341
OSMOTICCOEFFICIENTS OF AQUEOUS SODIUM CHLORIDE SOLUTIONS
Osmotic Coefficients of Aqueous Sodium Chloride Solutions from 125 to 13O01& by Chia-tsun Liu and W. T. Lindsay, Jr.lb Westinghouse Research Laboratories, Pittsburgh, Pennsylvania
16296
(Received J u n e 90, 1969)
Osmotic coefficients have been determined by vapor pressure lowering measurements on aqueous sodium chloride solutions of 0.1, 0.25, 0.5, and 1.0 nz concentrations at 25" intervals from 125 to 300". Apparatus and methods are described. The results of this work extend high-temperatureosmotic coefficient data to concentrations on the dilute side of the osmotic coefficient minimum. They are consistent with limiting slopes and with concentration and temperature trends established by other data at higher concentrations and/or lower temperatures. High-temperature osmotic coefficient data now seem adequate for calculation of excess thermodynamic quantities for both water and salt up to 300".
Introduction There have been very few investigations of aqueous electrolyte solutions a t high temperatures that have yielded results of good precision. Accurate and precise data are needed to determine how structural and other temperature-sensitive changes in water affect solution properties. Sodium chloride solutions have perhaps been studied more extensively than any other system at temperatures over loo", yet little useful thermodynamic information even on sodium chloride was available until Gardner, Jones, and de P;ordwal12 recently completed a study of osmotic coefficients for the 1-3 m concentration range. We report here the results of osmotic coefficient determinations by vapor pressure-lowering measurements in the concentration range of 0.1-1 m. The data now seem adequate for calculation of activity coefficients and excess thermodynamic quantities, for salt as well as water, with reasonable assurance up to 300". It is expected that data extending over such a wide temperature range will provide a new dimension for test and evaluations of the several competing theories for chemical potentials of strong electrolytes in aqueous solutions of moderate concentration. If this expectation is realized, these results may help shed light on the nature of electrolyte solutions at ordinary temperatures in addition to providing useful information about, high-temperature solutions.
tus and techniques that were developed for this work are described briefly in the following parts of this section. More detail is given el~ewhere.~ Vapor Pressure Cells. As shown in Figure 1, the vapor pressure cells consist of two main parts: a lower body, made of Inconel Alloy 600 and fitted with a platinum cup to contain the solution, and a pressuresensing head made of AIS1 Type 304 stainless steel, containing a stainless steel bellows isolating water vapor in the cell. The construction is such that it is impossible for leaking .gasket's to allow intermixing of water vapor and pressurizing gas. Bellows position is sensed by a linear variable differential transformer (LVDT) located above the oil bath, with the LVDT magnetic core attached to the top of the bellows by a connecting rod within a pressurized tube. The LVDT coil windings sense movement of the magnetic core and bellows inside the pressure system. The coil windings are supported by an outer, unpressurized tube to avoid pressure effects in position sensing. A hydrogen diffuser is provided to remove gas generated by corrosion reactions between steam and the cell materials. Temperature Control. A "double thermostating" system was adopted for this work. Two identical cells were installed in a symmetrical manner in a massive aluminum block, as shown in cross-sectional view in Figure 2. This entire assembly was immersed in a vigorously stirred oil bath regulated to *0.001".
