5526
J. Phys. Chem. 1992, 96, 5526-5529
dipole moments and polarizabilities for R113 and RE245 have not, to the best of our knowledge, been reported before.
References and Notes ( 1 ) Downing, R. C. Fluorocarbon Refrigerants Handbook; Prentice-Hall: Englewood Cliffs, NJ, 1988. (2) Butcher, S. S.;Cohen, R. A.; Rounds, T. C. J. Chem. Phys. 1971, 54,
4123. (3) Hirano, T.; Nonoyama, S.; Miyajima, T.; Kurita, Y.; Kawamura, T.; Sato, H. J. Chem. Soc., Chem. Commun. 1986, 606. (4) Meyer, C. W.; Morrison, G. J . Phys. Chem. 1991, 95, 3860. (5) In order to describe materials and experimental procedures adequately,
it is occasionally necessary to identify commercial products by manufacturer's name or label. In no instance does such identification imply endorsement by the National Institute of Standards and Technology, nor does it imply that the particular product or equipment is necessarily the best available for the purpose. (6) Chae, H. B.; Schmidt, J. W.; Moldover, M. R. J. Phys. Chem. 1990, 94, 8840. (7) Defibaugh, D.; Morrison, G. To be published. (8) Goodwin, A. R. H.; Weber, L. A.; Morrison, G. To be published. (9) Benning, A. F.; McHarness, R. C. Ind. Eng. Chem. 1940, 32, 814. (10) Meyer, C. W.; Morrison, G. J . Chem. Eng. Data 1991, 36, 409. (1 1) Born, M.; Wolf, E. Principles of Optics; Pergamon: London, 1959. (1 2) Bottcher, C. J. F. Theory of Elecrric Polarization; Elsevier: New York, 1952. (1 3) McClellan, A. L. Tables of Experimental Dipole Moments; W. H. Freeman: San Francisco, 1963; Vol. 1.
(14) McClellan, A. L. Tables of Experimental Dipole Moments; Rahara Enterprises: El Cerrito, CA, 1973; Vol. 11. (1 5) McClellan, A. L. Tables of Experimental Dipole Moments; Rahara Enterprises: El Cerrito, CA, 1989; Vol. 111. (16) Carey, F. A.; Sundberg, R.J. Advanced Organic Chemistry, Part A: Structure and Mechanisms; Plenum/Rosetta: New York, 1980. (17) Wiberg, K.; Murcko, M. A.; Laidig, K. E.; MacDougall, P. J. J. Phys. Chem. 1990, 94, 6956. ( I 8) Mizushima, S. Structure of Molecules and Internal Rotation; Academic Press: New York, 1954. (19) Wiberg, K. B.; Murcko, M. A. J . Phys. Chem. 1987, 91, 3616. (20) Hammarstram, L.-G.; Liljefors, T.; Gasteiger, J. J . Compur. Chem. 1988, 9, 424. (21) Dewar, M. J. S.; Rzepa, H. S. J. Am. Chem. SOC.1978, 100, 58. (22) Buckley, G. S.; Rodgers, A. S. J . Phys. Chem. 1983, 87, 126. (23) Dixon, D. A.; Smart, B. E. J. Phys. Chem. 1988, 92, 2729. (24) Huber-Walchi, P.; Giinthard, Hs. H. Chem. Phys. Lett. 1975,30,347. (25) Freisen, D.; Hedberg, K. J. J. Am. Chem. Soc. 1980, 102, 3987. (26) Yamanouchi, K.; Sugie, M.; Takeo, H.; Matsumura, C.; Kuchitsu, K. J. Phys. Chem. 1984, 88, 2315. (27) Fernholt, L.; Kveseth, K. Acta Chem. Scand., Ser. A 1980, 34, 163. (28) Harris, W. C.; Holtzclaw, J. R.; Kalasinsky, V. F. J . Chem. Phys. 1977,67, 3330. (29) Balthuis, J.; van den Berg, J.; Maclean, C. J. Mol. Struct. 1973, 16, 11. (30) Abraham, R. J.; Kemp, R. H. J . Chem. Soc. B 1971, 1240. (31) Mountain. R. D.: Morrison. G. Mol. Phvs. 1988. 64. 91. (32) Handbookof Chemistry ad'physics, 53rd ed.;The Chemical Rubber Co.: Cleveland, 1972.
