11612
J. Phys. Chem. 1995,99, 11612-11625
New Apparatus for Conductance Measurements at High Temperatures: Conductance of Aqueous Solutions of LiCl, NaCl, NaBr, and CsBr at 28 MPa and Water Densities from 700 to 260 kg m-3 Gregory H. Zimmerman? Miroslaw S. Gruszkiewicz? and Robert H. Wood* Department of Chemistry and Biochemistry and Center for Molecular and Engineering Thermodynamics, University of Delaware, Newark, Delaware 19716 Received: October 14, 1994; In Final Form: March 31, 1 9 9 9
A new flow conductance apparatus for measurements of aqueous solutions near the critical point of water has been used to measure the conductance of aqueous LiC1, NaC1, NaBr, and CsBr at pressures up to 28 MPa and temperatures between 579 and 673 K (water densities from 700 to 260 kg m-3). At a water density of 300 kg m-3 the new instrument can make measurements with a precision of about 1% at concentrations as low as 2 x mol dm-3. At higher concentrations and higher water densities the precision is 0.1% or better. Values for infinite dilution conductance AO and dissociation constant K8, for the four salts under these conditions are reported. The differences in AO and for the four salts at the same temperature and pressure are quite small. This instrument extends the region where accurate measurements of & and can be made. An analysis of the behavior of I\o indicates that on average only a small number of water molecules are carried along by the ion even under conditions where there is extensive long range hydration, Ne, x 150.
e
I. Introduction High-temperature aqueous solutions play an important role in a wide variety of industrial and natural processes. Mineral transport, deposition and alteration, hydrocarbon formation, migration and accumulation, electric power boiler corrosion, and hydrothermal reservoir utilization are examples of these processes. More recently, there has been great interest in using supercritical water as a reaction medium because the environmental damage of using this medium is potentially much less than the alternatives. The present apparatus was constructed because of a lack of accurate conductance measurements on aqueous solutions near the critical point of water. In the region of the critical point there have been scattered experimental measurements starting with the pioneering investigations of Fog0 et al.'S2 At higher temperatures and higher densities there have been extensive systematic investigations of the conductances of aqueous electrolytes by Franck and c o - w o r k e r ~ ~and - ' ~ by Marshall and c o - w ~ r k e r s . ' ~ Measurements -~~ were extended to very high temperatures, 1073 K, and very high pressures, 400 MPa, but did not include the region close to the critical point. The experimental apparatus used by Franck, Marshall, and coworkers limited the measurements to molalities of 0.001 mol kg-' or higher. Marshall and co-workers found that the association constant at temperatures from 673 to 1073 K and densities from 750 to 300 kg m-3 was a simple function of density and temperature. They also found that at high temperatures and pressures the limiting conductance was a simple function of density (at constant temperature), and it was apparently independent of temperature above 673 K. It was not clear that a simple extrapolation of these results as a function of density and temperature into the region of the critical point would be accurate because the high compressibility and the very long correlation length in this region produce very large and long+ Present address: Chemical and Analytical Sciences Division, Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, TN 37831-6110. * To whom correspondence should be sent. Abstract published in Advance ACS Absrracfs, June 1, 1995. @
0022-365419512099-11612509.0010
range hydration of the ions and the ion pairs which should reduce the mobility of the ions. The increased hydration should increase the dielectric constant near the ion and decrease the association constant. Very close to the critical point, the viscosity of the solution increases, but this occurs quite close to the critical point and so will be very difficult to observe. (The viscosity increase due to critical point effects is greater than 2% only for pressures less than 23 MPa and densities between 260 and 390 kg m-3.) It was thought that significant improvements in the speed and accuracy of conductance measurements could be made by (1) designing the instrument as a flow-through cell so that the solutions were not exposed to high temperatures for long periods of time and so that once the instrument was at high temperature a large number of measurements could be made very rapidly, (2) using the flow stream to sweep contaminants dissolving from the sapphire insulator away from the measuring zone and out of the conductance cell, (3) using a flow cell to eliminate adsorption effects on the walls of the cell and, thus, decrease the lowest concentration that can be measured, (4) using the same batch of solvent for both the blank solvent run and the conductance run to decrease inaccuracies in solvent conductance corrections, and (5) using a flow-through cell to eliminate the vapor space and the need to estimate solute partitioning between the liquid and vapor phase when below the critical point. This paper reports the details of the construction of such an instrument and reports our first measurements with it on alkali halides in the region near the critical point. These measurements demonstrate that the present apparatus allows measurements to be made very quickly at very low concentrations and with great precision at 28 MPa and at temperatures from 579 to 677 K (densities from 700 to 260 kg m-3.)
