V. E. BOWER AND R. A. ROBINSON
1524
A limited comparison between this system and the cyanide system is warranted and evolves three significant items. (1) The chemical boundaries of the formate system on Dowex 2 resin are sharper than those of the cyanide system, indicating greater suitability of the former system for extended column operation. (2) Since, under similar experimental conditions, twice the C14 enrichment was obtained in less than one-third the resin bed length for the HCN as compared with the HCOOH system, it is likely that B (= K - 1) for the cyanide system is a t least six times as great as the 4.4 X room temperature value found for the formate system. (3) From the standpoint of practicality, the quantitative aspects of the formate system make it the superior of the two. The economical feasibility of producing C12 and C13 of relatively high purity cannot be accurately determined without resort to pilot plant operations. Although the separation factor for the formate system is smaller than that in some C1z-C13 gas-liquid exc h a n g e ~ , *the ~ combination of a relatively small plateheight and inherent ease of operation could conceivably (23) C. A . Hutchison, D. 8, 532 (1940).
IT.Stewart, and H. C. Urey, J .
Chem. Phys.,
Vol. 67
outweigh this. Withdrawal of depleted product and addition of more HCOOH feed solution a t strategic intervals would enhance the specific separation. The time factor, determined by the rate of approach to isotopic equilibrium, and the durability of the resin must also be considered. Both chloride and excess acetate are recoverable in the regenerative step as a mixture of their ammonium salts. During column operation, displaced acetate is recoverable as its acid. It is logical to assume that the formate system may be successfully applied to carbon-dating experiments in the laboratory. If enough starting material is available (as would be the case for age determinations of peat beds), the C14 content could be concentrated in the leading fractions by a factor of 10-20 after a month or two, using multiple-column operation with much larger columns than those employed here. Acknowledgments.-We wish to thank Dr. B. G. Dunavant and the University of Florida for use of the Tri-Carb liquid scintillation spectrometer, Mr. Joseph Kinard for assistance in the laboratory, and the Dow Chemical Company for supplying the resins used in the cross-linkage experiments. C. N. D. is grateful to the National Science Foundation for a graduate fellowship during the 1961-1962 academic year.
THE THERMODYNAMICS OF T H E TERNARY SYSTEIU: UREA-SODIUM CHLORIDE-WATER A T 25 O BY V. E. BOWERASD R. A. ROBINSOS Solution Chemistry Section, National Bureau of Standards, Washington, D . C. Received January 51,1965 Isopiestic vapor pressure measurements have been made on this system a t 25"; the activity coefficients of urea in sodium chloride solution and of sodium chloride in urea solution have been evaluated and the extent to which solubilities of one solute in a solution of the other can be calculated is discussed.
Introduction Previous work has dealt with aqueous solutions of two co-solutes, of which one was rnannito1.l That solute was chosen because it was one component of some ternary systems in which diff usioii measurements were being made. Mannitol has, however, limited solubility in water (1.185 M a t 25") and, in order to obtain measurements over a much greater concentration range, the system urea-sodium chloride-water has now been investigated.
ISOPIESTIC
(1) (a) R. A . Robinson and R. H. Stokes, J . Phys. Chem., 66, 1954 (1961); (b) F. J. Kelly, R. A. Robinson, and R. H. Stokes, ibid., 66, 1958 (1961); (0) R. A . Robinson and R. H. Stokes, ibid., 66, 504 (1962).
mo
mB
mc
mB
6.9657 1.0257 0.5329 8.1817 1.0395 .5384 ,8251 10.427 1.6247 11.058 3.6345 1.6876 11.184 3.7667 1.7391 a B = urea; C = NaC1.
