IONIZATION BEHAVIOR OF NaCl IN DIOXANE-WATER SOLUTIONS of the ion mobility on fo. The value of fo, calculated from f K , depends very strongly upon the depression of ,the dielectric constant circle plot (see Figure 8). Since the circle plot cannot be drawn with sufficient accuracy to indirectly determine fo, j n was used as a direct indicator of fo.
Summary A theory has been proposed to explain the low-frequency dielectric properties of porous particles with uniform volume distribution of fixed charge N . It predicts a relaxation in which the change AKZ in the effective, homogeneous dielectric constant is proportional to dfl and to the radius R of the particle and in ~ independent of the environmental salt which A K is concentration no and counterion mobility u. The
1099
relaxation frequency is proportional to u/R2. Experimental tests with colloidal suspensions of ion-exchange resins were found to agree both qualitatively and quantitatively with the theoretical predictions. The mechanism is very similar to that proposed by Schwara for solid colloidal particles with a fixed surface charge. However, in the present case, all counterions in the region of the high static radial electric field (those counLerions just inside the porous particle as well as those outside the surface of the particle) are part of the ion cloud which flows about the surface of the particle under the influence of the electric field.
Acknowledgment. The authors are indebted to Mrs. Sally Child for her technical assistance and to Drs. R. E. Marquis, L. P. Hunter, and W. Striefer for helpful discussions.
Electrical Conductances and Ionization Behavior of Sodium Chloride in Dioxane-Water Solutions at 100"and Pressures to 4000 Bar&&
by LeRoy B. Yeatts,' Lawrence A. Dunn,*Ib and William L. Marshall* Reactor Chemistry Divaswn, Oak Ridge National Laboratorg, Oak Ridge, Tennessee 37830
(Receiued August 3, 1970)
Publication costs assisted by the Oak Ridge National Laboratory, U.S.Atomic Energy Commission
The ionization behavior of NaCl in dioxane-water at 100' to pressures of 4000 bars was determined from electrical conductance measurements of dilute solutions (0.001-0.02 m) The conductance equation of Shedlovsky was used to calculate the limiting equivalent conductances (A,) and conventional ionization constants (Kd) for NaCl in solvent mixtures whose compositions ranged from 30 to 70 wt % dioxane. For these calculations, estimates of dielectric constants, densities, and viscosities were made and are presented. The complete ionization constant (KO), which includes the polar solvent water as a reactant species, has a value of 10-12J; the net change in the number of solvating water molecules ( k ) is equal to 7.8. These values are identical with those established earlier for NaCl in dioxane-water at 100' and at saturation vapor pressure. Hence, this study supports the earlier proposal that the complete constant is independent of both pressure and dioxane-water solvent composition and is only temperature dependent. I
Introduction The concept of a complete isothermal equilibrium constant (KO)proposed earlier2J has been applied successfully to numerous electrolytes in aqueous, polar organic, or mixed aqueous-nonpolar organic solvents. The basic tenet of this principle is that the polar solvent molecules are undergoing a change in concentration during an ionization reaction involving ions, ion pairs, and the solvent. Therefore, polar solvent molecules must be considered participants in the reaction and included in the equilibrium constant expression. Both solubility and ionization equilibria,2-4 including
the ionization of water,5 are described accurately by this principle under such widely varying conditions as temperatures to 800" and pressures to 4000 bars. Generally, data at higher temperatures or pressures than these are not available to test this hypothesis. (1) (a) Research sponsored by the U. S. Atomic Energy Commission under contract with the Union Carbide Corporation. Presented before the Division of Physical Chemistry at the 160th National Meeting of the American Chemical Society, Chicago, Ill., Sept 13-18, 1970. (b) Department of Chemistry, University of Tasmania, Hobart, Tasmania 7001, Australia. (2) W. L. Marshall and A. S. Quist, Proc. Nat. Acad. Sci. U.S., 58, 901 (1967). (3) A. S. Quist and W. L. Marshall, J. Phys. Chem., 7 2 , 1536 (1968). The Journal of Physical Chemistry, Vol. 76, No. 8,1971
1100
However, the molar ionization constant of ammonia in water at 45" has been determined by Hamann and Strausse at pressures up to 12,000 bars and the complete constant principle continues to be applicable.' Recently, this approach was further generalized by extending it to include the rates of reactions,' such as the hydrolysis of methyl and isopropyl bromides.* The concentration of the polar solvent can be changed significantly at the lower temperatures only by using a solvent containing both a polar and a nonpolar component while a t higher temperatures, or lower densities, pressure can be used also to produce this effect. Dunn and Marshall9 have used essentially nonpolar dioxane to reduce the water concentration in order to study the ionization of sodium chloride, by conductance measurements, at 100' and saturation vapor pressure. From these measurements they were able to obtain values for KO, the complete ionization constant, and k , the net change in the number of waters of solvation for the ionization equilibrium. Their value of 7.8 at 100" for k was close to that predicted elsewherelo from the values of this constant at 25' and saturation vapor pressure for NaCl in dioxane-water and from 400 to 800" for NaCl in pure water at various densities. The purpose of this present study was to make conductance measurements of NaCl in dioxane-water at 100" while varying the pressure on this system from 1 to 4000 bars to establish whether these values for KO and k are independent of pressure, as one would predict from the original complete constant concept. Since values for density, dielectric constant, and viscosity as a function of pressure needed for calculating conventional ionization constants (Kd)are not available, estimates of these properties were made for the various compositions of the dioxane-water solvent. With these estimates the agreement with the earlier resultse at 100" and saturation vapor pressure is remarkably good.