11. Experimental Apparatus The key to making measurements quickly and accurately at high temperature and pressure was the use of a flow-through cell. This method has been used very effectively in calorimeters at high temperatures. (For a review of this development see Wood,30Christensen et al.,31332and Wormald et a1.33,34)The 0 1995 American Chemical Society
J. Phys. Chem., Vol. 99, No. 29, I995 11613
Conductance Measurements at High Temperatures
0 Aluminum
HB Valve Pressure Gauge
Figure 1. Schematic diagram of the conductance instrument: BP, backpressure regulators; C, conductance cell; CC, containment chamber; HB, heater box; P, pump; PK, PEEK tubing; PR, platinum-rhodium tubing; PT, pressure transducer; S, syringe; SF, sample flask; SL, sample loop; T, Rosemount platinum resistance probe; V, HPLC valve; W, deionized water flask.
present apparatus was constructed by one of us (G.H.Z.) and is described in detail in his Ph.D. di~sertation.~~ In the present apparatus shown schematically in Figure 1, an HPLC pump P was used to pump degassed, deionized water W into the hot zone where the measurement was made and then through two back-pressure regulators BP (Circle Seal) which controlled the pressure in the system. A polyether ether ketone (PEEK) 17 mL sample loop SL (3.2 mm o.d., 1.6 mm i.d.), HPLC pump (Constametric I), and three sections of PEEK tubing PK (1.6 mm o.d., 0.51 mm i.d.) were connected to a two-position, sixport HPLC valve V (Rheodyne 7010). Two of the PEEK sections were used for filling and the prepressurization of the sample loop. The other PEEK section was connected to the platinudrhodium tubing of the instrument PR (1.6 mm o.d., 1.0 mm i.d., 80% Pt and 20% Rh by mass) just outside of the containment chamber CC (88 cm on each side) with a PEEK union. Capillary tubing of this same FVRh composition (1.0 mm o.d., 0.5 mm i.d.) continued throughout the rest of the instrument until emerging from the high-temperature zone outside of the containment chamber, where stainless steel and PEEK tubing were connected to the two back-pressure regulators. Two preheaters raised the temperature of the solution close to the desired temperature. Three sets of heaters were used to control the temperature of the conductance cell and were fastened directly to the outermost heater box HB (29 cm on each side). The conductance cell resided inside of three concentric stainless steel boxes, the outermost heater box, the middle box (24 cm on each side), and a yet smaller four-sided box (20 cm on each side; no top or bottom). After the preheaters, the tubing traveled directly to the innermost of these boxes and was loosely coiled around the conductance cell C for 1 18 cm before entering the conductance cell. The innermost box was filled with aluminum spheres (about 1 mm diameter), covering completely the coil and the cell. The outlet from the cell passed directly out of the hot zone to outside of the containment chamber. The outer heater box was surrounded
Figure 2. Schematic diagram of the conductance cell: BW, Belleville washer springs; CP, CP‘ compression plates; GW, gold washer; IE, inlet electrode; IT, inlet tube; MB, stainless steel body; OT, outlet tube; LT, stainless steel tube;PC,platinum-rhodium cup; QT, quartz tubing; SH, stainless steel shield; SI, sapphire insulator; SR, sapphire rods; TT, platinum-rhodium tubing; TW, stainless steel washer; TW’, aluminum washer.