2.8575 3.2362 3.8430 4.0304 4.0580
mB
mc
14.008 14.306 17.826 18.401
4.7792 4.8323 5.6440 5.7660
TABLE I1
Experimental Isopiestic measurements were made on this system by the method described previously"; some improvement was made in the device for closing the lids of the isopiestic dishes with the desiccator under vacuum, by drilling a small hole in the center of the copper block; a spike on the lower part of the rotating device fitted into the hole and gave a smoother rotation when closing the lids. Sodium chloride (Fisher Certified) was recrystallized once from nmter and dried a t 300". Urea (Fisher Certified) was recrystallized twice from methanol and dried i n vacuo a t room temperature. Calcium chloride (Baker and Adamson, A.C.S. reagent) was recrystallized twice from very slightly acidulated water. A stock solution was prepared and analyzed for chloride content; the analysis was confirmed by allowing solutions of
TABLE I" SOLUTIONS O F UREA A N D SODIUM CHLORIDE'
OSMOTIC A N D ACTIVITY COEFFICIENTS OF UREA m
(0
Y
m
Q
Y
m
(0
Y
0,996 0.992 2 . 0 0.931 0.864 9 . 0 0.827 0.653 ,2 .992 ,983 2.5 ,919 .839 9 . 5 ,824 ,644 ,3 ,987 .975 3 . 0 ,908 .817 10.0 ,820 ,636 .4 ,983 ,967 3 . 5 ,899 .798 11. O ,814 ,621 .5 ,979 .955 4 . 0 ,891 ,780 12.0 .809 ,608 .6 .976 .951 4 . 5 ,882 .763 13.0 ,804 ,596 ,7 .970 .942 5 . 0 ,874 ,747 14.0 ,799 ,584 ,8 ,966 .934 5 . 5 ,867 ,733 15.0 ,794 ,573 ,9 ,962 ,927 6 . 0 ,860 ,719 16.0 ,789 .563 1. O ,958 ,921 6 . 5 ,853 ,706 17.0 ,786 ,554 1.2 ,952 ,908 7 . 0 ,847 ,694 18.0 ,782 ,545 1.4 ,947 ,896 7 . 5 ,841 ,683 19.0 ,779 ,537 1.6 ,942 ,885 8.0 .836 ,672 20 . O .777 .530 1.8 ,936 .874 8 . 5 .831 ,662
0.1
July, 1963
‘FHERMODYNAMICS O F THE
1525
TERNARY SYSTEM UREA-SODIUM CHLORIDE-WATER
TABLE 111” THESYSTEM:UREA-SODIUM CHLORIDE-WATER -A
mrsf.
mB
mc
mmc
%b
+o. 11
0.9497 1.3933
0.3437 ,1175
0.0334 .0232
0.6992 1.9058 2.7444
1.3657 0.8129 .4229
,0115 .0183 .0214
2.8575
1.6410 3.3504 5.6181
2.2042 1.5257 0.5908
.0027 ,0049 ,0092
+ + +
3.2735
1.1875 2.8039 4.6672 6.4725
2.8232 2.2196 1,5129 0.7941
,0007 ,0025 .0052 .0066
-
4,0304
5.3875 7.4397 9.3321
2,1870 1.4450 0.7123
.0013 .0006 .0005
- .I1 .08 .12
4,0580
1.3681 2,5894 3.9752
3.5868 3.1775 2,7050
-
6.8252 8.2784 9.9866 11.822
2.5671 2,0828 1.4792 0.7897
- ,0004 ,0002 ,0006 .0027
4.7792
2.5380 6.0157 11,146
3.9813 2.9078 1.1409
4.8323
1.3415 4.4403 8.7605
4.4082 3.4657 2,0790
-
5.6440
1.6963 5.6620 11.262
5.1551 4.0765 2.4182
0.8251 1.6876
4.7089
5.7660
3.7400 8.7785 15.188
4.7425 3.3588 1.2597
,0011 ,0003 .0002
,0023 ,0007 ,0015
,0023 - ,0001 - .0011 - .0024 ,0006 - ,0001
-
,0013 ,0008 ,0007
-
mB
mc
mBmC
3.0369
3.6315 5.5480 8.1565
5.3725 4.9085 4.2555
.0015 .0032 ,0034
$08
+
.07 - .04 - .05
.07 .13 .02 .02 .01 .09 .04
+ + -
.07 .13 .05
.02 .09 - .11 - .22
+ +
+ -
+ + + +
.02 .02 .14 .05 .11 .10 .06 .08
.11 .06 .17 .16
+ + .15 - .13 + .05
-A -
mref.