Experimental Section The experimental method consisted of measurement of the difference in gas pressures required to balance the vapor pressures of solution and pure water in two separate pressure cells held at identical temperatures in an oil bath. Although simple in principle, the method is complicated a t high temperatures by the high vapor pressures and the aggressive attack of water and solutions on materials. The unique features of appara-
(1) (a) Presented in part a t the 151st National Meeting of the American Chemical Society, Pittsburgh, Pa., March 1966, and a t the 153rd National Meeting, Miami Beach, Fla., April 1967; (b) to whom correspondence should be addressed. (2) E. R. Gardner, P. J. Jones, and H. J. de Nordwall, Trans. Faraday Soc., 59, 1994 (1963). (3) A detailed description of all features of the apparatus and procedures is given by w. T. Lindsay, Jr., and Chia-tsun Liu in "Vapor Pressure Lowering of Aqueous Solutions at Elevated Temperatures," OSW Research and Development Progress Report No. 347. Available from Superintendent of Documents, TJ, s. Government Printing Office, Washington, D. C. 20402. Volume 74, Number 2 January 22, 2970
342
CHIA-TSUN LIU AND W. T. LINDSAY, JR. were balanced by helium gas pressure applied to the bellows in the two cells. The pressurization system was adapted for automatic control during extended equilibration periods. Fine adjustment of pressure was accomplished manually when measurements were being taken. The bellows-LVDT sensing systems for vapor pressure balance were calibrated for eff ectsof temperature and pressure on shift of null position. The total shift on change of conditions from vacuum at 25" to 1250 psi
Cell Stirrer Shall
--
n
-1VDT Magnetic Core
-Helium Cas Pressure Tube
4 V D T Coil Supporting Tube
Dilluser Vacuum Connectton-
M , ounitg
Plaie
I
I
4
DiIfuS6r Vacuum COnnKliQn
VIP:Phlle
COnncliOn
Figure 1. Cross sectional view of vapor pressure cell.
Preliminary experiments with resistance thermometers installed in dummy cells indicated a maximum difference of 0.0004" to be expected between the temperatures of the two cells. Temperatures during the vapor pressure measurements were determined with a Leeds and Northrup Model No. 8163 platinum resistance thermometer calibrated against the laboratory standard thermometer throughout the temperature range of the measurements. It was used with a Leeds and Northrup Model 8067, Type G-2 RSueller bridge, whose calibration was checked against NBS-certified standard resistors. The thermometer was located in a well extending into the bath fluid. Although the measured temperature is of the bath fluid rather than the interior of the cells, the difference between these temperatures cannot be very large after equilibration. Differences between the measured temperature and the actual cell temperatures have a second-order effect on the results if the two cells are at the same temperature. Diflerential Pressure Measurement. Vapor pressures The Journal of Physical Chemistry
I 12"
Pressure Indicating 8ellows
II
I Permanent Magnet Stirrer Drive
r Assembly lor Stirrers
Figure 2. Assembly of vapor pressure cells in aluminum thermostat block.
a t 300' was equivalent to about 2 mm pressure difference, which was compensated mechanically by adjustment of the sensing coil position for each temperature of measurement. The precision of pressure balancing was better than k0.1 mm. Differences in balancing gas pressures were determined for most of the runs by a high-pressure, mercury filled differential manometer, described el~ewhere.~The manometer has (4) W. T. Lindsay, Jr., and T. S. Bulischeck, accepted for publication in Rev. Sci.Instrum.
OSMOTIC COEFFICIENTS OF AQUEOUS SODIUM CHLORIDE SOLUTIONS
a differential pressure measurement capacity up to 2500 mm at total pressures to 3000 psi, with a differential pressure measurement reproducibility of about *0.1 mm. Differential pressures exceeding the capacity of the manometer were determined by a calibrated Texas Instruments quartz-spiral Bourdon gauge in a pressure capsule. Preparation of Cells. Experience showed that extreme care was necessary in cleaning the cells to prevent accumulation of noncondensable gases during the measurements. The gases, primarily CH4 and COZ, are apparently generated by contact of nonvolatile organic compounds with water and steam and are not eliminated by a simple evaculation and baking of the cells before use. Successful cleaning of the cells was accomplished by the following combination of procedures: (1) initial rinsing and ultrasonic cleaning of all parts with reagent grade acetone and trichloroethylene, followed by steam cleaning at atmospheric pressure for several hours; (2) exposure of the interior of the assembled and sealed cells to steam at 700 to 800 psi and 300" for 2 full days followed by removal of steam and evacuation at this temperature; and (3) a final overnight baking at 150" under vacuum. Preparation of Solutions. Solutions were prepared immediately before use from dried reagent grade sodium chloride and triply distilled water. Degassed water was withdrawn by syringe from the bottom of a boiling vessel and injected into an evacuated bottle containing a known weight of the salt. Additional degassing was caused to occur by boiling of the contents of the bottle with continued evacuation, followed by mixing and weighing of the remaining contents of the sealed bottle. Thirty-five milliliters of solution was withdrawn from this bottle by syringe and injected into the cooled evacuated solution cell through platinumiridium alloy capillary tubing. An equal volume of degassed pure water was injected into the evacuated reference cell. Conduct of Runs. The capillary tubes used for sample injection were crimped off and sealed by gold brazing the ends. The entire assembly as shown in
Figure 3. Typical experimental plot of pressure difference measurements illustrating constancy of measurements.