by a minimum of 25 cm thickness of Fiberfrax Durablanket ceramic fiber insulation (Carborundum). The temperature was measured with a Rosemount platinum resistance temperature standard T, Model 162 CE (25.5 S2 with calibration traceable to the National Bureau of Standards), and a b e d s and Northrup G-2 Mueller bridge. The Rosemount temperature was recorded immediately after each conductance measurement because the temperature stability usually oscillated periodically by about 0.05 K every 10 h. The temperature gradients from the bottom to the top of the innermost box were less than 0.6 K. For most measurements the pressure was measured using a Digiquartz pressure transducer PT (Model 760-6 ParoScientific) with a manufacturer’s stated accuracy of f O . O l % . For the measurements at 579 K a Perma-Cal gauge accurate to f 0 . 2 MPa was used. The pressure fluctuations due to the opening and closing of the back pressure regulators were about f0.05 MPa in the worst case, resulting in periodic oscillation in resistance of about 5% at the higher temperatures. The conductance cell (Figure 2) was constructed from a platinum-rhodium cup PC (7.87 mm o.d., 1.22 mm wall thickness, 22.23 mm length, 80% Pt and 20% Rh by mass, Engelhard), to which the inlet tube IT was gold-soldered into a 1.07 mm hole. This cup with volume of about 0.5 mL served as the outer electrode and was housed horizontally in the stainless steel body MB (76.2 mm o.d., 39.7 mm length, stainless steel 303). On the rim of the cup was placed an annealed gold washer GW (6.35 mm o.d., 4.76 mm i.d.) and on top of this a sapphire insulator SI (12.7 mm o.d., 1.78 mm i.d., 6.35 mm length, Insaco Inc.). This sapphire had a hole in the center through which the inner electrode lE (1.6 mm 0.d.) passed, extending about 9.5 mm into the cup. The inner electrode was made from tubing (1.6 mm o.d., 0.51 mm i.d.) that was goldfilled at one end. At the back of the inner electrode where it was no longer gold-filled were two small holes for the solution to flow out of the cell and into the tubing. The inner electrode also passed through another annealed gold washer (4.76 mm o.d., 1.6 mm i.d.) which was between the sapphire and a shorter thicker piece of Pt/Rh TT tubing (3.28 mm o.d., 1.6 mm i.d., 3.3 mm length). The shorter thicker WRh tubing was gold soldered on to the inner electrode after the two small outlet holes. The WRh outflow tubing OT passed through a heavywalled, stainless steel tube LT (3.97 mm o.d., 1.6 mm i.d., 6.35 mm ledge o.d., 41.3 mm length), after which it went out of the
Zimmerman et al.
11614 J. Phys. Chem., Vol. 99, No. 29, 1995 hot zone to outside of the containment chamber. Three sapphire rods SR (1.6 mm o.d., 10 mm length) were used to electrically insulate the inner electrode assembly from the outer electrode. The seals between the platinum cup and sapphire (outer seal) and the inner electrode assembly and sapphire (inner seal) were made by compressing the gold washers with a force of 1800 and 1300 N, respectively, generated by two independent sets of Belleville washer springs BW (19.05 mm o.d., 6.53 mm i.d., 1.02 mm thickness, 0.38 mm dish height, Inconel 750 X, Key Belleville). For the outer electrode seal, a thick stainless steel washer TW (19.05 mm o.d., 6.53 mm i.d., 3.18 mm thickness) was placed between the Belleville washer springs, sapphire, and outer compression plate (50.7 mm o.d., 6.53 mm i.d., 6.35 mm thick). For the inner electrode seal, the force was applied by the Belleville washers through a stainless steel tube with a ledge in the middle, a stainless steel washer (25.4 mm o.d., 3.97 mm i.d., 3.2 mm thick), an aluminum washer TW' (25.4 mm o.d., 6.53 mm id., 4.76 mm thick), sapphire rods, and the inner compression plate (50.7 mm o.d., 6.53 mm i.d., 6.35 mm thick). For the outer seal, six Belleville washers were used (three facing each way), and for the inner seal four Belleville washers were used (two facing each way). The solution flowed into the cup, through the center hole of the sapphire, and then through two holes at the back of the inner electrode and into the outlet tubing. The constant flow of the solution swept dissolving sapphire away from the measuring electrodes and out of the cell. Heavy platinization (about 10 C cmP2) was used on the cup and the inner electrode to reduce polarization. All resistance measurements were made at 10 and 1kHz using a 1654 General Radio impedance comparator capable of a resolution of 0.03% in resistance and 0.0003 rad in phase angle difference when using 0.3 V as a test voltage. The standard resistors used for resistances less than 111 kQ were composed of General Radio 510 decade resistance units. To measure the resistance of the solvent and the most dilute solutions, a decade with a range of 10 MQ was used ( E T Labs, Inc., accuracy of 1%). Measuring solvent resistances in excess of about 1.8 MQ required shunting the conductance cell with a 1 MQ resistor. All measurements were corrected for the lead resistances which were a few tenths of an ohm. The resistances of the solutions measured ranged from 20 Q to 800 kQ. The resistances were linearly extrapolated to infinite frequency as a function of the inverse of the square root of the frequency. The difference between the 1 and 10 kHz measurements was usually about 1% at the lowest resistances (less than 200 several tenths of a percent at intermediate resistances (500-50 OOO Q), up to 2% at the highest solution resistances (200-800 kQ), and up to 20% at the highest pure solvent resistances (5-8 MQ).