Effects of Pressure, Temperature, and Concentration on the Viscosity of an Aqueous Solution of Sodium Chloride Seiji Sawamura,* Yukihiro Yoshimura, Kiyoshi Kitamura, and Yoshihiro Taniguchi Department of Chemistry, Faculty of Science and Engineering, Ritsumeikan University, Tojiin, Kita- ku, Kyoto, 603, Japan (Received: January 2, 1992)
The viscosity of aqueous sodium chloride solution was measured in the ranges of 0.5-3 mol kg-l,283.15-323.15 K, and 0.1-375 MPa, and the activation energy of viscous flow and Jones-Dole's B coefficient were estimated. The activation energy has a minimum at about 200 MPa as well as that of pure water, and the minimum becomes shallow with increasing the concentration. The B coefficient has a maximum at about 100 MPa and the enhancement up to 100 MPa is remarkable at low temperature. These phenomena were interpreted from the standpoint of pressure, temperature, and concentration effects for the water structure,
Introduction Viscosity measurements of electrolyte solution have produced information about the interaction between ions and water. Most of them have been done as a function of concentration and temperature. In the present work, another function of pressure is added. The main study of the concentration effect on the viscosity of electrolyte solutions is to relate the viscosity to the Jones-Dole's equation (eq l),l where 7 and q0 are the viscosities of solution and 7/70
=1
+
+ Bc
(1)
water, respectively, and c is the concentration (mol dm-3). The coefficient of A is related to the Coulombic interaction between solute ions and has a positive valueU2 The coefficient of B is concerned with the interaction between ions and solvent and has a positive or a negative value, depending on the sort of solutes and solvents. Nightingale has proposed to divide electrolyte solutes into two types.3 One is the solute whose B coefficient is positive, and the other is negative. The former solute is thought to enhance the water structure because the viscosity increases with increasing concentration, and the latter is called the structure breaker. These effects of structure maker and breaker of electrolytes on water are easy to be imagined using an ionic hydration model of Frank
and Wen.4 Two types of hydration water, outer and inner, are supposed to surround an ion. The inner hydration water is strongly attracted to an ion by the Coulombic interaction and its fluidity is reduced. The outer hydration water is thought to be the water whose structure is that of bulk water disturbed by the weak Coulombic interaction. Therefore, this water is more fluid than both inner hydration water and bulk water. The B coefficient depends on the degree of these hydration domains and strength of the hydration. On the other hand, the temperature dependence of the viscosity has been represented by the activation energy of viscous flow proposed by Eyring (eq 2).5 Equation 3 is derived from eqs 2
[%Ip=%
and 1 neglecting the term of A c I / ~in eq 1, where &(sol) and
Ev(H20)are the activation energies of solution and water. If B increases with increasing temperature, &(sol) is smaller than Ev(H20),suggesting that the water structure is broken by adding
0022-365419212096-5526%03.00/0 0 1992 American Chemical Society
The Journal of Physical Chemistry, Vol. 96, No. 13, 1992 5527
Viscosity of an Aqueous Solution of NaCl electrolytes. Because the B of an electrolyte can change sign depending on temperature, the temperature dependence of B has been thought to be a more fundamental parameter for water structures6 There are two interesting viscosity phenomena of water at high pressure. The viscosity vs pressure plots at the temperature below 308 K have a minimum at 0-200 MPa, depending on temperature, and the activation energy of viscous flow has a minimum at about 200 MPae7 These reductions of viscosity and activation energy with increasing pressure on the low-pressure side of the minima have been ascribed to a break of the bulky water structure like hydrogen-bonded tetrahedra.3 Pressure dependences of B and the activation energy of electrolyte