343
Figure 2 was then placed in the bath and heated first to 125.00", where the absolute pressures in each cell could be checked by the manometer. When all indications were favorable and conditions were stable, the differential vapor pressure was determined by repeated measurements over a several-hour period. Measurements were made successively at 25" intervals from 125.00 t o 300.00" and then again at 125.00" to determine any effects of the operational period at higher temperatures. Equilibration periods before measurements were 16 to 48 hr a t the lower temperatures, while 6 to 10 hr was sufficient at the higher temperatures. Figure 3 illustrates the precision of the measurements obtained in a typical run. Mass spectrometric analyses were used to determine the quantity and composition of any noncondensable gases present after the final measurements on each solution. After opening of the cells, t,he solution and water remaining were checked for changes in volume and such properties as pH, electrical conductivity, and total dissolved solids.
Results Measurements were made on solutions nominally 0.1, 0.25, 0.5, and 1.0 m. The results of runs not showing acceptable constancy or reproducibility of differential pressure measurements or otherwise not meeting acceptance criteria were discarded, and the runs were repeated. Duplicate sets of measurements were obtained at nominally 0.1 m and 1.0 m to establish reproducibility and to obtain firmer results. The considerable number of differential pressure measurements obtained after equilibration at each temperature (Figure 3 is typical) were averaged, the manometer null difference correction was applied, and the differential pressures were corrected to the density of mercury at 0". The final corrected difference A p is the difference between the vapor pressure of pure water po and the vapor pressure of the solution p at the same temperature. Concentrations of solutions at each temperature were calculated from the initial concentration (as determined from the preparation on a weight basis) by using the known volume of the cell, the initial volume of liquid, and the density of steam. Expansion of the liquid solution was approximated by the expansion of pure liquid water. Table I contains the experimental results. The poorest reproducibility was obtained a t the temperatures and concentrations giving the smallest vapor pressure lowering. Consequently, the results at 125" for 0.1 m have been discarded, and the values in the table for 0.1 m solutions at 150, 175, and 200" are averages of two or three duplicate runs of somewhat poorer reproducibility than the others. These averages should be given a weight equal to the other individual results. The osmotic coefficients reported in Table I are all applicable to the solution when under a total pressure Volume 74, Number 9 January 92, 1970
344
CHIA-TSUN LIU AND W. T. LINDSAY, JR. ~~~
Table I : Experimental Results of Vapor Pressure Lowering Measurements for Sodium Chloride Solutions AP = Pa
- P,
T,"C
Molality
mm
125.00
0.2458 0.5309 1.0039 0.1013 0.2463 0.5328 0.9967 1.0061 0.1021 0.2472 0.5360 0.9590 1.0045 0.1025 0.2486 0.5409 0.9641 1.0149 1.0170 0.1064 0.2507 0.5484 0.9718 1.0228 1,0365 0.1077 0.2536 0.5596 0.9829 1 ,0342 0,1095 0.2580 0.9988 1 ,0506 0.1124 0,2644 1.0220 1 ,0743
14.47 30.17 58.31 12.02 29.99 62.44 118.46 118.91 23.78 56.78 117.76 211.37 221.49 42.67 100.62 213.01 377.97 399.11 397.20 72.64 172,44 353.60 636.55 672.28 679,92 120.62 277.34 587.83 1028,65 1076,47 197.24 442.58 1615.32 1675.18 320.52 691,95 2487.56 2568.79
150.00
175.00
200.00
225.00
250.00
275.00
300.00
Table I1 : Contribution of Terms to Calculation of Osmotic Coefficientsa
Osmotic coefficient 4 at P
=