a),
III. Cell Constant Determination The cell constant (k % 0.22 cm-I) was calculated from measurements on KCl(aq) near 25 "C using equations given by Justice36 and Barthel et al.37 for A vs c of KCl(aq). For the first few runs the cell constant was determined by a series of six to seven measurements on dilute solutions with molalities of O.OOO1-0.025 mol kg-' made from stock KC1 solutions that were prepared from Fisher A.C.S. grade KCl that was recrystallized twice from conductivity water. All weights were corrected to vacuum. Conversion from mol kg-' solvent to mol dm-3 solution at 25 "C was done using the densities calculated from the equations and parameters given by Sohnel and N o ~ o t n y . ~ *Agreement to 0.1% for the cell constant was obtained over the complete range of molalities. This procedure ensured that polarization, the Parker effect, and the lead
resistance corrections were not introducing significant errors. For later runs the cell constant was determined using a stock solution of KC1 prepared from 99.999% pure single crystal KCl (Research Organic/Inorganic Chemical Corp.) dissolved in conductivity water. At least two different concentrations were always used to determine the cell constant. The cell constant was also determined once at 25.3 MPa and 25.00 "C to ensure that bubbles did not form inside the cell and interfere with the measurements, using the results of Fisher and at these conditions. The cell constant found at high pressure agreed to the room pressure cell constant within 0.1%. It was later found that the measured cell constant changed after heating to about 656 K and then cooling to room temperature. In one case it increased by about 1.4% from the initial measurement at room temperature. However, a second cycling to 573 K showed an insignificant change in cell constant before and after heating. In another case (after a new platinization and cell assembly) the cell constant decreased by 0.6% after heating to 677 K and then cooling to room temperature. The changes in cell constant could be attributed to both (1) changes in the platinum black deposit on the electrodes (resulting likely in an increase of the cell constant) and (2) annealing (with a compression of the soft gold washers, increasing the length of the inner electrode, and decreasing the cell constant.) The values of k obtained after the temperature cycling were used for the calculations when it seemed that these values were stable. Otherwise, an average of the values before and after cycling was used. The change of the cell constant with respect to temperature due to thermal expansion of the materials was calculated from the known coefficients of thermal expansion of sapphire and platinum (the maximum change was 0.4%).
IV. Solutions The stock solutions of NaC1, NaBr, and LiCl were made from Fisher Certified A.C.S. Reagent grade salts without further purification. The stock solution of CsBr was prepared without further purification from 99.9% pure salt obtained from Aldrich. Stock solutions of about 1 and 0.025 mol kg-' were then made from conductivity water and stored in glass bottles. The molalities of the stock solutions were determined to 3~0.1%by measuring the conductance at 25 "C with a glass cell calibrated with KCl using conductances from the literature (for LiCl from Jervis et aL40 and Shedlov~ky;~' for NaBr from Broadwater and Kay$* Jervis et al.?O and P ~ s t l e r for ; ~ ~NaCl from Chiu and F u o ~ sGunning ,~ and Gordon,45and Shedlovsky et and for CsBr from Hsia and F u o ~ and s ~ ~Justice et al.48). For preparing the most dilute samples, solutions with compositions of about 0.0006 mol kg-' were then made from the stock solutions by weight. The conductivity water used was distilled and then passed through an ion exchange column (UltraPure from Barnstead). In all measurements done at 25 "C the solvent correction as measured in the cell was never greater than 0.5 pS cm-I and was usually about 0.2 pS cm-l. At high temperatures, with the instrument operating correctly, the solvent conductance was never greater than 16% of the conductance of the lowest concentration measured, and it was usually 2-5%. At 677 K the cell developed a high-resistance leakage path. The measured background resistance decreased suddenly from several megaohms to 0.108 M&. Because of the reduced accuracy caused by this change, only NaCl(aq) was measured at this temperature. For these measurements, the solvent correction was as high as 85% of the conductance of the lowest concentration.
