1938, (6)Scatchard, G.;Hamer, W. J.; Wood, S. E. J.Am. Chem. SOC. 60,3061. (7) Bower, V. E.; Robinson, R. A. J. Phys. Chem. 1963, 67,1524. (8)Stokes, R.H. J. Phys. Chem. 1966,70,1199.Stokes, R.H.; Hamilton, D. J. Solution Chem. 1972,1, 213. (9) Egan, E. P.; Luff, B. B. J. Chem. Eng. Data 1966,11,192. 1940,62,1464. (10)Gucker, F. T.;Pickard, H. B. J. Am. Chem. SOC. Stokes, R.H.; Hamilton, D. J. Solution Chem. 1972,1, 223. (11)Gucker, F. T.; Ayres, F. D. J. Am. Chem. SOC.1937,59, 2152. 1934,56,848. (12)(a) Miller, F. W.; Dittmar, H. R. J.Am. Chem. SOC. (b) Shnidman, L.;Sunier, A. A. J. Phys. Chem. 1932,36,1232.
0022-3654/81/2085-3480$01.25/00 1981 American Chemical Society
Isotope Effects in Aqueous Systems
The Journal of Physical Chemistry, Vol. 85, No. 23, 1981 3481
T A B L E I: T h e r m o d y n a m i c Properties of Urea-h, quantitya
e,.
S. AH.form G:IT melting temp AH(fusion)
temp,
"C
25 25 25 25 26 132.6 132.6 0 25 50
value
ref
93.14 J / m o l 104.6 J / ( m o l d e g ) -333.1 k J / m o l - 333.39 k J / m o l -660.8 J/(mol deg)
21 25 22 23 29 12a 24 26 26 26
13.6 k J / m o l 45.08 cm3/mol 45.49 cm3/mol 45.72 c m 3 / m o l a The superscript ( 0 ) designates the crystal reference state.
v.
Since the early seventies new enthalpy,14J5density,15J6and adiabatic cornpressibilityl6 data have appeared, but only a t 25 "C, and only over a limited concentration range. Data on the solution thermodynamics of the urea-d4/ DzO system are quite limited. Choi and Bonner17 have reported apparent molar volumes (0, 25, and 40 "C to 8 m),but the results are in very poor agreement (25 "C) with those of Philip, Perron, and Desnoyers.15 The latter authors also report apparent molar heat capacities (25 "C) but only at two concentrations below 1 m. Also, Bonner18 has reported isopiestically determined osmotic Coefficients at 25 "C (vs. NaCl/DOD) but he employed the isopiestic standard of KerwinIg which was later shown to be in error.20 Thus, little or no reliable thermodynamic information was available for the deuterio system at the time that we initiated the present study. In order to define a reference standard state for the solution process, thermodynamic data on the pure crystal, the supercooled liquid, and the real vapor are useful. For urea, however,+,&hermodynamicmeasurements on the high-tempereature solid or on the liquid are complicated by irreversible isomerization to ammonium cyanate and/or other decomposition, and reliable information is not available above 40 or 50 "C. That which we have located in the temperature range of interest (273 K to the melting point) is summarized in Table I. It is worth noting that the heat capacity data of Ruehrwein and HuffmanZ1end a t 45 "C, and therefore it is not possible to calculate the standard thermoydnamic properties at higher temperatures with confidence. The enthalpies, entropies, and free energies of formation found in various standard references based on the heat of combustion determined by Huffmann have been corrected by using the recently recommended values of Johnson.23 The enthalpy of fusion determined by Zordan, Hurkot, Peterson, and Hepler by DSC techn i q u e ~while , ~ ~ not of high precision, is certainly more reliable than the often quoted (ref 25, for example) value of 14.52 kJ/mol derived from the temperature coefficient of solubility of aqueous urea.lZa That result is certainly ~
~
~
~~~~~~
(13)Gucker, F.T.; Gage, F. W.; Moser, C. E. J. Am. Chem. SOC. 1938, 60,2582. (14)Cabani, S.;Conti, G.; Martinelli, A,; Matteoli, E. J. Chem. SOC. Faraday Trans. 1 1973,69,2112. (15)Philip, P. R.;Perron, G.; Desnoyers, J. E. Can. J. Chem. 1974,52, 1709. (16)LoSurdo, A.;Shin, C.; Millero, F. J. J. Chem. Eng. Data 1978,23, 197. (17)Choi, Y.S.;Bonner, 0. D. 2.Phys. Chem. (Wiesbaden) 1973,87, 188. (18)Bonner, 0.D.J. Chem. Thermodn. 1971,3,837. (19)Kerwin, R. E. PbD. Thesis, University of Pittsburgh, Pittsburgh, PA, 1964. (20)Pupezin, J.; Jakli, G.; Jancso, G.; Van Hook, W. A. J. Phys. Chem. 1972,76,743. Chan, T. C.; Jakli, G.; Van Hook, W. A. J. Solution Chem. 1972,4, 71. (21)Ruehrwein, R. A.; Huffman, H. M. J . Am. Chem. SOC. 1946,68, 1759. (22)Huffman, H. M.J. Am. Chem. SOC.1940,62,1009.