solution may remarkably change at these pressures because these properties should include those of pure water. Therefore, the viscosity of aqueous electrolyte solution at pressure not only below 200 MPa but also above it has aroused our interest. Viscosities of sodium chloride solution and sea water at high pressure have been measured by Cohen at 0.1-100MPa? Howe and Johnson at 0.1-200 MPa,8 and Suzuki et al. at 0.1-50 MPa.Io Kestin et al. have extensively measured the viscosity of aqueous solutions of sodium chloride," potassium chloride,I2 sodium carbonate," potassium carbonate,13 sodium sulfate,I4 and potassium sulfate14as a function of concentration, temperature, and pressure, though their pressure is at most 30 MPa, not exceeding 200 MPa. Horne and Johnson estimated the activation energy of aqueous sodium chloride solution, which decreased with increasing pressure up to 200 MPaa8 But there has been no data of the activation energy above 200 MPa and B a t any high pressure. In the present work we measured the viscosity of aqueous sodium chloride solution at several concentrations, temperatures, and pressures up to 375 MPa using a high-pressure rolling-ball viscometer designed by us,15and estimated the activation energy of viscous flow and Jones-Dole B coefficient at high pressure.
Experimental Section Sodium chloride (Nacalai Teque Co.) was recrystallized from water and dried under reduced pressure. Water was purified by distillation after deionization. Sample solutions were prepared at the concentrations of 0.500,1.000,2.000,and 3.000 (f0.0002) mol kg-I using a chemical balance. The sample solution was passed through a membrane filter and directly injected into the inner cell of the high-pressure rolling-ball viscometerI5 after the first few cubic centimeters of the solution was discarded. The viscosity, q, was estimated using eq 4,where K is a constant, p b and pm are 7
= K(Pb - ps)At
0.51
,
0
,
,
,
,
I
200 400 P / MPa
2
1 0.5
0
I
0
200
400
P / MPa
a" E
\
c
(4)
the densities of a ball of the viscometer and the sample solution, respectively, and At is the time required to roll the ball through the inner cell. The K at 0.1 MPa was estimated from the viscosity and density data of a sample solution and the At, and the deviation of K at high pressure was corrected using the compression datal6 of glass which is the material of the inner cell and ba11.15 The At was measured for each sample solution a t temperatures of 283.15,298.15,and 323.15 (fO.O1) K and pressure up to 375 MPa. At least two sample solutions of the same concentration were used for the measurement. The reproducibility of At was less than fl%. The p s of aqueous sodium chloride solution at high pressure was estimated by fitting the recommended density datal7 up to 100 MPa to Tait-Whole equation.I8 The q values of aqueous sodium chloride solution a t atmospheric pressure were cited from Kestin et al." and Out et
Results and Discussion A. Viscosity at High Pressure. Figure 1 shows pressure dependences of the viscosity of aqueous sodium chloride solution and pure water. The viscosity minimum, observed for pure water, seems to disappear with not only increasing temperature but also addition of sodium chloride. The dotted lines in Figure 1 are estimated from the correlating equation, applicable to pressure up to 35 MPa, by Kestin et al." and extended up to 150 MPa.
.'~\'
0
200 400 P / MPa
Figure 1. Pressure dependences of the viscosity for aqueous sodium chloride solutions at 323.15 K (a), 298.15 K (b), and 283.15 K (c). m = 0, 0.5, 1, 2, and 3 mol kg-I. Curves for pure water (m = 0 mol kg-') are cited from ref 7. Dashed lines are extrapolated lines cited from Kestin et al."
Pressure dependences of our viscosity at 298.15 and 323.15 K well fit to these dotted lines up to 35 MPa, respectively, except for those a t 283.15 K. The deviations at 283.15 K are ascribed to the temperature being out of the range, that is, 293.15-423.15K, for the correlating equation by Kestin et al." Our data are fitted for the second polynomials of pressure (eq 5) within fl%. The q
= a.