Conductance Measurements at High Temperatures
V. Method A 1 or 2 L flask (SF in Figure 1) was outfitted with a balloon, a septum, Tygon tubing with polypropylene stopcock with Teflon plug, polyether ether ketone (PEEK) tubing, and a PEEK valve, and on the inside with a Teflon-coated stirring bar. To perform a series of experiments, the flask was flushed thoroughly with helium, weighed to the nearest tenth of a gram, and filled with conductance water through the Tygon tubing and stopcock with the PEEK valve closed, blowing up the balloon. This method prevented any exposure of the water to the atmosphere. The water left in the filling arm of the solution flask was blown out by opening the valve and allowing the positive pressure of the helium balloon to expel the water. The solution flask was then connected to the HPLC valve, and a sample of 50 mL was drawn through the sample loop from the flask with a polyethylene syringe S . The sample was then prepressurized to about 1 MPa below the actual experimental pressure and injected into the conductance cell flowstream. (Failure to prepressurize when at high temperatures usually resulted in cracking the sapphire insulator in the cell. Apparently, the sudden pressure loss resulted in rapid localized cooling which fractured the sapphire.) In 3-4 min the solvent entered the conductance cell, and after approximately 18-25 min (depending on flow rate) a plateau lasting about 6 min was reached in which the resistance changed at most a few hundredths of a percent at the lowest temperatures and 0.3% at the highest temperatures. After resistance measurements during the plateau, the HPLC valve was then returned to the load position, and the same procedure was followed to measure another solvent sample. A large conductance spike occurred when the front of a new sample reached the conductance cell. This contamination did not interfere with the measurements as long as the volume of the sample (17 mL) was large enough. During the measurements at 670 K, however, when the concentrations were lower than 2 x mol dm-3, the sample volume was no longer sufficient to rinse the conductance cell. It was found that a thorough rinsing of the HPLC valve and the prepressurization circuit before starting the measurements practically eliminated the problem. All the rest of the system was well rinsed by the water flowing through it overnight. Once the solvent correction was determined using the water kept under helium, a dilute solution was made using this solvent. The solution flask was weighed to the nearest 0.1 g, and a stock solution of known concentration was injected through the rubber septum into the solution flask, using a polyethylene syringe as a weight buret (weighed to the nearest 0.0001 g). The newly made solution was stirred, loaded into the sample loop, prepressurized, and measured. This procedure was repeated with increasingly more concentrated solutions. Most of the experiments were done at a flow rate of about 0.5 mL min-I. At the temperatures 655 and 665 K the flow rate was reduced to 0.23 mL min-' to be sure that the thermal equilibration was complete. The results obtained after changing the flow rate back to 0.5 mL min-I were the same within the bounds of the experimental error. A further indication of thermal equilibration of the fluid was that the temperature gradient between the inflow tubing and the cell was never greater than 0.1 K as measured by a pair of iron-constantan thermocouples.
VI. Results The equivalent conductance results for the four systems investigated are given in Tables 1-3. Solvent densities necessary for obtaining concentrations were calculated from the Hill equation of state.49 Small differences between the densities
J. Phys. Chem., Vol. 99, No. 29, 1995 11615
of pure solvent and those of solutions were estimated assuming a linear dependence of the solution density on molality for dilute solutions and using the experimental densities obtained previously in this l a b ~ r a t o r y . ~The ~ - ~corrections ~ to the equivalent conductance for the change in density with molality were less than 0.1% for most measurements and less than 4% at the highest molalities. A rigorous treatment of the solvent correction applied to the aqueous solution conductance measurements requires inclusion of the effect of the ionic strength on the dissociation quotient of water.57 The magnitude of this effect was estimated by calculating the conductance of pure water using the equivalent conductivities at infinite dilution for NaCl (this study), HCl,I9 and NaOH26and the equation of Marshall and F r a n ~ for k ~ the ~ ion product of water. The pure solvent conductance calculated in this way was always at least 20% smaller than the measured solvent conductance (see Table 3). This increased conductance was assumed due to impurities and to be constant for all solutions. The conductance contribution from water as a function of ionic strength was then calculated using eq 3 for activity coefficients and added to the corrosion conductance, resulting in a total solvent correction. The conductivities of the solutions obtained by subtracting this total solvent correction and those obtained by subtracting the measured solvent conductance differed by less than 0.1% in all cases and were usually on the order of a few hundredths of a percent. Consequently, the contribution from the effect of ionic strength on the dissociation quotient of water was not included in the solvent correction. The equivalent conductances at infinite dilution & and the thermodynamic equilibrium constants of the dissociation reaction K", (1 mol kg-' standard state) were found by least-squares fitting of the results in Table 1 to a conductance equation at each of the different pressure and temperature conditions. The linearized form of the conductance equation for associating electrolytes,
+
A = a ( A o - Sc"2a'12 E c a ln(ca)
+ J,ca -tJ2c
a
312 312)
(1) is based on the theoretical treatment of Fuoss and H ~ i a In .~~ eq 1, c is the concentration of the sample solution, and coefficients S, E, and JI can be calculated following the equations given by Femfindez-Prini,60 with viscosity from Johnson et a1.,6I dielectric constant from Archer and Wang,62 and water properties from Hil!9 In previous work many workers have used the S h e d l ~ v s k y ~ ~ equation at high temperatures. We feel that this is not the best choice. The Shedlovsky equation was found empirically to fit the conductances of aqueous 1-1 electrolytes at room temperature. Because of its empirical nature, there is no reason to expect it to fit conductance under any other conditions, and in fact, it does not fit accurately aqueous 2-2 electrolytes at 25 "C, nonaqueous electrolytes, or the present results.35 In contrast, eq 1 accurately fits electrolytes under all of these conditions. The degree of dissociation a is obtained from the relation
e
= d , c = a2cy,/(l - a )
with the mean activity coefficient of the free ions y i calculated from the Debye-Huckel limiting law,
(3) where K is the reciprocal radius of the ionic atmosphere. Following the recommendation of Justice,36the ionic diameter a in the denominator of eq 3 was set equal to the B j e r "
11616 J. Phys. Chem., Vol. 99, No. 29, 1995
Zimmennan et al.