in error because of the nonideality of the solutions (ref 3, vide infra). The crystal molar volumes as calculated from densities from three different sources26-28 are not in good agreement. The vapor pressure of the gas (73 t < 95 "C) has been reported by Suzuki, Onishi, and KoideaZ9 At 298.15 K extrapolation predicts a vapor pressure of 1.2 X loi torr. It is unfortunate that no information is available on the heat capacities, densities, or similar properties for either liquid or gas. Jancso and Van Hook30131and others32have pointed out that data on isotope effects on thermodynamic properties form useful probes in studies of the effect of intermolecular forces on the properties of condensed-phase molecules. This is because the isotope effects can be rather directly related to the condensed-phase partition functionsa which may be written down under the assumption of an isotope-independent potential energy surface (within the precision of the Born-Oppenheimer approximation). In the present paper we present new data on osmotic coefficients of urea-h4/HOH and urea-d4/DOD solutions (15-60 "C; 4,8,12,16,18, and 20 m and saturation). In HzO,the data therefore check, as well as supplement and extend the values calculated by Stokes from isopiestic measurements at 25 "C and freezing point and heat of dilution data. Those earlier results are over the ranges 0-40 "C and 0.5-12 rn. In addition to the osmotic coefficients and their isotope effects, we calculate and report activity coefficients and standard-state (infinite-dilution) free energies and their isotope effects to the saturation limit. For the calculation of standard-state properties, information on the solubility of the crystals is required, and this is reported. No previous measurement of the standard free energy of solution is available. From the various temperature coefficients of the data, standard-state and relative partial molar enthalpies and heat capacities and their isotope effects (asappropriate) are obtained. We also report new data on the densities of urea-h4/H20and urea-d4/D,0 solutions at 15, 25, and 40 "C. The ureah4/H20data are interpreted with the aid of an association model and isotope effect data are discussed in terms of the theory of isotope effects in condensed phases. Experimental Section Vapor Pressure Measurements and Solutions. Osmotic coefficients and osmotic coefficient isotope effects were calculated from differential vapor pressure measurements made on the University of Tennessee apparatus previously d e s ~ r i b e d .In ~ ~this ~ ~apparatus ~ (1980 configuration) the temperature is controlled (k-0.0003 "C) by using a Tronac PTC-40 thermostat. Temperature is measured with ~
(23)Johnson, W. H. J. Res. Natl. Bur. Stand., Sect. A 1975,79,487. (24)Zordan, T. A.; Hurkat, D. G.; Peterson, M.; Hepler, L. G. Thermochzm. Acta 1972,5,21. (25)Landolt-Bornstein "Tabellen"; Springer-Verlag: Heidelberg, 1961;Band 11, Teil 4,p 358. (26)Landolt-Bornstein "Tabellen"; Springer-Verlag: Heidelberg, 1971;Band 11, Teil 1, p 692. (27)Weast, R. C., Ed. "Handbook of Chemistry and Physics", 52nd ed.; Chemical Rubber Publishing Co.: Cleveland, OH, 1972;p C530. (28)Worsham, J. E.; Levy, H. A.; Peterson, S.W. Acta Crystallogr. 1956,IO, 319. Jpn. 1956,29, (29)Suzuki, K.; Onishi, S.; Koide, T. Bull. Chem. SOC. 127. (30)Jancso, G.; Van Hook, W. A. Chem. Reo. 1974,74,689. (31)Jancso, G.; Van Hook, W. A. Acta Chim. Acad. Sci. Hung. 1978, 98,183. (32)Bigeleisen, J.; Lee, M. W.; Mandel, F. Annu. Reu. Phys. Chem. 1973,24,407. Wolfsberg, M. Acc. Chem. Res. 1972,5,225. Friedman, H. L.;Krishnan, C. V. In F. Franks, Ed. "Water; A Comprehensive Treatise"; Franks, F., Ed.; Plenum Press: New York, 1973; Vol. 3, Chapter 13. (33)Bigeleisen, J. J. Chem. Phys. 1961,34, 1485. (34)Jakli, G.;Van Hook, W. A. J . Chem. Eng. Data 1981,26, 243.