PO
0.9153 0.8881 0.9155 0 . 8820a 0.9060 0.8770 0.8970 0.8921 0,8995' 0.8891 0,8549 0.8643 0.8653
125 160 175 200 225 250 275 300
[RT l n e
vmMlRT
P
-
1
Ti
+
0.94187 0 I94944 0.95597 0.96694 1.00237 1,02209 1.07339 1.13339
solution-------Tz
+
- 0,02536
- 0,04097 - 0.06229 - 0,09074
- 0.13030 - 0 17843 - 0,24561 - 0.33469
Ta
- 0.00126
- 0.00252 - O.OO460 - 0.00793 - 0,01328 - 0.02097 - 0.03304 - 0.05137
indicate experimental precision.
0.8683 0.8497 0.8527 0,8563 0.8504 0,8502 0.8588 0,8098 0,8301 0.8339 0.8313 0,8400 0,8227 0.7967 o ,8006 0.7971 0.8298 0,7947 0.7633 0.7534 0.8102 0.7474 0.7128 0.7010 Average
(dP - P1"(1)4p]
(1)
In this expression, 4 is the osmotic coefficient, v is 2, m is molality, M I is the molecular weight of water, R is the gas constant, T i s absolute temperature, and p is the vapor pressure of the solution as determined by po A p . The first term in the brackets gives the familiar form of the expression applicable at low vapor pressures, the second term gives the correction for deviation of the vapor from the perfect gas law, and the third term is an adequate approximate correction for isothermal compression of the solution from its own vapor pressure to the vapor pressure of pure water. The analytical The Journal of Physical Chemistry
0.91525 0.90595 0.88907 0.86827 0.85879 0.82269 0.79473 0,74743
=
a Headings TI, Tn, Ts refer in sequence to the three terms of eq 1. Significant figures are those carried in calculations and do not
equal to the vapor pressure of pure water at each temperature. They were calculated by the expression ____ 'Oo0
4
0.8880"
a Average value of three experimental results. value of two experimental results.
4 =
0.25 m NaCl
T,OC;
expressions given by Smith, Keyes, and Gerrys were used for the integrand ( of the second term in the brackets, for Vl0(1), the molar volume of pure water at its saturation pressure (an approximation for the partial molar volunie of water in the solution), and for calculation of PO. When each of the terms in the brackets of eq. 1 is multiplied by the common factor, we have the osmotic coefficient as the sum of three terms. Table I1 shows the relative magnitudes of the three contributing terms for the typical case of 0.25 m solutions. Sote that term T,, the effect of gas iniperfection for the vapor, is not negligible a t any of the temperatures and becomes very large at 300". We believe, however, that the properties of pure water vapor are sufficiently well known that uncertainties in the constants used for this correction have a negligible effect on the osmotic coefficients. Note also that the third term T1, correcting the pressure to pol is not insignificant at the higher temperatures. We estimate that the maximum error in osmotic coefficient introduced by use of the molal volume of pure water in this term, rather than the partial molar volume of water in solution, is 0.0002, occurring at 1 m and 300".
Discussion The duplicate runs for approximately 1.O nz. solutions at temperatures 150, 175, 250, 275, and 300", and the triplicate runs for this concentration at 200 and 225", give one measure of the reproducibiility of the determinations. Neglecting the effects of the small concentration differences among these solutions of nominally 1.0 m, the average deviations of the osmotic coefficients in Table I range from around *0.002 at the lower temperatures up to =tO.OOj at 275" and *0.006 at 300". This degree of reproducibility is consistent with the sources of random error in the measurements (5) L. B. Smith, F. G. Keyes, m d H. T. Gerry, Proc. Am. Acad. Arts Sci., 69, 137 (1934). See also J. H. Keenan and F. G. Keyes, "Thermodynamic Properties of Steam," John Wiley & Sons, Inc., New York, N. Y., 1936.