3.1667
15.833
2.5562
.0040
3.3061
12.944 16.047 18.107
4.0138 3.1609 2.5183
.0095 .0m1 ,0085
3.3066
5.9585 7.5353 9.2642 11.097
5.6617 5.3145 4.9271 4.4907
.0097 ,0095 .0099 .0099
3.5831
15.002 18.697 21.176
4.6521 3.6828 2.9449
8.8029 10.902 13.146
3.6420
3.7085
3.8600
%b
+ + +
+
.18 .15 .26 .22
-
.11 .32 .25 .14 .02 .01 .05
,01566 ,01426 .01438
-
.14 .15 .14
6.2085 5.7980 5.3200
.01866 ,01829 .01759
-
.11
-
.05
10.660 14.069 17.432 21.729
6.0841 5.3722 4.5849 3.3889
.01950 ,01818 ,01686 ,01518
0 +0.20 .13 .26
14.077 15.994 18.074 20.009
6.0165 5.6170 5.1455 4.6360
.02274 ,02163 .02040 ,01921
.03 .09 .I1 .13
+ + -
.26
+ + + + +
+ -
.07 .04 .04 - .02
3.9293
16.416 17.982 19.642 21.442
5.8467 5.5005 5.1060 4.6450
,02357 ,02246 ,02142 ,02051
4,1372
19.749
6.1820
.02714
....
6.9942 6.4167
(03271) (03139)
...
4.3435
20.775 23.648
.... I
.... 4.4443 21.340 7.3814 (03445) 3.7410 ,0034 .... 22.988 7.0751 (03365) 9.7975 24.463 (03313) 12.967 .... 2.8263 ,0037 6.7849 ,0023 .... 1.1117 24.759 6.7269 (03308) 18.009 a B = urea; C = NaCl. I n the first eleven sets, sodium chloride was the reference electrolyte; in the remainder, calcium The difference is positive if A calculated by eq. 1 is greater than the experimental. chloride. 3.0130
sodium chloride and of calcium chloride to equilibrate in the isopiestic apparatus; the equilibrium concentrations agreed with those reported previously.2
Results A few equilibrations were made between solutions of sodium chloride and of urea (Table I); a large scale plot of the isopiestic ratio against the urea molality showed excellent agreement with the data of Scatchard, Hamer, and Wood.3 However, the interpretation of any isopiestic measurement depends on the values assigned to the osmotic coefficients of the reference salt, in this case sodium chloride, and the values used by Scatchard, Hamer, and Wood differ slightly from those used4 in previous work in this series.l I n order to maintain consistency with the mannitol work, osmotic and activity coefficients of urea have been calculated (Table 11) on the same basis. (2) R. 1%.Stokes, Trans. F’araday SOC.,41, 637 (1946). ( 3 ) G. Scatchard, W. J. Hamer, and S. E. Wood, J. A m . Chem. Soc., 6 0 , 3061 (1938). ( 4 ) R. A. Robinson and €1. H. Stokes, “Electrolyte Solutions,” Second Edition, Butterworths Scientific Publications, London, 1959, Appendix 8.3.