3482
The Journal of Physical Chemistty, Vol. 85,No. 23, 1981
a platinum thermometer calibrated in our laboratories and a G-2 Mueller bridge. The differential pressures generated between solvent and solution, or between the solutions of the different isotopic isomers, are measured by differential capacitance manometers using Datametrics 521 and 531 transducers with a 1018 controller/readout unit. Calibration procedures have been discussed.34 For the measurements reported in this paper, final calibration was effected by measuring the pressure differences generated between pure water and aqueous sodium chloride solutions. Standard pressures thus generated were obtained from the temperature by using results of the thermodynamic analysis of Clarke and G l e ~ This . ~ ~calibration technique has the advantage of exposing both sides of the capacitance gage to water vapor during the calibration just as they are in the experiments themselves. Experience with this apparatus has shown that the precision is limited by the differential capacitance manometry and is -0.2 70 of AP/P. Materials. Laboratory distilled water was treated with basic potassium permanganate and redistilled 2 times in an all-glass apparatus. Heavy water obtained from Merck and Co. (analytical grade) was used without further purification. H/D analysis of heavy water samples was made from the densities by using a Mettler-Paar densitometer.36 Urea (Fisher analytical grade) was recrystallized from water and dried under vacuum to constant weight while maintaining the temperature below 40 OC to minimize decomposition. We found no detectable difference between the osmotic coefficients of solutions made from the recrystallized or untreated analytical-grade material. Stokes3 earlier made the same observation. Four different samples of deuteriourea were employed (Stohler Isotopes or Merck). In each case purity was checked by melting point (vide infra) and (if necessary) the sample purified by equilibration with heavy water (near 0 "C), recrystallization, and vacuum drying at room temperature. A 20 m stock "mother" solution was prepared gravimetrically and diluted as appropriate with heavy water from the sample previously equilibrated with the urea-& By this technique identical isotopic composition for all solutions were ensured. Both normal and heavy water solutions were prepared gravimetrically and then degassed on the vapor pressure apparatus. Ca. 25-mL samples are required, and the gravimetrically calculated original concentrations were corrected for solvent loss to the vapor phase as the temperature of the measurements increased. Melting points were determined by the capillary method. We were particularly interested in the isotopic difference in melting point, as the value for pure urea is well established (132.6 "C), and employed a Beckman thermometer for the measurements. Densities were measured with a Mettler-Paar densitometer by using techniques previously reported from this lab~ratory.~~ Solubilities were determined gravimetricallyby sampling the liquid phase of an equilibrated crystal/solution mixture and evacuating to constant weight at room temperature except for the high-temperature point near 60 "C which was obtained by determining the dissolution temperatures of gravimetrically prepared samples. Raman spectra were recorded by using a Jobin-Yvon Ramanor 2000M laser-Raman spectrophotometer with a (35) Clarke, C. W.; Glew, D. N., private communication. (36) Dutta-Choudhury, M. K.; Van Hook, W. A. J.Phys. Chem. 1980, 84, 2735.
Jakli and Van Hook
TABLE 11: Osmotic Coefficients of Urea-h,/H,O Solutions Obtained from Differential Pressure Measurements, 6J" = P H ' ( ~-) PH(m,t)
t , "C 6.64 10.90 15.15 19.34 23.54 27.69 19.94 24.09
t . "C m = 4.00114 0.867 28.10 0.871 32.06 0.877 36.04 0.883 39.95 0.889 44.04 0.894 48.07 0.886 52.08 0.891 56.05
0.895 0.899 0.904 0.906 0.909 0.914 0.914 0.914
7.65 18.08 26.42 30.37 34.23 38.15
m = 8.0040 0.812 42.32 0.825 46.50 0.838 50.63 0.841 54.94 0.845 59.11 0.850 63.17
0.854 0.857 0.860 0.861 0.863 0.859
9.75 13.79 17.99 22.22 26.36 30.58 34.66
m = 11.9859 0.784 34.66 0.791 38.91 0.799 43.08 0.805 47.09 0.811 51.31 0.816 55.47 0.820
0.819 0.824 0.828 0.831 0.833 0.834
33.43 37.90 42.02 46.35 50.49 54.47 58.54
m = 15.9774 0.803 60.43 0.806 29.45 0.806 33.83 0.807 38.13 0.808 42.59 0.812 47.04 0.812
0.811 0.797' 0.801' 0.805' 0.807' 0.809'
29.91 31.99 36.04 40.31 44.54
0.779 0.779 0.783 0.786 0.788
6
m
6
= 19.9932
48.78 52.94 57.04 61.09
0.790 0.793 0.794 0.795
' m = 15.9978. 1-m double monochromator. A Spectra-PhysicsModel 171 argon ion laser was used at a power of 0.2 W at 5145 A for excitation.