TABLE 1: Measured Equivalent Conductances A; 8A Is the Deviation of the Experimental Results from Eq 1 m, c, 10-6 A, S ah, S m, c, 10-6 AS T,”K
moVkg
mol/dm3
cm*/mol
cm2/mol
T,O
K
m0Vk.g
mol/dm3
cm2/mol
dA, S cm2/mol
NaCl 579.42 579.44 579.39 579.39 579.41 579.45
156.72 156.72 346.75 346.75 580.07 580.07
109.71 109.71 242.75 242.75 406.10 406.10
1022.2 1022.2 1015.0 1015.0 1007.3 1007.2
p = 9.8 MPa -1.8 579.46 -1.8 579.46 0.5 579.51 0.5 579.55 1.3 579.56 1.3 579.55
604.52 604.5 1 604.50 604.56 604.61 604.60
41.721 41.721 149.81 149.81 378.21 378.21
27.971 27.971 100.44 100.44 253.57 253.57
1059.3 1056.1 1047.4 1048.5 1034.3 1034.3
p = 22.47 MPa 1.5 604.59 -1.7 604.59 -0.3 604.59 0.7 604.59 -0.5 604.59 -0.5
601.74 601.75 601.77 601.76
58.130 58.130 179.69 430.45
40.191 40.191 124.24 297.62
1040.3 1038.4 1032.4 1020.6
63 1.70 631.71 631.70 63 1.70
55.605 55.605 172.90 379.06
33.942 33.942 105.55 23 1.4
642.58 642.57 642.57 642.57 642.57
55.883 55.883 172.80 406.13 642.72
648.93 648.93 648.92 648.91 648.91
2408.5 2408.5 7559.9 7559.9 18566 18566
1686.4 1686.4 5295.8 5295.8 13017 13017
967.25 967.36 911.75 91 1.63 851.11 851.13
0.4 0.5 -0.5 -0.6 0.1 0.1
630.92 3263.3 8309.6 15336 15336
423.01 2188.5 5575.5 10297 10297
1024.9 966.00 907.59 859.09 859.15
0.6 0.5 -0.5 0.1 0.1
p = 28.01 MPa -0.5 601.74 -2.5 601.72 0.8 601.70 1.3 601.70
672.05 3575.4 9019.4 17800
464.68 2472.7 6240.2 12323
1011.7 953.70 898.91 847.60
1.3 0.1 -0.7 0.3
1135.8 1136.7 1125.3 1109.4
p = 27.99 MPa -2.2 63 1.70 -1.3 631.69 1.1 631.67 1.4 631.65
624.13 3352.9 8811.0 17203
381.02 2048.2 5389.2 10543.