Isopiestic measurements were made with solutions of urea and sodium chloride equilibrated with either sodium chloride or calcium chloride solutions as references. The results are given in Table 111; the first column gives the molality of the reference salt, which was sodium chloride in the first eleven sets and calcium chloride in the remainder. The second and third columns give the molalities of the mixed solutions which were in equilibrium with the solutions whose molalities are given in the first column. I n the analysis of these results we use the function A, defined by A/55.51 = In u w ( B ) In %(c) - In aw(~ where ) u w ( M ) is the water activity of a solution containing nzg moles of urea and mc moles of sodium chloride in 1 kg. of water; uw(g)that of a solution of i n B moles of urea only in 1 kg. of water; u , ( ~ )that of a solution of mc moles of sodium chloride only in 1 kg. of water. RTA is therefore the free energy change of water when a solution of ing moles of urea in a kg. of water is mixed isothermally with a solution of inc moles of
+
V. E. BOWERAND R. A. ROBINSON
1526
Vol. 67
fit with the experimental values of A/(nzBmc)was not as good as we desired. After a considerable amount of
4
0
8
12
16
20
24
??LB.
Fig. 1.-The
function given by eq. 1; two of the experimental points are shown.
sodium chloride in a kg. of water and a kg. of water is then separated by means of an osmotic membrane. The quantity - A/(ingmC) is given in the fourth column of Table 111. The last six entries are enclosed in parenthses because binary systemsof urea-water with the molality given in the second column and of sodium chloride-water with the molality given in the third column would have been considerably supersaturated. The A function, therefore, had to be calculated using values for the water activity of urea solutions and of sodium chloride solutions extrapolated into the supersaturated regions; for this reason, the last six entries may be unreliable. Before turning to a discussion of the results, it is worthwhile looking a t the magnitude of these effects. I n dilute solutions, A/ (mBmc)is comparatively large and negative, as was found in the systems mannitolNaC1-water'b and mannitol-KC1-water.lC Thus, at mB = 0.9497, mc = 0.3437, 55.51 In aw(At)= -1.5340. 55.51 In u w ( B ) = -0.9119, and 55.51 In u,(c) = -0.6330, so that the mixture effect, as measured by A, is -0.0109 and A/(mBmc)= -0.0334. I n more concentrated solutions, A becomes less negative and at 7fig = 11.262, mc = 2.4182, A is almost zero. A threedimensional plot of A/(mBmc)aganst mB and mc shows a region where A has small but positive values but in concentrated solutions A again becomes negative and large. For example, a t n z B = 14.077, mc = 6.0165, the three 55.51 In a, terms are -24.615, -15.305, and -11.236 for the mixture, the urea solution, and the sodium chloride solution, respectively. Consequently, A is -1.926 and A/(mnmc)is -0.02274. Discussion I n order to evaluate the activity coefficients of urea and of sodium chloride in these mixed solutions, we seek, as in earlier work,'" an analytical expression for A/(mBmc) in terms of mB and mc where n z B and mc denote molalities, ie., moles of urea and moles of sodium chloride, respectively, per kilogram of water. Even after eliminating the last six entries of Table 111, for reasons already given, we found that a ten-parameter equation
+ BmB + Cmc + DmB2 f Em2 f FmBmc 4-GmB3f Hmc3 + ImB2mC4-JmBmc2 (1) A/(mBmc) = A
was needed. Even with ten parameters, however, the