Results Osmotic coefficients for 63 data points at concentrations of 4,8,12,16, and 20 m and ranging to temperatures near 60 "C are presented in Table I1 and Figure 1. These data were obtained from differential pressure measurements at temperature t between solvent water and solution (concentration, m), 6P = PH"(t) - PH(m,t). Osmotic coefficient isotope effects obtained from differential pressures of urea-h4/Hz0and urea-d4/Dz0 solutions at the same aquamolality and temperature, hp = PH(m,t) - PD(m,t),are reported in Table 111. Osmotic coefficients for the saturated solutions obtained by differential pressure measurements, 6Py(satd) = PY"(t) Py(m,,t),where s refers to saturation and Y = H or D, are found in Table IV. The results of our measurements of solubility, solubility isotope effect, and melting point isotope effect are found in Table V. Measurements of partial molar volumes and their isotope effects are reported in Table VI. Osmotic coefficients for the unsaturated solutions (Table 11)were calculated from the pressure differences by using eq 1. In this process, P H " was calculated from the tem-
The Journal of Physical Chemktry, Vol. 85, No. 23, 198 1 3483
Isotope Effects in Aqueous Systems
la
.90
TABLE 111:
Osmotic Coefficient Isotope Effects Obtained from Differential Pressure Measurements,
A P ( m , t ) = P ~ ( m , t ) -PD(m,t)
,d
t,"C
t .J
Figure 1. Osmotic coefficients of urea-h,lH,O solutions: (0)experimental points: (-) eq 3; (- - -) Stokes (ref 3). Isopiestic (25 "C) measurements: (0) Ellerton and Dunlop;' (A) Scatchard, Hamer, and Wood;' (*) Bower and R~binson.~
m perature by using the relation given by Wexler and G r e e n ~ p a nthe , ~ ~partial molar volume of the solvent was taken from Stokes3 or present data, and the virial coefficients were taken from Dymond and Smith.38 For calculations of the isotope effect on 4, a difference equation can be written A@ = $JH- @D =
+m 55.508
A In R (2) m where correction terms in P and b have been dropped as they are readily shown to make a negligible contribution. The term In ( P H I P D ) is readily obtained from the measurements and eq l; the pure solvent vapor pressure isotope effect (VPIE) has recently been remeasured by Jakli and Van Hook on the present apparatus and reported e1sewhe1-e.~~ The present measurements in H 2 0 are compared with other results in Figure 1. Except for a few data derived from measurements of the freezing point depression: all earlier work3,&' is based on 25 "C isopiestic measurements against NaCl as the reference. The results of stoke^,^ Ellerton and Dunlop: Scatchard, Hamer, and Wood! and Bower and Robinson' are in excellent isopiestic agreement with each other. Those differences which do exist (see, for (37) Wexler, A.; Greenspan, L.J. Res. Natl. Bur. Stand., Sect. A 1971, 75,213. (38) Dymond, J. H.;Smith, E. B. "The Virial Coefficients of Gases"; Clarendon Press: Oxford, 1969.
lo4*
(A 1 n R )
104.
t,"C
(A 1 n R )
3.82 8.75 12.86 17.02 21.12 25.25 25.33
m = 3.9643 22 29.37 21 29.39 14 33.54 8 37.70 5 42.00 2 46.24 3 50.52
4 2 -2 2 1 8 9
24.64 29.14 33.45
m = 3.9787 4 37.79 3 47.18 2 51.42
4 8 14
7.13 8.51 11.02 14.71 ia.54 22.32 26.26 30.26
m = 7.9926 28 34.09 24 37.89 25 41.56 27 45.53 24 49.50 23 53.48 22 57.25 18
6.32 8.73 10.98 15.60 20.10 24.53 29.01
m = 7.9953 24 33.48 24 37.92 24 42.47 23 47.00 24 51.47 21 55.97 22 60.40
12.93 15.95 21.71 26.05 30.41 39.12
m = 12.0112 51 43.39 52 47.63 44 52.04 43 55.85 40 58.90 35
23.34 26.51 28.79 32.01
m = 15.9828 52 23.33 44 25.53 42 28.78 39 32.23
23.99 28.52 33.05 37.45 42.38
m = 17.9885 37 46.78 35 51.07 35 51.12 36 54.92 38
28.46 32.89 37.32
m = 17.9953 47 41.70 35 46.04 37 50.49
26.59 30.77 35.15 39.50 43.77
m = 19.9944 54 48.85 53 53.06 50 57.34 46 61.56 43
20 19 22 23 27 25 28
24 24 25 26 29 29 26 36 60 38 39 38
51 40 41 36 38 40 41 42
33 37 42 40 40 41 40
a A In R = In PHo(t)/PDo(f) - In P H ( m , f ) / P D ( m , t=) ( m / 55.5) A@.
