Journal of Solution Chemistry, I/ol. i0, No. 12, 1981
Conductance of Aqueous NaCI Solutions at Pressures up to 2000 Atm 1 F. H. Fisher 2 and A. P. Fox 2 Received April 24, 1981; ~'evised December 5, 1981 Electrical conductance measurements are reported for aqueous NaCI solutions at 25 ~ as a function o f concentration up to O.02M and pressures up to 2000 atm. The data were analyzed with the Fuoss-Hsia-Fernandez-Prini (FHFP) equation. The standard error o f fit, cr A, varies from 0.04 at 1 arm to 0.10 at 2000 atm. The increase o f cr A with pressure arises from increasing non-randomness in the distribution o f errors about the FHFP equation suggesting that modifications in the theory are necessary. The pressure dependence o f A o for NaCl and KCI is nearly identical
KEY WORDS: Conductance; high pressure; NaCI; aqueous solutions.
1. INTRODUCTION
We have measured the effect of pressure on the conductance of aqueous solutions of NaCI up to 0.02M at 25~ in the same manner as we reported for KCI solutions. (1) Those data have been analyzed with the Fuoss-Hsia-Fernandez-Prini (FHFP) conductance equations, c2,3) With our analysis and the Chiu-Fuoss C4) data we find no evidence for association at atmospheric pressure for concentrations up to 0.1M. We find, as we did for the KCI solutions, a progressive increase in non-randomness of differences between theory and experiment as pressure increases. While the effect of pressure on the equivalent conductance at infinite dilution for NaC1 and KCI is nearly identical, the distance parameter shows contrasting behavior. For NaCI solutions, the distance parameter decreases by 17% for a pressure change of 2000 atm in contrast to the 8% increase reported for KCI. (1~ Our results for
1Contribution of the Scripps Institution of Oceanography, New Series. 2University of California, San Diego, Marine Physical Laboratory of the Scripps Institution of Oceanography, San Diego, CA 92152. 871 0095-9782/81/1200-0871503.00/0 9 1981 Plenum Publishing Corporation
872
Fisher and Fox
NaCI are in excellent agreement with those of Gancy and Brummer (5,6) and Pribadi. (7) The effect of solution vs. solvent viscosity at atmospheric pressure was investigated and found to be negligible over the concentration range of this work. 2. EXPERIMENTAL
Measurements were made at atmospheric pressure in 180 ml cells and at elevated pressures in 30 ml cells. The 180 ml cells were calibrated with KC1 solutions using the conductance data of others. (5~6) Alpha-Inorganic Ultra Pure fused NaC1 was used for the preparation of the solutions. The experimental procedures for this work are identical to those we reported for the pressure work on KCI. (1) 3. RESULTS
The measured values of equivalent conductance are given in Table I. The data are results from a single run at each concentration. Measurements from a duplicate run, made as a check, were all within 0.04% of the values reported in Table Ib The data shown were analyzed with the FHFP conductance equation A = A o -- Sc 1/2 --If- Eclogc + Jlc - - J2 r