+ a l p + a2P2
(5)
values of the parameter are shown in Table I. B. Activation Energy of Viscous Flow. The logarithm of the viscosity of 1.000mol kg-' aqueous sodium chloride solution is plotted against the reciprocal of temperature in Figure 2. The lines at 0.1 and 100 MPa cross each other at about 283.15 K. This
Sawamura et al.
5528 The Journal of Physical Chemistry, Vol. 96, No. 13, I992 TABLE I: Numerical Values of the Coefficients in Eq 5 T/K m/mol kg-' u ~ / ~ OPa - ~s a1/10-I2 s ~ ~ / 1 0 Pa-' - ~ 's ~~
283.15 298.15
323.15
I
3.0
1
3.2 T-1
2.42 2.1 1 1.68 1 .oo 0.72 1.18 0.55 0.26 0.32 0.3 1 0.43
-0.467 -0.172 0.233 0.056 0.208 0.199 0.541 0.253 0.254 0.353 0.343
1.352 1.400 1.534 0.927 0.972 1.074 1.197 0.575 0.606 0.675 0.755
0.5 1 2 0.5 1 2 3 0.5 1 2 3
,
'0.05t
.5
I
,
,
1
2 3 4 c / mol dm-3 Figure 4. (q/qo- 1 - A C ' / ~ ) /vsC c for aqueous sodium chloride solution at 298.15 K and 0.1 MPa: (0)Kaminsky;2 (A)Kume et a1.;2' (0)Afml et a1.;22(v)Out et al.;I9 (---) correlating equation of q(P,t,c) by Kestin et al." 0
1
I
3.6
3.4 10-3 K-1
Figure 2. In q vs 1/ T for 1 mol kg-' aqueous sodium chloride solution. The line at 0.1 MPa is drawn using the data of Out et al.19 and the correlating equation by Kestin et al." c
/ mol dm-3
Figure 5. (q/qo- 1 - A c ' / ~ ) /vs c c for aqueous sodium chloride solution at 298.15 K and several pressures: (0)0.1 MPa; (A) 100 MPa; (0) 200 MPa; (v)300 MPa; (0) 375 MPa.
all of water molecules may be thought to contact with the ions at 4 ( - 5 6 / 1 3 ) mol kg-'. When the E, at 0-2 mol k g ' in Figure 3 is linearly extrapolated to 4 mol kg-', the dotted line in Figure 3 is obtained. It suggests that E, increases with increasing pressure at 4 mol kg-' without having any minimum. C. Jones-Dole B Coefficient. Equation 6 is an extended Jones-Dole equation, where A, B, and D are constants, qo is the q/qo = 1
0
200
400
MPa Figure 3. Pressure dependences of the activation energy of the viscosity for m mol kg-' aqueous sodium chloride solution at 298.15 K. P /
phenomenon comes from the viscosity minimum in Figure 1. The lines in Figure 2 are fitted to the second polynomial of 1/ T, and the activation energy, E,, was estimated from the slope at 298.15 K using eq 2. The results are shown in Figure 3. The fact that the E, at 0.1 MPa decreases with increasing concentration has been ascribed to the breaking of the water structure,8 by the addition of sodium chloride. The minimum observed for pure water at about 200 MPa becomes shallow with increasing concentration of sodium chloride. The reason for such lowering of the pressure dependence on the E, at high concentration is that water structure which should be broken by increasing pressure is already broken by addition of sodium chloride. The E, of aqueous sodium chloride solution measured by Horn and Johnson8 was reduced by about 10% at 200 MPa but did not depend on the concentration between 1 and 2 mol kg-'. It may ascribed to the small temperature range, that is, 277-283 K, to estimate the E,, which is about one-seventh of our temperature range in the measurement. The fact that the minimum remains at 2 mol kg-' in Figure 3 shows that the water structure is not completely destroyed at this high concentration yet. Because the number of water molecules which contact with sodium or chloride ions is 13:O
+ A c ' / ~+ Bc + Dc2
(6)