example, the data points plotted at 8 m and 25 "C in Figure 1) are accounted for by the selection of different isopiestic standards by the several groups. Since the data which we report are in quantitative agreement a t 25 "C with the smoothing relation suggested by Stokes (25 "C, 0-20 m), we have elected to express our data in terms of
3484
The Journal of Physical Chemlstty, Vol. 85,No. 23, 1981
TABLE IV Osmotic Coefficients of Saturated Solutions of Urea-y,/y,O from Differential Pressure Measurements, 6Pv(satd)= Pv"(f) - Pv(ms,tp urea-d, in D,O
urea-h, in H,O t. "C 25.00 28.86 24.99 29.45 34.23 34.30 38.95 39.04 44.12 48.70 53.14 55.99 60.44 38.81 5.26 5.29 7.40 7.41 9.93 14.59
t, "C 18.28 22.37 31.06 40.27 43.01 47.45 51.90 56.25 59.19 14.47 18.12 21.04 23.08 25.40 27.45 29.71 32.84 35.02 38.34
6
0.777 0.776 0.777 0.772 0.768 0.768 0.764 0.763 0.758 0.752 0.743 0.736 0.720 0.763 0.779 0.780 0.778 0.780 0.779 0.778
6 0.764 0.765 0.764 0.756 0.753 0.750 0.743 0.735 0.727 0.766 0.766 0.767 0.768 0.767 0.764 0.763 0.762 0.761 0.759
IE's from Measurements on Saturated Solutions at Rounded Concentrations 104. f,W A6S ( A In R ) 12 2.85 0.013, 43 16 15.21 0.011, 48 20 25.17 0.010, 51 24 33.48 0.009, 52 28 40.59 0.008, 49 32 46.77 0.006, 44 36 52.21 0.005, 36 40 57.07 0.004, 25 a
y = H or D.
TABLE V : Results of Solubility, Solubility Isotope Effect, and Melting Point Isotope Effect Measurements for Urea-h,/HOH and Urea-d,/DOD Solutions
t , "C 6.85 15.13 18.35 24.75 24.95 59.94 62.13a 132.6
In (XH,~)" -1.6534 -1.4965 -1.4428 -1.3334 -1.3255 -0.8378
A In (X)" 105[A(1/T)] 0.060 02b 4.031d 0.047 93b 3.285d
0.039 35b
2.76gd
0.024 13c
1.761b 0.607b
0
a Solution temperature of 97%urea-d,/D,O. Observed. Calculated from A ( l / T ) and eq 5. Calculated from A In X and eq 5. e X = mole fraction of urea.
an empirical difference equation referenced to the Stokes equation:
4JHht)=
@~*(m,25) + DT + E?