Experimental Section The preparation of the sodium chloride-dioxanewater soIutions,g as well as a description of the experimental procedures and the conductivity apparatus,*& were presented earlier. Two inner electrodes with cell constants at 100" of 0.501 and 2.103 cm-I, determined from 0.01 and 0.1 demal potassium chloride, were used to make the conductance measurements in this study at asignal frequency of 2 kHz. The smoothed experimental specific conductances ( K ) at 100" for the various compositions of dioxane-water solvent are listed in Table I. I n general, five sodium chloride solutions in the range of 0.001-0.02 m were studied for each of five solvent compositions. The solution resistances were usually in the range of lo3 to lo4 ohms. Values for the density (d), dielectric constant ( D ) , and viscosity (7) of these dilute solutions are assumed to be the same as those of the two-component solvent alone. At saturation vapor pressure, approximately 1bar, the The Journal of Physical Chemistry, Vol. 76,No. 8,1971
L.B.YEATTS,L. A. DUNN,AND W. L. MARSHALL values of these properties given elsewhereg were used in this paper. Estimates of the three physical properties for higher pressures were made by the methods discussed below. Densities. The specific volume of pure dioxane at 100" as a function of pressure up to 500 bars wm calculated by the method of Lydersen, Greenkorn, and Hougenlla as discussed by Reid and Sherwood.llb This method relates the specific volume of a liquid to its reduced temperature, reduced pressure, and critical compressibility. (Reduced properties are fractions of liquid-vapor critical properties; for example, P, = PIPc where P,, P, and Po are the reduced pressure, the pressure on the given system, and the critical pressure, respectively.) The values reported by Hgjendahl12for the critical temperature (312O), critical pressure ( 4 0 bars), and critical density (0.36 g/cm8) of pure dioxane were used for the calculations. A reliable experimental specific volume or density value, at a temperature as close as possible to the temperature for which the calculations are to be made, is required also. The experimental value of 0.965 g/cmS for the density of dioxane at 80" and saturation vapor pressure waa used since both Geddes13 and Hovorka, et aZ.,14 report this value from independent determinations. Presumably, this method of calculating densities is reliable in this case up to pressures of 1500 bars but the calculated densities indicated that dioxane waa a little less compressible than water above 500 bars. This did not appear to be reasonable; hence, above 500 bars pressure it was assumed that dioxane had the same absolute increase in density per unit increase in pressure as that of water. The densities of water which were used are those compiled by Sharp16 from the publishedls and (4) (a) A. S. Quist and W. L. Marshall, J.Phys. Chem., 72,684 (1968); (b) A. 9. Quist and W. L. Marshall, ibicl., 72, 1545 (1968); (c) A. 8. Quist and W. L. Marshall, ibid., 72, 2100 (1968); (d) A. 8 . Quist and W. L. Marshall, ibid., 72, 3122 (1968); (e) L. A. Dunn and W. L. Marshall, ibid., 73, 723 (1969); (f) E. U. Franck, 2. Phys. Chem. (Frankfurt am Main), 8 , 107, 192 (1956). (5) W. L. Marshall, Rec. Chem. Progr., 30, 61 (1969); A. S. Quist, J . Phys. Chem., 74, 3396 (1970). (6) S. D. Hamann and W. Strauss, Trans. Faraday Soc., 51, 1684 (1955). (7) W. L. Marshall, J.Phys. Chem., 74, 346 (1970). (8) B. T. Baliga and E. Whalley, ibid., 73, 654 (1969). (9) L. A. Dunn and W. L. Marshall, $bid., 73, 2619 (1969). (10) W. L. Marshall, Rev. Pure Appl. Chem., 18, 167 (1968). (11) (a) A. L. Lydersen, R. A. Greenkorn, and 0. A. Hougen, "Generalized Thermodynamic Properties of Pure Fluids," Vol. 4, College of Engineering, University of Wisconsin, Engineering EXperiment Station Report, Madison, Wisc., Oct 1955; (b) R. C. Reid and T. K. Sherwood, "Properties of Gases and Liquids," McGrawHill, New York, N. Y., 1958, pp 60-65. (12) K. H$jendahl, Kgl. Danske Vidensk. Selsk., Mat.-Fys. Medd., 24 (2), 1 (1946). (13) J. A. Geddes, J . Amer. Chem. SOC.,55, 4832 (1933). (14) F. Hovorka, R. A. Schaefer, and D. Dreisbach, ibid., 58, 2264 (1936). (15) W. E. Sharp, "The Thermodynamic Functions for Water in the Range - 10 to 10000 and 1 t o 250,000 Bars," University of California Radiation Laboratory Report, UCRL-7118, 1962.