345
OSMOTIC COEFFICIENTS OF AQUEOUS SODIUMCHLORIDE SOLUTIONS
-2 L
1.00
1. 1 1. 0
I
I
I
I
I
200
250
0.9 E 1.0
.95
2
0.9 E 1.0 3
10.9
2 1.0 U
3 0.9 F
e
e 1
4.
I
.-u ._
1.0 v) 0.9 m 1.0 a 0. 9 .-.5 1.0
-
I
..
1
g 0.9
0 u
.- 1. 0 I
0.9 0.8 0.7 0
0.4 0.8 1.2 1.6 2.0 2.4 Square Root of Concentration IMoleslKg H20)li 2
Figure 4. Concentration dependence of high- temperature osmotic coefficients for sodium chloride solutions. Filled circles, this work; open circles, Gardner, et a1.;2,6 triangles, Fabuss and K o r o ~ i . ~Numbers indicate multiple points.
and is perhaps as good as can be expected, considering the experimental difficulties. Figure 4 shows the results of Table I compared with all other known osmotic coefficient data at high temperatures on plots of osmotic coefficient vs. square root of concentration. The data for the Harwell group shown on this plot include both the first published report2 and more recent resultsS6 We have extended extrapolation of the Harwell data to 275” for more direct comparison with our results at that temperature. The osmotic coefficients attributed to Fabuss and Korosi’ were calculated by us from their reported p/po data. Examination of Figure 4 shows that the osmotic coefficient data from the several sources correlate reasonably well with concentration and with the indicated DebyeHuckel limiting slopes at each temperature. At 1 rn there is a multiplicity of data which cannot be shown as separate points on a plot of this scale. The concentration dependence below 1 m is now fairly well established for sodium chloride solutions at high temperatures, since our results extend to solutions on the dilute side of the osmotic coefficient minimum. Correlation of the data by relations reducing to the Debye-Huckel limiting slope at high dilution should therefore be sufficiently accurate to allow calculation of activity coefficients and excess thermodynamic quantities for the salt by integration of the Gibbs-Duhem equation. Figure 4 shows that the principal effect of increasing temperature is a progressive decline in osmotic coefficients for moderately concentrated solutions and a decreasing importance of concentration-dependent ef-
.90
C
c L
m
su .85 .-e
0
E,
0
.80 .
NaCl O n e Molal
.75
.70 0
50
100
150 Temperature,
OC
Figure 5 , Temperature dependence of osmotic coefficients for 1 m sodium chloride. Open circles, this work; open squares, Gardner, et a1.2; filled square, Gardner, et aL2, extrapolated to 275’ ; squares with diagonal, Gardnere; triangles, Fabuss and Korosi?; filled circles, low-temperature data tabulated in standard texts.*
fects tending to raise the osmotic coefficients at higher concentrations. Figure 5 shows the temperature dependence for osmotic coefficients at 1 rn on a larger scale plot. Here it is seen that the high-temperature data are in good accordance with the temperature-dependent trend established by earlier measurements8 at lower temperatures. Comparison may also be made on a plot of this scale among the hightemperature results from the various investigating groups. The solid line on Figure 5 and the solid lines on Figure 4 represent a correlation equation of the extended Debye-Huckel type with temperature-dependent parameters determined by fitting the high-temperature data from 125 to 300” at all concentrations. Although the effect of temperature on osmotic coefficients above 100” is superficially in accord with a decreasing extent of hydration and/or an increasing degree of association of the salt ions, we believe these (6) E. R. Gardner, Trans. Faraday SOC.,6 5 , 91 (1969). We are grateful to Dr. Gardner for making some of his results available to UE before publication. (7) B. M. Fabuss and A. Korosi, Desalination, 1, I39 (1966). (8) 13. S. Harned and B. B. Owen, “The Physical Chemistry of Electrolytic Solutions,” 3rd ed, Reinhold Publishing Company,,, Inc., New York, N. Y., 1958. R. A. Robinson and R. H. Stokes, Electrolyte Solutions,’’ 2nd ed, Academic Press, Inc., New York, N. Y . , 1959. Volume 7d7Number 2
January $2, 1970
WILLIAML. MARSHALL
346 possibilities must be examined carefully and compared with other factors that may have an influence on thermodynamic properties, particularly the effects of water structure breakdown, for a proper evaluation of the significance of the data. Such an evaluation is assisted by inspection of the temperature and concentration dependence of excess free energies, enthalpies, and entropies for both water and salt. A succeeding paper will deal with correlation of all available high-temperature osmotic coefficient data, calculation of activity coefficients and excess functions for salt as well as water, and some interpretations of the significance these
have for aqueous solutions at both high and low temperatures.