+FT'~'
10 I t I 60 "C (3)
In equation 3, $H*(m,25)is the expression given by Stokes? T = ( t - 25), and D, E, and F are least-squares parameters. 4J~*(m,25)= 1 + AX + Bx' x = m/(l + bm) (4) From ref 3 we have A = -0.042783, B = -0.0004198, and b = 0.15 with, we are told, an average deviation of S4* = 0.0005 unit. A least-squares fit of the points in Table I1 to eq 1 gives D = (1.47 f 0.04) X E = (-1.77 f 0.17) X with a variance of fit and F = (-7.5 f 3.9) X
Jakli and Van Hook
u2 = 5.7 X lo4. While the rms deviation of the present is larger than Stokes' average deviation fit, u = 2.3 X for the fit to 25 "C isopiestic data, u* = 5 X it is to be recognized that this later figure does not include any uncertainty in the $'s for the isopiestic reference. Also, in the present case, much smaller values for u would have been obtained had we elected (as did Stokes) to make individual fits with respect to temperature at the different experimental concentrations (or with respect to concentration at selected temperatures), thus minimizing small systematic differences between the data and eq 1, especially at higher concentrations and temperatures (cf. Figure 1). We, however, prefer the economy in number of parameters which is implicit in the single fit to the entire concentration-temperature data field. The vapor pressure experiments on the urea/water system extended well above 60 "C, but in every case a marked drop-off in the osmotic coefficients was observed to occur around 60 "C together with an increase in scatter. We have ascribed this behavior to decomposition or isomerization of the urea and have not included any data points above 60 "C in the least-squares analysis or in Table 11. The dotted linea shown in Figure 1 at 4, 8, and 12 m (0-40 "C)are those calculated by Stokes from freezing point and isopiestic 25 "C data, and the enthalpy of dilution and heat capacity data of Gucker and co-workers.9J0 Agreement with the present results is good except at 8 m. Since the smoothing relation, eq 1, is in good agreement with the temperature dependence of the present data at all concentrations investigated and disagrees with the Stokes calculation only at 8 m, we conclude that the present results are to be preferred. In a later section partial molar relative enthalpies, L1, derived from the present data are presented and discussed. Rounded values are presented in Table IX. Solubility, Solubility Isotope Effect, Melting Point Isotope Effect. These data are reported in Table V. For urea-h4/H20solutions the present measure.ments are in excellent agreement with Schnidman and SunierlZb(SS), as demonstrated in Figure 2A. Over the same temperature range, 6 < t < 60 "C, the data from other workers39scatter badly and are not further considered. The results of Miller and Dittmarl%(MD) at higher temperature, 68 < t < 132.6 " C , join smoothly to the curve defined by SS and the present results. Over our temperature range, 6 < t < 60 "C, the data show significant curvature on a In X vs. 1 / T diagram (Figure 2A) even though SS earlier reported a two-parameter fit to their data. Our improved fit to the 22 SS and 6 present data points is reported as eq 5. In In X H ,=~(-2070 f 117)/T + (17.496 f 2.56) -t (-2.086 f 0.380) In T 0 < t < 70 "C (5)
this equation XH,Bis the mole fraction of urea&( in the saturated solution. The variance of fit, u2 = 1.7 X corresponds to an uncertainty in the solubilities of -0.4%. Miller and DittmaP2*showed concern that the SS data did not logarithmically extrapolate to the melting point as would be required were the solution ideal. I t was for this reason that they reported data in the high-temperature region which, as expected, shows reverse curvature and extrapolates nicely into the melting point (XH = 1 at t = 132.6 "C). MD unfortunately oversimplified the analysis, fitted their high-temperature data to a two-parameter equation, In XH = A / T + B, interpreted A as an enthalpy (39) Shenkin, Y. S.;Zaikina, L. N. Zh. Fiz. Khim. 1978, 52, 1763. Pinck, L. A,; Kelley, M. A. J. Am. Chem. SOC.1926,47,2170. Speyers, W. A. Am. J.Sci. 1902,14,294. Krummacher,R. 2.Biol. (Munich) 1906, 46, 302. Janecke, M. 2.Electrochem. 1930,36,647.
The Journal of Physical Chemistty, Vol. 85, No. 23, 1981 3485
Isotope Effects in Aqueous Systems
TABLE VI ( A ) Apparent Molar Volume and Apparent Molar Volume Isotope Effects (cm3/mol)for Some Urea-h,/H,O and Urea-d,/D,O Solutions ~
~~
t , "C
m 14.9806 9.4882 4.7557 2.4024 1.1965 0.5996
15
dDDzO
17.9763 9.4519 4.7300 2.3905 1.2000 0.5973 doD,O= 1.104464, 99.77%D
25
40
17.9858 14.9395 9.4883 4.7098 2.4024 1.1965 0.5996
41.75 0.50 -0.099
ref,b 1 a
0
~
+
bm3'l or A @ = A@' 25 "C
43.46 f 0.01 0.53 i 0.03 0.212 i 0.008 -0.045 t 0.017 -0.031 i 0.002 0.0069 t 0.0042 *,1.8 *,8.9
A@;
a Aa b Ab
~3 ~
Excluded from least squaring.