IONIZATION BEHAVIOR OF NaCl
IN
DIOXANE-WATER SOLUTIONS
1101
Table I: Properties of Dioxane-Water Solvent Compositions a t 100" from 1 to 4000 Bars
-
Pressure, bars Dioxane , wt %
V.P."
29.7 40.3 50.8 60.5 70.5
0,970 0,970 0.968 0,964 0.960
29.7 40.3 50.8 60.5 70.5
Satn
35.3 28.6 22.6 16.8 11.8
500
0.984 0.986 0.987 0.988 0,989 36.2 29.4 23.0 17.4 12.2
1000
1500
1.004 1.006 1.007 1* 008 1.009
1.021 1.023 1.024 1.025 1.026
37.1 30.1 23.5 17.9 12.5
0.42 0.45 0.48 0.50 0.51
0.43 0.47 0.50 0.53 0.54
0.45 0.49 0.53 0.56 0.57
29.7 40.3 50.8 60.5 70.5
4.1 1.6 0.8 0.5 0.2
4.4 1.8 1.o 0.6 0.2
4.6 2.0 1.1 0.7 0.2
Densities,b g/cm8 1.037 1.039 1.040 1.041 1.042
2600
3000
3500
4000
1.051 1.053 1.054 1.055 1.056
1.064 1.066 1.067 1.068 1.069
1.078 1.079 1,080 1.081 1.082
1,090 1.091 1.092 1.093 1.094
Dielectric Constantsb 39.4 38.7 32.0 31.4 25.0 24.5 18.9 18.6 13.0 13.2
37.9 30.8 24.1 18.2 12.7
29.7 40.3 50.8 60.5 70.5
2000
0.48 0.51 0.56 0.59 0.60
Viscosities,b OP 0.50 0.54 0.59 0.62 0.64
Specific Conductances 5.0 2.3 1.2 0.8 0.2
40.0 32.5 25.4 19.2 13.4
0.52 0.57 0.62 0.66 0.68
of Solvent,c ohm-1cm-1, 5.3 5.7 2.5 2.8 1.4 1.6 0.8 0.9 0.3 0.3
0.55 0.60 0.66 0.70 0.72
x
106 6.0 3.1
1.7 1.0 0.3
40.7 33.0 25.8 19.5 13.6 0.58 0.64 0.70 0.74 0.77
0.61 0.68 0.74 0.79 0.82
6.3 3.4 1.9 1.1 0.3
6.7 3.7 2.1 1.1 0.3
a Saturation vapor pressure is approximately 1 bar for all these solutions. Data are from Dunn and Marshall, ref 9. values (see Experimental Section of text). c Values derived from experimental measurements.