(1)
by varying A o and the distance parameter d to minimize the standard error of fit, the same procedure used for KCI. (1) In our analysis we used the density data of Kell and Whalley (s) extrapolated to 2000 atm, the dielectric constant data of Srinivasan and Kay, (9) and the viscosity data of Bett and Cappi.(~~ In the free (A o, d) fit, the distance parameter showed a steady decrease with pressure with the exception of the value for 250 atm. By constraining the distance parameter to vary smoothly with pressure d(P) = 3.657 -- 1.927 x
10-4(p-1)
--
5.675 x 10"8(P-1 ) 2 __..06
(2)
we obtained the pressure dependence of the parameter for Eq. (1) as shown in Eqs. (3-7) Ao(P) = 126.506 + 4.646x 103(p-I) --3.171• 10-6(p-1) 2 + 3.806x 10-~~
3 ---.02
(3)
873
Conductance of Aqueous NaCI a! High Pressure
Table I. Molar Conductance for A q u e o u s NaC1 at 25~ Function of Pressure
as a
P (atm) 104c
1
250
500
750
1000
1250
1500
1750
2000
0.0 b (126.51)(127.47) (128.08) (128.37) (128.36) (128.10) (127.63) (126.97) (126.16) 2,305 125.19 126.04 126.75 127,05 127.10 126.86 126.37 125.79 125.00 2,749 125.04 125.93 126.58 126,90 126.95 126.67 126.14 125.57 124.88 4,039 124.77 125,64 12632 126,68 126.74 126.44 125.98 125.34 124.60 5,011 124.51 125.42 126.04 126,44 126.45 126.15 125.68 125.07 124.32 9.541 123.79 124.74 125.40 125,63 125.66 125.37 125.03 124.24 123,52 17.76 122.86 123.86 124.47 124.73 124.73 124.46 123.93 123.50 122.60 52.05 120.55 121.45 122.07 122.35 122.33 122.15 121.62 121,00 120.30 101.0 118.44 119.38 119.94 120.23 120.25 120.09 119.60 118.98 118.21 207.2 115.60 116.58 117.15 117.47 117.50 117.24 116.81 116.21 115.52 S 89.37 89.11 8 8 . 5 8 8 7 . 7 9 8 6 . 8 0 85,67 8 4 . 4 6 8 3 . 2 3 82.01 C 46.58 4 5 . 1 0 4 3 . 6 6 42.33 4 0 . 8 3 3 9 . 4 0 3 8 . 0 3 3 6 . 6 8 35.34 J1 209.47 203.32 196.40 188.72 180.97 172.66 164.02 155.61 146.97 J2 2 3 0 . 9 0 220.78 209.35 196.75 184.45 171.42 158.01 145.38 132.60 ~A 0.04 0.04 0.03 0.05 0.07 0.06 0.08 0.09 0.10 aUnits: mol-dm"3. bExtrapolated.
S(P)
= 89.365--3.038 x 10-4(p-1) - 2.847• 10-6(p-I) 2 + 5.794x 10l~
E(P)
• (0.01)
(4)
= 46.576 -- 5.918x 103(p-I) + 1.481 x 107(p-1)2 •
(5)
J1(P) =
209.492 -- 2.339• 102(P-1) - - 6.539• 106(p-I) 2 + 1.299• 10-9(p-I) 3 ---.09
(6)
JE(P) = 230.98 -- 3.919• 102(P-I) -- 9.999• 106(p-I) 2 + 2.501 • 109(p-I) 3 ___.21
(7)
T h e constrained fit yields a o-A shown in Table I at each pressure which is only slightly greater than that obtained with the free fit. At one a t m o s p h e r e the following equation represents our results for NaCI
Fisher and Fox
874
9
25 ~ NoCI
9
9 1 ATM & 1OO0 ATM 9 2 0 0 0 ATM
.i
-
OA
I
[
2.0
3.0
4.0
so
Fig. 1. Effect of pressure o n distance parameter for NaC1 at 25~ by ~ A vs. d fits to F H F P conductance equation.