9~ - @D
45.18 44.81 44.47 44.22 44.06 44.12
0.12 0.20 0.22 0.26 0.29 0.15a
0.25 0.32 0.37 0.44 0.52 0.48
0.16 0.18 0.19 0.20 0.22 0.15'
+ A a m t Abm"'
44.20 0.32 i 0.02 0.15 -0.027 f 0.009 -0.021 0.0039 f 0.0020 13,*,4.3
40 "C
50 "C
45.19 f 0.01 0.24 t 0.02 0.093 i 0.005 -0.011 f 0.005 -0.012 f 0.001 0.0016 f 0.0010 *,1.4 *,5.1
45.60 0.095 -0.015 3
An asterisk denotes this work.
of solution, and improperly used it to calculate the enthalpy of fusion of urea-h4since they assumed the solutions were ideal. That error has since propagated%even though a more recent value for iVIH(fusion) obtained by DSC experiments has become available (ref 24, Table I). It is clear that in the limit XH 1, the solution approachesthe Raoult's law limit and the slope of Figure 2A should approach (-RP)(MH(fusion)). A comparison between the solubility and thermal data is made in Figure 2A, and we conclude (see insert to the figure) that the limiting slope of the solubility data is consistent with the thermal d a h z 4 The marked departure from this slope, however, as the water activity increases indicates a significant deviation from ideality even at relatively low water concentrations, and this observation is consistent with the data reported in this paper at lower temperatures. We have been unable to find an empirical representation of the solubility valid over the entire temperature range, 6 C t 132.6 "C, which preserves an economy in a number of parameters. For empirical representation of solubilities, we suggest the use of eq 5 for 6 < t C 91 "C (91 "C is the point of intersection), followed by the MD equation (91 C t C 132.6 "C), In XH,, = -1745/T + 4.298. The present data (Table V) on solubility and melting point isotope effects have been represented in two ways. Using, in each case, XDg(tD) (the mole fraction of saturated urea-d4in D20 at the temperature tD) as a reference, and applying eq 5 in an isotopic difference form, 6 In X,,, = In x,,(tH) - In x,,(tD) = (2070/ P - 2.086/ T ) AT, lt is possible to transform the IE's on the concentration differences at a given temperature, tD,into the I E s on sat-
-
9" (D) 44.57 44.24 43.77 43.41 43.15 43.09
45.81 45.98 18.0101 45.65 45.89 12.1087 45.49 45.73 8.0580 45.32 45.52 4.8073 45.15 45.36 2.3911 45.29 0.5973 45.09 45.24 d'D,O = 1.1099952 (99.77%D); d 0 ~ , = o 0.992219
(B) Fits to & = 9; t a m 15 "C
0°C
9 ;
m 14.9783 44.82 9.4946 44.54 4.7084 44.15 2.3911 43.86 1.2000 43.68 0.5973 43.56 1.105786 (99.77%D); d ' ~ , o= 0.999098
9 v (HI
uration temperature at a given concentration XD although it makes no sense to transform the IE on the mefting point into the concentration domain. It is reasonable to expect the X i s and AXls to display an approximate van%Hoff dependence. Least-squares analysis of the IE's in the two domains yields
+
A In X, = (95482 f 15446)/P - (565.3 f 101.O)/T (0.8607 f 0.1645) (6)
az = 9.7 x 10-7
+
A(l/"), = [(6.325 f 1.563) X lo*] [(-6.151 f 4.342) X lo4] In X [(7.562 f 2.492) X 10*](ln X)2 (7)
+
u2 = 2.5 X
Calculations reported in the later sections of this paper use eq 6 because it is a better representation in the region of interest, 10 < t < 60 "C, since it is not forced through the IE at the melting point, 132.6 O C . Even so, the two representations are in good agreement, as shown in Figure 2B. Osmotic Coefficients and Their Isotope Effects for Saturated Solutions. Measured differential pressures, 6Py(s,t) = PY"(t)- Py(m,,t), were combined with solubility values from eq 5 or eq 5 and 6 using eq 1 to obtain the osmotic coefficients reported in Table IV. These are shown in Figure 3, where they delineate the ends of the &(?) and 4D(m)isotherms. Several isotherms are included in
3486
Jakli and Van Hook
The Journal of Physical Chemistty, Vol. 85, No. 23, 1981
I 1.4
I\\
1
-74 2.6
3.4
3.0 ,
I
.
,
,
4
.
12
20
28
36
rn
Flgure 3. Osmotic coefflcients as a function of concentration at several temperatures and osmotic coefficients of saturated solutions: (-) d,(m) at 10, 25, 40, and 60 O C from eq 3; (---) dD(m) at 25 and 40 O C from eq 3 and 12; (0)4 H(ms)experimental (Table IV and eq 5), the line labeled Sh is that of eq 8; (X) $D(mJ experlmental (Table IV and eq 5 and 6), the line labeled S, is that of eq 9.