viscosity of water, and c is the concentration (mol dm-3) of the electrolyte. This equation can be changed to eq 7 as a linear function of c. ( q / q o - 1 - A C ' / 2 ) / C = B + Dc (7) Some viscosity data' of aqueous sodium chloride solution at atmospheric pressure are plotted in this form as shown in Figure 4, where A is calculated from the t h e ~ r y . ' ~The . ~ ~data may be divided into two types: one is the data from Kaminsky,8 Kume et a1.,21and Out et al.,19 and the other is the data from Kestin et al." and Afzal et a1.22 The former measurements were intended to estimate the B in eq 7 and done at low concentration, and the B can be estimated to be about 0.08 mol-' dm3 in Figure 4. The latter were done not at low concentrations but in a wide range of the concentrations without regard to the estimation of the B. Therefore, their values of (q/qo- 1 - Ac1i2)/care not necessarily precise at low concentration. Figure 4 in any event shows that the value of ( q / q o - 1 - A c ' / ~ ) /isc linear to c up to 4 mol dm-3 and the B coefficient can be roughly estimated at zero concentration of the linear line. Our viscosity data at high pressure are plotted in Figure 5 in the same manner. Linear correlations were observed at all pressures. Then B was estimated from the intercept at c = 0 mol dm-3. The pressure dependences are shown in Figure 6. B at 283.15 K steeply increases with increasing pressure up to 100 MPa and then mildly decreases. This increase of B by pressure up to 100 MPa becomes small with increasing temper1~19921922
The Journal of Physical Chemistry, Vol. 96, No. 13, 1992 5529
Viscosity of an Aqueous Solution of NaCl
1 I
0
L 00
200 P /
error
D. Conclusion. The activation energy for viscous flow and Jones-Dole’s B coefficient of aqueous sodium chloride solution have an inversion point at 200 and 100 MPa, respectively. These phenomena may be concerned with the phase transition of ice Ih to ice I1 or I11 caused at about 200 MPa. Registry No. Sodium chloride, 7647-14-5.
1
References and Notes (1) Jones, G.; Dole, H. J . Am. Chem. SOC.1929, S I , 2950. (2) Kaminsky, M. Z. Phys. Chem. N . F. 1956.8, 173. (3) Nightingale, E. R., Jr., Chemical Physics of Ionic Solutions; Conway, B. E., Barradas, R. G., Eds.; John Wiley & Sons: New York, 1966; p 87.
I
MPa
Figure 6. Pressure dependences of Jones-Dole E coefficient of sodium chloride in water.
ature. On the other hand, the B at pressure above 100 MPa seems not to depend on temperature. The increase of B by pressure up to 100 MPa may be ascribed to the water structure at atmospheric pressure being broken by addition of sodium chloride, and this breaking effect of the electrolyte becomes less clear at high pressure because the water structure is already broken by pressure. Therefore, E apparently increases with increasing pressure up to 100 MPa. Ibuki and Nakahara24have correlated the B to some solvent properties using Hubbard-onsager’s electrohydrodynamic equation for electrolyte solution based on the continum model as shown in eq 8, where eo, q, 7 are the dielectric constant, viscosity,
B = (7/qe0)3/4
(8)
and dielectric relaxation time of solvent, respectively. A similar equation has been introduced by Clarkz5changing the exponent of 3 / 4 in eq 8 to 1. Using the high-pressure data of to,z6 q,7 and 727 at 298.15 K, it can be estimated that the value of (7/qt0) decreases by 13% at 100 MPa and 23% at 200 MPa. This reduction does not coincide with our results for B up to 100 MPa. It shows that the water up to 100 MPa is not a dielectric continuous fluid supposed by eq 8. At high pressure above 100 MPa E decreases with increasing pressure. The degree of the reduction of B is about 10% for a pressure change from 100 to 200 MPa as an example, and is close to that of ( T / ~ c , , ) ,Le., 10% (=23-13%). It suggests that the pressure breaks any water structure and the water at high pressure above 100 MPa becomes the dielectric continuous fluid. Further, the fact that B at high pressure above 100 MPa hardly depends on temperature suggests that the water structure which is constructed by hydrogen bonding disappears at the pressure.