e.o
as determined
A = 126.506 -- 89.37c 1/2 + 46.58c log c + 209.49c -- 230.98c 3/2 _+ .04
(8) In Table II we see that the distance parameter decreases by 17% for a pressure change of 2000 atm. For KC1 (1) we found the opposite behavior for d; an increase of 8%, very nearly the same as that shown for the dielectric constant in Table II. In neither case does the pressure dependence of the distance parameter vary, as expected, inversely with the dielectric constant. By varying the value of d at atmospheric pressure and constraining it to have the same pressure dependence as in Table II, we obtained the results for o- A vs. d as shown in Fig. 1. The distance parameter obtained with our procedure is located at a fairly sharp m i n i m u m in cr A vs. d at all pressures; the results for 1, 1000 and 2000 atm are shown in Fig. 1. For comparison, we show the results ofo- A vs. d for KC1 in Fig. 2. Departures of our data from theory as a function of concentration and pressure are shown in Fig. 3. We show an increasing non-random effect with concentration and pressure, which is opposite in sign to that reported for KC1. (1)
Conductance of Aqueous NaCI al High Pressure
98 ~ ' -
875
25 ~ KCI
-
-
e 1 ATM A 1 0 0 0 ATM .7
6 --
5
eA4
.3
2
ol
I
2.0
I
I
3.0
I
4.0
I
I
5.0
I
I
6.0
d.~,
Fig. Z. Effect of pressure on distance parameter for KC] at 25~ as determined by o-A VS. d fits to FHFP conductance equation. Our values for A o as a function o f pressure are in excellent agreement with those of Gancy and B r u m m e r (5) and Pribadi, (7) except at 2000 bars. F r o m Eq. (2) we find that A o has a calculated m a x i m u m value at 869 atm for NaCI compared to 844 atm calculated for KCI. The ratios A o ( P ) / A o ( 1 ) , shown in Fig. 4, for both NaCI and KC1 demonstrate nearly the same behavior except over the pressure range
between 1000 to 1750 atm. For both salts the A o maximum occurs well above the solvent viscosity minimum around 500 atm. The greater hydration ascribed to the sodium ion to explain its lower equivalent conductance, compared to the potassium ion which has a larger crystallographic radius, does not produce any substantial differences between these two ions for the pressure dependence of A o. 4. EFFECT OF V I S C O S I T Y
In making measurements at concentrations up to 0.02M one needs to ask what effect does viscosity have on conductances at high pressure? Using the Jones-Dole equation (n>
876
Fisher and Fox
Table II. Dielectric Constant and Comparison of Free Fit and Constrained Distance Parameters for Aqueous NaCI at 25~
P,atm
Dielectric Constant
Free Fit a
Constrained Free Fit a
1 250 500 750 1000 1250 1500 1750 2000
78.45 79.37 80.26 81.13 81.98 82.81 83.61 84.40 85.17
3.58 3.72 3.56 3.45 3.38 3.34 3.25 3.10 3.08
3.66 3.61 3.55 3.48 3.41 3.33 3.24 3.15 3.05
aUnits, fl,. "0/'0o = 1 -4- .4c 1/2 + B c
(9)
we find at atmospheric pressure that "0/'0o is 1.0027 for NaC1 and 1.0005 for KCI at 0.02M. The coefficients of Eq. (9) are ion specific with .4 coefficient values of 67x 10 4 and 5.2x 10402) and B values of 0.0793 and -0.0140 (13) for NaC1 and KCI, respectively. It is clear that at the higher concentrations effects of solution viscosity must be considered. However, present theory does not incorporate this specific ion effect although Leist (14) and Wishaw and Stokes (15) have attempted to treat the problem on a simplified ad hoc basis. Inasmuch as ion-specific viscosity effects have not been treated in the FHFP theory at atmospheric pressure, we do not wish to pursue the point further at this time. 5. ASSOCIATION
We find no evidence for association in NaC1 (nor KCI) solutions in our analysis using the same (Ao, Kin, d) search procedure as described in our divalent sulfate paper. (16) Our distance parameter is very nearly the same as the 3.57/~ Bjerrum distance; 3.66-----0.06 A for NaCI and 3.44+--0,03 ~ for KCI. These distances are much smaller than those reported by Chiu and Fuoss, (4) 6.11 A for NaCI and 5.66/~ for KC1. However, they used a different equation in their analysis to
Conductance of Aqueous NaCI at High Pressure
0
O~
877
10
15
v~ Yig. 3. Difference 8 a = Aex p - Atheory aS a function of concentration at various pressures for aqueous solutions of NaC1 at 25~
obtain distance parameters and association constants. Even with their analysis, Chiu and Fuoss conclude that association is unobservable for Cmax <~ = 0.04 molar. We did use the FHFP equation to analyze their results up to 0.1 molar and found no evidence for association. However, without accounting for ion-specific viscosity effects, the validity of such an analysis is open to question. 6. SUMMARY
Our analysis of equivalent conductance in NaCI solutions at elevated pressures has revealed non-random errors between experiment and the FHFP equations, with the non-randomness in the opposite direction to that reported for KCI. From our agreement with the Gancy and Brummer data, and the Pribadi data for NaCI as a function of pressure, we conclude that some modifications are required in the FHFP conductance equations, especially for such ion-specific effects
878
Fisher and Fox 1.018 MAX.