31-
Here tH is the saturation temperature of a solution of urea-h4/Hz0at m = mD, readily obtained from eq 5 and 6. The quantity (d$/dt), for m 5 20 is available from eq 3. For higher concentrations, large-scale plots of the isotherms from eq 3 join smoothly with the values of 4H(ms) (see Figure 3) so the approximation
%
1031s 2.6
3.0
I
3A
Flgure 2. (A) Solubility of urea-h, in H,O X is the mole fraction of urea in the solution: (0)data of Schnidman and Sunier;Ia (0)present data; (X) data of Miller and Dtttmar (MD); (a) two-parameter fit of MD; (b) two-Parameter fit of Schnidmn and Sunier; (c) line with slope defined by thermal data of ref 24 and intersecting the melting point (insert); (d) line defined by eq 5. (B) Isotope effects on solution temperature and melting point for ureas: (+) experimental from measurements of A(I/r)s; ( 0 )experimental from measurements of A In Xs(tD) and transformation to l/Tdomain (see text); (-) calculated from eq 6 and transformed to 1/ T domain; (- - -) calculated from eq 7.
the figure to illustrate the behavior. Least-squares analysis of the r#q(m8) curves yields 4H(ms) = (0.7737 f 0.0026) + [(1.166 f 0.211) X 10-3]m, - [(5.55 f 0.40) X 10-5]m,2 (8) 4D(m,) = (0.7566 f 0.0037) + [(1.505 f 0.295) X 10-3]m, - [(5.60 f 0.55) X 10-5]m,2 (9) with $(H) = 2.1 X lo4 and $(D) = 1.5 X lo4. The isotope effects, A+&m),obtained by subtracting eq 9 from eq 8 are at constant m, but different saturation temperatures. (10) A& = 4H(ms,tH) - d ) ~ ( m ~ , t ~ ) A quantity of more direct interest, A+(m,t), may be obtained at a reference temperature and concentration, e.g., t D and m,(D), by the operation A@(m,t)= +H(mD,tD) - +D(mJdD) =
< m < m,,t)
= @H(20,t)+ J;(a+H/am),
dm = 4~(20,t)+ (A@/Am)(m- 20) (12) is reason able. A+/Am can be evaluated from the differences between the data at 20 m (eq 3) and saturation (eq 81, so d4~(20,t) +d -(m-20) (13) = dt dt Am @H@O
(%),,,
[
]
is available from eq 3 , 5 , 8 , and 12. The osmotic coefficient isotope effects thus calculated for rounded concentrations at saturation temperatures, t,(H), are reported at the foot of Table IV and some are shown in Figure 4. They serve as independent confirmatory measurements of IE's obtained from differential pressures of unsaturated solutions. When one makes comparisons, however, it is important to recognize that the uncertainty in A+(m,t) calculated from eq 11is dominated by the uncertainty in A+8 (eq lo), u A@, = 3 X That uncertainty is rather larger than that for direct measurements of the isotopic differential pressures themselves and is a direct consequence of the propagation of errors through the several different experiments required to determine A+(m,t). Osmotic Coefficient Isotope Effects for Unsaturated Solutions. Isotope effects on solvent activity (Table 111) are plotted in Figure 4. We have chosen to display the E's in terms of A In R instead of AI$ because A In R is more directly connected to the experimental procedure, and also since this plot nicely spreads out the data. Defining In R = In [PH(m,t)/PD(m,t)]and In Ro = PHO/PDO,we have to within corrective terms easily shown to be negligible2" In Ro - In R = A In R = (m/55.508) A+(m,t) (14) The data (Figure 4A) show very small isotope effects and very little temperature dependence. At a given concentration there appears to be a shallow minimum which tends
Isotope Effects in Aqueous Systems
The Journal of Physical Chemistry, Vol. 85,No.
23, 198 1 3487
standard-state free energy of solution (Henry's law standard state) is available from the material presented above. '1.
- p o = RT In ma + RT In ys
(15)
In eq 15, po is the partial molar free energy of the urea-y4 Cy = h or d ) at infinite dilution in solvent Y20 (Y= H or D) at a specified temperature. Also p* is the partial molar free energy of crystalline urea-y4at that same temperature. The solute activity coefficient, ys,at saturation, ma,can be obtained from the osmotic coefficients via a GibbsDuhem integration, setting the upper limit equal to ma: In y = (4 - 1) + J m ( @ - 1)d In m
(16)
0
For the moment we focus on the data for urea-h4/H20. For those data at t # 25 "C, all taken at m I 4, the limiting deviation from the 25 "C reference fit as expressed by eq 3, limk%5 [@(m,t) - @*(m,25)] # 0 as would be required for thermodynamic consistency. The reason of course lies in the fact that the first data points of this study were taken at the relatively high concentration, m = 4,and the concentration dependence in this region is not the same as at high dilution. We suppose that the true difference, @(m