Stokes, R. H.; Mills, R. Viscosity of Electrolytes and Related Properties; Pergamon Press: Oxford, U.K., 1965; Chapter 4. Horvath, A. L. Handbook of Aqueous Electrolyte Solutions; John Wiley & Sons: New York, 1985; Chapter 2.14. (4) Frank, H. S.; Wen, W. Y. Discuss. Faraday SOC.1957, 24, 133. (5) Glasstone, S.;Laidler, K. J.; Eyring, H. The Theory of Rate Processes; McGraw-Hill: New York, 1941; Chapter 9. (6) Desnoyers, J. E.; Arel, M.; Leduc, P.-A. Can. J . Chem. 1%9,47, 547. (7) International Association for the Properties of Steam. The IAPS Formulation 1985 for the Viscosity of Ordinary Water Substance; 1985. (8) Horne, R. A,; Johnson, D. S. J. Phys. Chem. 1967, 71, 1147. (9) Cohen, R. Ann. Phys. 1892, 45, 666. (10) Suzuki, H.; Nagashima, A. Nippon Kikaigakkai Ronbunshu (Trans. Jpn. SOC.Mech. Eng.) 1980, B46, 1574. (11) Kestin, J.; Khalifa, H. E.; Correia, R. J. J . Phys. Chem. Ref Data 1981, 10, 71. (12) Kestin, J.; Khalifa, H. E.; Correia, R. J. J. Phys. Chem. Ref Data 1981, 10, 57. (13) Correla, R. J.; Kestin, J.; Khalifa, H. E. J . Chem. Eng. Data 1980, 25, 201. (14) Correla, R. J.; Kestin, J. J . Chem. Eng. Data 1981, 26, 43. (15) Sawamura, S.;Takeuchi, N.; Kitamura, K.; Taniguchi. Y. Reu. Sci. Instrum. 1990, 61, 871. (16) Adams, L. H. J . Am. Chem. SOC.1931, 53, 3769. (17) Rogers, P. S. 2.;Pitzer, K. S. J . Phys. Chem. Ref Data 1982, 1 1 ,
15. (18) Weal, K. E. Chemical Reactions at High Pressures; E. and F. N. Spon Limited: London, 1967; Chapter 2.2. (19) Out, D. J. P.; Los, J. M. J . Solution Chem. 1980, 9, 19. (20) Heinzinger, H. Lecture Notes in Chemistry 44, Supercomputer Simulations in Chemistry, Dupuis, M., Ed.; Springer-Verlag: Berlin, 1986; p 261. (21) Kume, T.; Tanaka, M. Nippon Kagaku Kaishi ( J . Chem. Soc. Jpn.) 1960,81, 534. (22) Afial, M.; Saleem, M.; Mahmood, M. T. J . Chem. Eng. Data 1989, 34, 339. (23) Falkenagen, H.; Vernon, E. L. Philos. Mag. 1932, 14, 537. (24) Ibuki, K.; Nakahara, M. J . Chem. Phys. 1986,85, 7312. (25) Clark, G. J. J . Chem. Phys. 1976,65, 1403. (26) Owen, B. B.; Miller, R. C.; Milner, C. E.; Cogan, H. L. J. Phys. Chem. 1961, 65, 2065. (27) Pottel, R.; Asselborn, E.; Eck, R.; Tresp, V. Ber. Bunsen-Ges. Phys. Chem. 1989, 93, 676.