unpublished work of Kennedy, et al. T o estimate the densities of the solutions at different dioxane-water compositions and a given pressure, it was assumed that ideal solutions were formed at 100": solvent density = density of pure water X volume fraction of water density of pure dioxane X volume fraction of dioxane. These solution densities are given in Table I. Dielectric Constants. When the dielectric constants ( D ) of Akerlof and Short1' for dioxane-water solutions a t 1 bar and at both 20 and 80" were plotted as log (D - 1) vs. log CH,o(mol/l.), straight lines resulted in both cases at solvent compositions less than 90 wt % dioxane. Since our solutions do not contain more than 71 wt % dioxane, the dielectric constants assigned by Dunn and Marshallgto several compositions of dioxanewater at 100" and saturation pressure were treated by a method of nonlinear least squares18 to calculate the slope and intercept of the best straight line which describes them. The equation for this line is
+
log (D - 1) = -0.56055
+ 1.32965 log C H l ~ (1)
By using the densities estimated previously to calculate the molar concentration of water, and with the assumption that eq 1 applies at 'high pressures, the dielectric constants were estimated with eq 1 for each experi-
41.3 33.4 26.1 19.8 13.8
Calculated
mental solvent composition a t various pressures to 4000 bars. Table I contains these estimated dielectric constants; again, it should be emphasized that these values are based on the assumed validity of eq 1 to high pressures. Viscosities. The viscosities (7) of water at 100" and pressures to 4000 bars which were used are those determined by Bett and Cappi.lg To estimate the viscosities of pure dioxane as a function of pressure, it was assumed that the fluidities (l/q) of dioxane decrease in absolute value with increasing pressure to the same extent as do the fluidities of water. The viscosities for various dioxane-water compositions at 100" and 1 bar given elsewheree were plotted against wt % dioxane; curves for the higher pressures were drawn symmetrical to this one through the previously fixed data points for pure water and pure dioxane. The solution viscosities estimated in this wanner are recorded in Table I. (16) G. C. Kennedy, W. L. Knight, and W. T. Holser, Amer. J . Sci., 256, 590 (1958). (17) G. Akerlof and 0. A. Short, J . Amer. Chem. Soc., 58, 1241 (1936). (18) M. H. Lietzke, U. S. Atomic Energy Commission Report ORNL-3269, Oak Ridge National Laboratory, Oak Ridge, Tenp., April. 1962. (19) K. E. Bett and J. B. Cappi, Nature, 207, 620 (1966).
The J O U Tof ~Phyaical Chemistry, Vol. 76, No. 8,1971
L. B.YNATTS,L. A. DUNN,AND W. L. MARSHALL
1102
Table I1 : Specific Conductances (ohm-' cm-1) X lo6 of NaCl in Dioxane-Water Solutions at 100" from 1 to 4000 Bars Dioxane, wt %
NaCl ( m x 109
Satn V.P.6
29.7
3.146 6.923 17.18 0,9510 2.889 7.313 13.24 21.79 1.015 1.931 3.047 7.086 16.28 1.015 1.654 3.278 6.948 16.43 0.9515 1.627 2.940 7.367 15.85
72.2 150.5 356.5 21.01 61.2 146.8 254.2 398 0 21.16 36.64 54.2 116.4 244.4 18.20 27.76 49.1 91.3 179.2 10.92 15.12 24.72 48.6 87.8
40.3
50.8
60.5
70.5
a
I
-
Pressure, bars----------
7
500
1000
1500
2000
2500
3000
3500
4000
70.2 147.2 349.7 20.28 58.9 142.2 248.3 387.6 20.44 35.16 52.0 112.3 237.5 17.32 26.22 46.6 87.6 173.4 10.27 14 43 23.70 46.7 84.7
68.5 144.1 343.1 19.62 57.0 138.2 242.0 376 4 19.75 33.82 49.8 108.5 230.7 16.49 24.80 44.3 83.9 167.5 9.69 13.78 22.74 45.0 81.6
66.8 141.1 336.5 18 99 55.3 134.3 236.1 367.4 19-08 32.52 47.8 104.6 223.7 15.70 23,50 42.2 80.5 161.9 9.18 13 19 21.86 43.2 78.5
65.3 138.1 330.1 18.41 53.8 130 8 230.3 357.8 18.46 31.30 46.1 101.2 217.2 14.95 22.34 40.3 77.2 156.5 8.73 12.64 21.06 41.6 75.5
63.8 135.2 323.8 17.85 52.4 127.4 224.8 348.6 17.88 30.20 44.6 98.0 210.5 14.25 21.30 38.57 74.2 151.4 8.32 12.11 20.28 40.1 72.7
62.4 132.5 317.8 17.34 51.1 124.4 219.2 340.0 17.32 29.14 43.3 95.0 205.1 13.61 20.36 36.95 71.4 146.7 7.93 11.60 19.56 38.60 70.0
61.1 129.8 312.0 16.86 49.8 121.5 213.9 332.0 16.74 28.12 42.0 92.1 199.1 12.99 19.50 35.40 68.7 142.4 7.56 11.10 18.82 37.25 67.4
59.8 127.3 306.4 16.39 48.7 118.7 208.5 324.4 16.20 27.16 40.6 89.3 193.2 12.40 18.68 34.05 66.1 138.2 7.20 10.62 18.08 36.00 64.6
I
I
I
I
I
See footnote a, Table I.