computation, we found that, if we eliminated the point a t mB = 19.749, mc = 6.1820, the remaining data gave, by the method of least squares: A = -3.9556 X lop2; B = 5.2731 X C = 2.1319 X D = -1.934 X E = -3.059 X F = -1.854 X G = 9.1 x 10-7; H = 1.14 x 10-4; I = 3.97 x 10-6; J = 8.96 X and we got more satisfactory agreement with the experimental data. The extent of the agreement can be assessed in terms of the experimental quantities by reversing the calculation so as to compute the molalities of the reference solutions which would have given the values of A/(mBmc)as calculated by eq. 1. The difference between these calculated molalities and the experimental, expressed as a percentage, is given in the last column of Table 111. The difficulty in fitting the point a t mB = 19.749, in0 = 6.1820 to an equation can be appreciated if a three-dimensional model of the surface represented by eq. 1 is constructed. Figure 1 is a cross-section of this surface for mc = 0.32m~. It ill be seen that, at low I ~ z B ,A/(mBmc) increases with increasing inB to a maximum a t about mB = 8 and then decreases to a minimum at about ing = 20, after which it rises rapidly. Up to about mB = 19, the curve can represent the experimental data very well but, a t higher concentrations, the equation gives too high values of the function. Clearly, the experimental point in question cannot be fitted to a curve of this type. The point may be experimentally erroneous but we do not think this is so, because the downward trend of A/(mumc)is confirmed by the last six entries in Table 111. We have pointed out that these six data were obtained with some extrapolation from the experimental region, but we do not believe that the points are so much in doubt as to bring them onto the calculated curve in Fig. 1. Equation 1, therefore, gives a satisfactory representation of the experimental data except a t high values of nzB and mc. It might, however, be dangerous to use the equation beyond the region of experiment, e.g., for nzB = 22, m c = 1, ormg = 1 = nzc = 7. Activity Coefficients.--It has been shown'" that if A/(?fiBmc)= f ' ( m ~ ) F'(mc) where j"' is a function of naB only and F' of mc only, then
+
Equation 1 is not of this form, for it contains crossproducts of mg and mc. However, by following the procedure used in the earlier paper,'" it can be shown that eq. 1 leads to the equations
+
+
+
+ +
In Yn = 111 y B 0 mc[A BmB l/2Crnc DmB2 '/&mc2 f 2/3FmBmc GmB2 ' / 4 " m B 3 3,r41mB2mc l / z J m B m ~ z ]
+ + + 2 In yc = 2 In yco + mB[A + ' / & m ~+ Cmc +
+
+
' / 3 D r n ~42 End 2/,FmBmC f 'l4GmB3f Hmc3 l/zImB2mc 3 / 4 J m B m ~ 2 ]
+
+
and -log These equations give the values of -log yc recorded in Tables IV and V. Considering the high solute concentrations that can be reached in this sys-
THERMODYNAMICS OF THE TERNARY SYSTEMUREA-SODIUM CHLORIDE-WATER
July, 1963
1527
tem, the change in activity coefficient is not large. The limiting activity coefficient of sodium chloride a t mc = 0 and m~ = 1 is 0.9804; in 1 M mannitol it is 0.986; even in 20 M urea, the activity coefficient has fallen only to 0.898. TABLE IV“ ACTIVITY COEFFICIENT OF UREAIN SODIUM CHLORIDE SOLUTION ntc
mB 0 1 2 5 10
15 20 a
0
0 0.0355 .0637 .1266 .1963 .2418 .2760
-
1 2 3 4 6 6 0 0130 0.0192 0.0208 0 . 0 1 9 8 0.0178 0 . 0 1 6 0 .0530 .0526 .0629 .0522 .0539 .0468 .OS26 .OS04 .OS09 .0782 .OS00 ,0734 .1502 .1404 .1442 .1357 .1379 .1324 ,2276 .2171 ,2039 .2093 ,1983 ,2004 .2791 .2580 ,2677 .2456 .2506 .2429 ,3159 .2984 .3073 ,2838 ,2902 ,27811
The negative logarithm of the activity coefficient is tabulated.
TABLE V” ACTIVITY COEFFICIENT O F SODIUM CHLORIDE I N UREA SOLUTIONS 7
mB
1 2 5 10 15 20 0 0086 0 0150 0,0299 0 0421 0 0449 0.0468 0 0 ,2100 .2165 ,2058 ,1905 .1986 1 0.1825 .1868 .2087 .1889 .1969 .1787 ,1828 ,1772 2 .1755 .1879 .1573 .1701 .1473 ,1491 3 ,1465 .1466 .1617 .1203 .1397 .lo54 ,1080 ,lOj.5 4 .lo61 .1312 ,0805 ,1059 .0580 ,0622 5 ,0586 ,05713 .0960 0387 ,0694 .0067 .0143 ,0059 6 ,0060 237 81.3 161 1 1 20 5 -2 2 AG, cal. mole-’
mo
0
The negative logarithm of the activity coefficient is tabulated.