Acknowledgments. This work was performed under contract from the Office of Saline Water. We are indebted also to Mr. T. s. Bulischeck for assistance in construction of apparatus and conducting the experiments, and to many others a t Westinghouse Research Laboratories who contributed to various phases of the work. We also wish to acknowledge useful and informative discussions with Professors R. 34. Fuoss and H. S. Frank.
Complete Equilibrium Constants, Electrolyte Equilibria, and Reaction Rates1 by William L. Marshall Reactor Chemistry Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 57890 (Received M a y 16, 1060)
Application of the complete equilibrium constant ( K O ) , which includes solvent as a reactant, has revealed recently several additional correlations of aqueous electrolyte behavior. Of particular importance, the conventionally derived standard state change in molar volumes (AV) between products and reactants (excluding solvent) is shown experimentally to be proportional merely to the compressibility of the solvent ; the significance of this relationship is discussed. All other conventional thermodynamic properties can be calculated as a function of both pressure and temperature from the variation of K O and IC (the assumed net change in waters of solvation) with temperature (only) and from the known pressure-volume-temperature behavior of the solvent. Analogous behavior for rate constants is considered, with the product being the activated complex. There appears to be no significant effect of viscosity on the complete constants within the precision of measurements. Several comparisons of the description of ionization behavior by means of K O , fugacity, and activity coefficients are presented. From these comparisons over wide ranges of pressure, temperature, and dioxane-water mixed solvent compositions, the overall utility of fugacity, with its defined relationship to chemical potential, is questioned in that the use of K O simplifies the description of electrolyte-solvent equilibria. A knowledge of fugacities (and/or activity coefficients) is unnecessary, and therefore the complete constant would appear to have much potential usefulness.
Complete Ionization Constants Isothermal ionization equilibria in aqueous fluids can be described by complete ionization constants (KO)
where KO and k (the assumed average net change in waters of solvation upon dissociation of solvated ion-pair species MA(H,O),) are found to vary only with temperature, K is a conventional constant (or quotient) that varies both with temperature and pressure, j , m, and n represent average waters of solvation, The Journal of Physical Chemistry
and all concentrations are expressed in moles per liter at a total pressure P.2-4 The conventional constant does not distinguish between contact ion pairs, ion pairs containing a discrete
(1) Research sponsored by the U. 9. Atomic Energy Commission under contract with the Union Carbide Corp. Presented before the Division of Physical Chemistry at the 158th National Meeting of the American Chemical Society, New York, N. Y., Sept 7-12, 1969. (2) E. U. Franck, Z . Phys. Chem. (Frankfurt am Main), 8 , 107, 192 (1966). (3) W. L. Marshall and A. 8.Quist, Proc. Natl. Acad. Sci. U . S., 58, 901 (1967). (4) A. S. Quist and W. L. Marshall, J.Phys. Chem., 72, 1536 (1968).