Results and Discussion
t = 100 "C I
Results. The conductance readings were converted to resistances and a correction made for the resistance of electrical leads between the bridge and electrodes. These values in turn were corrected to resistances at infinite signal frequency, since the conductances showed a slight (13%) frequency dependence. By using the appropriate cell constant, specific conductances were calculated and corrections for solvent conductance were made. (See ref 4a for detailed description.) Figure 1 shows the typical form of the curve produced when the corrected specific conductances (K) of NaC1 in various compositions of dioxane-water are plotted against pressure at 100". The gradual decrease in the specific conductance with increasing pressure at this temperature was found also for NaCl in aqueous solutions4* as well as for aqueous solutions of other 1-1 ~ a l t ~ . This behavior can be explained qualitatively on the basis of the effect of pressure upon density and viscosity. The values for these two physical properties increase with an increase in pressure (see Table I). However, increased densities (or water concentrations) promote ionization and thereby increased conductivity, while increased viscosities decrease ionic mobilities resulting in lowered conductivity. Therefore, at 100" and pressures to 4000 bars, the viscosity effect must be the dominant one in these cases. The decrease in specific conductance of NaC1, at isothermal and isobaric conditions, as the fraction of dioxane in the solvent rises is The JOUTWL~ of Physical Chemistry, Vol. 76,N o . 8,1071
(50
1 DIOXANE ( W l %) 29.7
t 25
40.3
-6 (00 L
E
-
50.8
0
%
75 60.5
'
~ ~ 25, ~ ~ , ~I ~ 0
4000
I
1
2000 3000 PRESSURE (bars)
1 4000
1 5000
Figure 1. Specific conductances of some NaCl solutions as a function of pressure in several dioxane-water solvent compositions a t 100'.
due to decreased water concentrations along with increased viscosities. From graphs similar t o Figure 1for all NaC1 solutions in the five dioxane-water solvent compositions,smoothed (20) A. 9 . Quist and W. L. Marshall, J . Phys. Chern., 73, 978 (1989).
IONIZATION BEHAVIOR OF NaCl
1103
DIOXANE-WATER SOLUTIONS
IN
specific conductances were read at 500-bar intervals. These values to 4000 bars are presented in Table 11. Equivalent conductances (A) were calculated from the smoothed specific conductances, the molalities of NaC1, and the estimated densities of the solvents, which were assumed to be the densities of these dilute solutions. The effect of pressure on the equivalent conductances of approximately 0.0071 m NaCl in different solvent compositions is illustrated in Figure 2. The equivalent conductances are seen to decrease by 30 5% as the pressure rises from 1 to 4000 bars. Figure 3 shows the effect of solvent composition upon the equivalent conductances for exactly 0.00710 m NaCl a t several different pressures. A solution with this exact molality was not measured in the various dioxane-water compositions (see Figure 2) ; hence, the equivalent conductances were interpolated from plots of A vs. m'lafor each solvent composition. Equivalent conductances for NaCl in pure water as solvent were interpolated from values of an earlier s t ~ d y . ~ The " dashed portions of the curves in Figure 3 are not included in the range of experimental measurements. However, this general shape for the curves is eubstantiated by the curve calculated for 1 bar from simple conductance theory (see inset, Figure 3). As an approximation, it was assumed that the activities of the species in solution were equal to one so that the conventional ionization or dissociation constant for NaCl was defined by
250
I = IOO'C
200 DIOXANE
-
IW! X ) 29.7
L
1,
(50
'5
E
40.3
l
r
50.8
N
6
I
100
=
-P 'k
2500
See footnote a, Table I.
400
--._
2000
250
N
s
1
P I
/
Earlier conductance studies with such diverse elecNaClJ4"NaBr,40NaI,4eHBr,4band trolytes as KHS0dJZ6 NH40H4d have shown a linear relationship between limiting equivalent conductance and density (or concentration) of the solvent water at constant tempere ture over a range as great as 0.4-1.0 g/cma. I n those investigations, applied pressure determined the densities so that this wide range of densities was attainable only at temperatures of 400" or greater, whereas a t 100" the range was only 0.96-1.09 g/cma. For the present, study at 100", however, concentrations (or densities) of water in dioxane-water solutions were varied largely by the addition of dioxane to the solutions; hence, the range is from