KCI
NaCI
!
]
r .00013
'~ f /
--
• .OO016
CALC. MAX.
1.010
1.008
!
1.006
1.004
1.002
1.000o--
"998f .996 0
I 500
I
1000
I
I
1500 2000 Pressure P ( A T M )
1
2500
3000
Fig. 4. Comparison of A o for NaCI with KCI as a function of pressure at 25~
as viscosity and compressibility at higher concentrations. We note the opposite behavior of the distance parameter with pressure for NaCI as opposed to KCI. At this point we can not offer any insight regarding this effect. Table III. Limiting Equivalent Conductances for NaC1 at 25~ and up to 2000 Bars
Gancy e t al. Pribadi This Work
1
500
Pressure, bars 1000
1500
2000
126.51 126.51 126.51
128.03 128.04 128.03
128.41 128.37 128.37
127.65 127.66 127.67
126.13 126.16 126.26
Conductance of Aqueous NaCI at High Pressure
879
A series of equations giving the pressure coefficients for all the parameters in the FHFP equation provides a good representation of the conductance of NaC1 solutions at 25~ up to 2000 atm for concentrations up to 0.02M. Since the theoretical basis for the FHFP equation apparently gives rise to non-random errors, the equations for NaCI must be regarded as a first attempt to provide an analytic representation of the equivalent conductance as a function of pressure. ACKNOWLEDGMENTS
T h i s w o r k was s u p p o r t e d by t h e N a t i o n a l S c i e n c e G r a n t s N S F O C E 76-02253 a n d N S F O C E 78-08488.
Foundation
REFERENCES
1. 2. 3. 4. 5. 6.
7. 8. 9. 10. 11. 12. 13. 14. 15. 16.
F. H. Fisher and A. P. Fox, J. Solution Chem 8, 627 (1979). R.M. Fuoss and K. L. Hsia, Proc. Natl. Acad. Sci., US57, 1550 (1967). R. Fernandez-Prini, Trans. Faraday Soc. 65, 3311 (1969). Y.-C. Chiu and R. M. Fuoss, J. Phys. Chem. 72, 4123 (1968). A. B. Gancy and S. B. Brummer, J. Phys. Chem. 73, 2429 (1969); J. Chem. Eng. Data 16, 385 (1971). R. L. Kay, 'Ionic Transport in Water and Mixed Aqueous Solvents,' in Water: A Comprehensive Treatise, F. Franks, ed., Vol. 3, (Plenum Press, New York, 1973), pp. 173-209. K. S. Pribadi, Ph.D. Dissertation, Carnegie-Mellon University, 1971. G. Kell and E. Whalley, Phil. Trans. Roy Soc., London A258, 565 (1965). K. R. Srinivasan and R. L. Kay, J. Chem. Phys. 60, 3645 (1974). K. E. Bett and J. B. Cappi, Nature 207, 620 (1965); J. B. Cappi, Thesis, Imperial College, University of London, 1964. G. Jones and M. Dole, J. Am. Chem. Soc. 51, 2950 (1929). H. S. Harned and B. B. Owen, The Physical Chemistry of Electrolyte Solutions, 3rd Ed., (Reinhold, 1958), p. 241. M. Kaminsky, Disc. Faraday Soc. 24, 171 (1957). M. Leis~ Z. Phys. Chem., Leipzig205, 16 (1955). B. F. Wishaw and R. H. Stokes, J. Am. Chem. Soc. 76, 2056 (1954). F. H. Fisher and A. P. Fox, J. Solution Chem. 8, 309 (1979).