1094.7 1003.1 915.64 841.99
1.6 -0.1 -0.8 0.3
3 1.794 31.794 98.315 23 1.09 365.74
1190.0 1189.5 1174.3 1150.0 1130.5
p = 28.00 MPa -1.1 642.56 -1.6 642.56 1.1 642.58 1.2 642.59 0.9
4599.3 8586.3 15078 15078
2620.5 4898.2 8618.9 8618.9
975.81 901.30 827.70 827.61
-0.3 -0.6 0.2 0.1
54.702 54.702 166.07 380.89 610.90
29.435 29.435 89.364 204.98 328.79
1232.8 1232.3 1213.6 1186.3 1164.6
-0.6 -1.1 0.5 0.5 1.4
648.91 648.90 648.90 648.90
3030.9 8239.0 15869 15869
1632.7 4446.8 8588.9 8588.9
1031.7 907.05 812.58 814.21
-0.7 -0.1 -0.7 0.9
655.86 655.85 655.86 655.88 655.90
29.939 29.939 64.380 64.380 170.35
14.765 14.765 31.751 31.751 84.020
1277.4 1276.9 1265.5 1265.8 1239.9
-0.1 -0.6 -0.4 -0.2 0.0
655.90 655.90 655.89 655.90 655.92
43 1.92 3370.4 8150.2 15296 15296
213.06 1665.8 4040.7 7618.5 7618.5
1196.4 98 1.40 847.22 748.27 748.77
1.7 -0.1 -0.7 -0.1 0.5
655.91 655.88 656.02 655.99 655.95 655.93 655.87
24.002 54.932 65.804 152.50 237.06 328.39 344.36
11.837 27.084 32.382 75.068 116.80 161.91 169.90
1268.7 1257.0 1253.0 1231.9 1214.7 1199.6 1197.6
0.9 0.2 -0.9 -0.3 -0.6 -0.1 0.5
655.93 655.94 655.84 655.93 655.83 655.82
423.49 523.04 637.80 658.44 944.57 1254.7
208.68 257.82 314.90 324.62 466.65 620.05
1185.0 1171.9 1157.9 1154.6 1125.5 1097.6
-0.3 0.3 0.5 -0.4 0.4 -0.3
665.43 665.43 665.44 665.46
11.566 34.61 1 119.98 403.16
4.4212 13.232 45.914 154.20
1316.3 1284.8 1215.3 1077.5
3.4 -1.5 -1.4 -2.0
665.48 665.52 665.53
3658.7 11410 20744
1403.7 4427.9 8170.9
694.64 511.98 439.22
2.5 -0.7 -0.2
670.16 670.14 670.1 1 670.07
3.0589 8.3415 3 1.746 137.70
0.91230 2.4899 9.4937 41.186
1269.3 1257.2 1184.9 968.99
-13.0 1.7 15.3 2.2
670.05 670.04 670.04
521.91 4350.1 15705
156.72 1318.7 4836.6
701.70 356.74 235.57
-7.1 -2.3 1.7
673.17 673.14 673.13 673.11
1.3257 5.1901 20.526 74.245
0.34476 1.3489 5.3370 19.288
1306.4 1252.9 1074.3 814.17
-8.6 8.3 3.4 -0.4
673.09 673.05 673.06 673.07
350.10 2608.2 11752 32037
91.059 682.49 3111.6 8717.6
495.83 233.35 135.53 105.54
-4.0 -1.5 -1.3 1.6
677.19 677.22 677.23 677.21
1.3352 8.2363 30.519 114.22
0.30203 1.8725 6.9066 25.867
1182.9 959.04 662.93 410.31
-8.6 19.5 -3.7 -9.5
677.19 677.18 677.16
454.40 4054.1 14286
102.97 922.06 3280.7
232.80 92.721 59.309
-7.0 -1.1 3.1
Conductance Measurements at High Temperatures
J. Phys. Chem., Vol. 99, No. 29, 1995 11617
TABLE 1 (Continued) m, 1 0 P
T," K
molkg
c , 10-6 mol/dm3
A, S cm2/mol
dA, S cm2/mol
molkg
c, 10-6 moUdm3
A, S cm2/mol
dA, S cm2/mol
m, 1 0 F
T,"K
LiCl 604.57 604.58 604.58 604.58 604.58
63.531 63.531 191.59 466.22 760.83
42.592 42.592 128.45 312.58 510.11
1016.2 1015.8 1006.2 992.9 982.21
p = 22.50 MPa -0.1 604.59 -0.5 604.58 -0.1 604.58 0.2 604.59 0.2
760.83 2857.4 8036.4 18497
510.11 1916.2 5392.4 12425
982.23 936.98 877.47 813.32
0.2 0.6 -0.6 0.1
601.70 601.70 601.70 601.70 601.69
54.912 54.912 184.29 502.83 83 1.66
37.972 37.972 127.44 347.72 575.14
1001.9 1000.2 992.1 1 976.72 966.22
p = 28.01 MPa 0.7 601.68 -1.1 601.67 0.6 601.67 -0.2 601.67 -0.0
3271.5 8433.1 16060 16060
2262.9 5835.9 11122 11122
919.72 867.66 821.93 822.01
0.1 -0.1 -0.0 0.0