The largest effect is found with 6 M NaCl; alone in water a t this concentration, sodium chloride has an activity coefficient, y = 0.986; in 20 M urea, it is 0.802. Similarly, the activity coefficient of urea in 1 114 solution, 0.921, is lowered to 0.885 by the addition of 6 M KaCl; for 20 M urea, the change is from 0.530 to 0.483 on the addition of a similar amount of sodium chloride. It will be seen from Table V that, while the effect of urea on the activity coefficient of sodium chloride is generally one of “salting-in,” there is a region (approximately mc 2 4, mB 5 2) where avery small “saltingout” effect is found. The quantity AG = 2RT In fc at tnc = 0, which can be calculated from the data in the second row of Table V, is the increment in chemical potential when a mole of sodium chloride is 1,raiisferred from a given mole fraction in water to the same mole fraction in urea-water mixtures in the limit when mc = 0, i.e., it is a measure of the medium effect. Values of AG are given in the last row of Table V That of -2.2 cal. mole-’ in 1 M urea can be compared with +13.6 cal. mole-’ already calculatedIc for sodium chloride in 1 M mannitol; that of 237 cal. mole-I in 20 M urea (54.8%) with 242 cal. mole-; for hydrochloric acid in 20% dioxane, Solubility Measurements.-As was shown in earlier papers,’aslb a knowledge of the A function over a range of 1 7 % ~and tnc, along with solubility data fop each solute in water, enables the solubility of B in solutions of C to be calculated and vice versa. The calculated solubilities of urea in sodium chloride solutions and of sodium chloride in urea solutions are shown in Fig. 2. Some direct solubility measurements were made. The solubility of sodium chloride in a 10.31 M urea solution Was determined by saturating the urea solution with the salt and analyzing an aliquot for chloride; the
0
4
8
m,,(moles
12
16
-
20
24
urea per kg water),
Fig. 2-Solubility relations: -, calculated solubility curves; through the experimental points; A, solubility of NaC1 in urea solutions; 0 , solubility of urea in XaC1 solutions; 0 , point of mutual saturation.
- - -, drawn
solubility was found to be 6.465 144, the calculated value being 6.475 M . I n 18.00 14 urea we found a solubility of 6.722 M whereas the calculated value is 6.927 M . Similarly, the solubility of urea in a 3.018 M sodium chloride solution was determined by evaporating to dryness in vacuo an aliquot of the saturated solution; ftom the amount of total solids and the known amount of sodium chloride in the aliquot, the solubility of urea could be determined: found, 21.20 M ; calcd., 21.00 144. In 5.520 114 S a C l solution, we found a solubility of 23.06 M urea compared with the calculated value of 22.48 144. Finally, the point of mutual saturation was determined by evaporating to dryness an aliquot of the solution saturated to both urea and sodium chloride; the amount of total solid and an analysis of the chloride content gave solubilities of 24.16 M urea and 6.712 M h’aC1. The calculated values are 22.70 M urea and 7.036 144 KaCl. We see, therefore, that we get reasonably good agreement when either the urea concentration (10.31 M)or the sodium chloride concentration (3.018 M ) is not too high. If either is high, then solubilities predicted by eq. 1 do not agree with those found experimentally; in particular, eq. 1 does not predict the point of mutual saturation. This might have been expected, for the parameters of eq. 1were derived with the full knowledge that they were not of much use at high values of mB and mc (specifically, mR = 19.749, ?nc = 6.1820); still less would we expect them to predict the even higher concentrations a t the point of mutual saturation. Acknowledgment.--We express our gratitude to Mr. J. M. Cameron for his expert advice about the representation of the experimental data and, in particular, for restraining our enthusiasm to apply empirical equations outside the region to which they have been fitted.