63 1.65 63 1.66 63 1.69 63 1.69 63 1.69
63.059 63.059 214.57 473.95 741.22
38.501 38.501 131.02 289.45 452.77
1105.0 1104.0 1089.4 1070.7 1055.9
p = 28.00 MPa -0.1 63 1.66 -1.1 63 1.64 0.5 63 1.63 0.4 63 1.63 0.5
3730.0 9000.4 9000.4 19076
2282.9 5527.9 5527.9 11794
963.69 883.70 883.76 801.58
0.1 -0.2 -0.2 0.1
642.67 642.68 642.68 642.67 642.63
63.51 1 63.511 179.96 420.80 694.91
36.121 36.121 102.36 239.39 395.43
1158.4 1158.8 1142.1 1117.3 1096.0
p = 28.01 MPa -0.4 642.62 0.0 642.61 0.3 642.62 0.0 642.62 -0.1
3072.2 838 1.4 16930 16930
1751.7 4800.4 9766.5 9766.5
990.69 879.53 787.47 787.45
0.1 -0.1 0.0 0.0
648.92 648.93 648.92 648.92
61.586 61.586 189.51 454.62
33.140 33.140 101.99 244.73
1199.6 1198.4 1178.4 1146.2
p = 28.00 MPa 0.4 648.90 -0.9 648.90 0.7 648.91 -1.0 648.92
725.83 3633.7 8925 16353
390.83 1962.2 4844.6 8940.7
1124.3 986.99 872.65 785.90
0.8 0.2 -0.5 0.2
655.84 655.83 655.82 655.82 655.82 655.82
36.289 36.289 80.643 80.643 193.98 193.98
17.882 17.882 39.740 39.740 95.603 95.603
1245.6 1244.0 1232.2 1231.9 1207.2 1207.0
0.1 -1.4 0.3 -0.1 0.6 0.4
655.83 655.83 655.85 655.86 655.86 655.85
502.92 502.92 3972.4 3972.4 12774 12774
247.95 247.95 1965.9 1965.9 6381.9 6381.9
1158.4 1158.1 938.14 937.98 758.80 759.83
0.3 0.1 -0.1 -0.2 -0.4 0.5
665.31 665.38 665.32 665.38 665.31 665.38
7.9550 11.775 37.919 98.498 144.62 245.62
3.0602 4.5098 14.548 37.637 55.576 93.863
1294.9 1285.7 1261.3 1211.9 1177.3 1128.5
p = 27.99 MPa 3.01 665.31 -1.1 665.38 2.5 665.3 1.6 665.53 -4.6 665.33 0.1 665.57
491.69 1407.2 3358.7 10340 12309 26587
189.03 539.90 1296.5 3975.5 4792.8 10437
1034.8 864.57 708.05 527.27 508.61 406.94
-5.0 2.9 -2.0 4.6 1.5 -3.1
669.56 669.55 669.55 669.54
3.9752 15.841 55.247 154.43
1.2239 4.8599 17.058 47.618
1299.3 1252.4 1146.3 986.58
p = 28.00 MPa -0.9 669.54 -0.0 669.55 2.6 669.56 -1.3
601.89 3842.3 11897
185.72 1194.7 3742.7
719.24 407.23 280.42
-1.8 2.9 -1.2
0.18350 0.48445 2.2439 13.127
1293.9 1303.4 1211.9 937.69
301.75 2502.2 13102
79.238 658.88 3500.1
563.84 256.48 143.07
-2.9 -2.7 1.5
2986.6 7419.1 13903 13903
2065.9 5133.4 9623.8 9623.8
958.48 91 1.91 870.78 870.79
-0.0 -0.2
876.37 3465.8 9263.8 17963
535.25 2118.0 5668.7 11013
1081.4 1006.8 925.20 858.26
0.0 -0.2 0.0 0.0
p = 27.95 MPa
672.90 672.89 672.89 672.89
0.69915 1.8488 8.5314 50.001
-17.4 11.8 8.3 -0.3
672.89 672.90 672.89
NaBr p = 28.02 MPa
601.69 601.68 601.68 601.67 601.67
60.974 60.974 183.71 44 1.93 743.10
42.168 42.168 127.05 305.64 513.94
1035.7 1032.5 1025.2 1013.4 1003.3
63 1.64 63 1.62 631.61 631.61
66.701 66.701 207.06 599.52
40.73 1 40.731 126.44 366.14
1134.3 1134.2 1121.0 1094.8
1.3 -1.9 -0.0
0.3 0.5
601.65 601.65 601.65 601.64
p = 27.99 MPa -0.5 631.61 -0.5 63 1.62 1.o 63 1.64 0.2 63 1.65
'
0.0
0.0
Zimmerman et al.
11618 J. Phys. Chem., Vol. 99, No. 29, 1995 TABLE 1 (Continued) T,a K
m, molkg
c, 10-6 mol/dm3
A, S cm*/mol
dA, S cm2/mol
m, molkg
c , 10-6 moVdm3
A, S cm2/mol
dA, S cm2/mol
3484.4 8706.8 17272 17272
1983.8 4965.2 9875.4 9875.4
1018.5 922.88 840.15 840.17
-0.0 0.2 -0.0 -0.0
4180.5 10068 16592 16592
2255.7 5444.4 8993.4 8993.4
1015.7 906.63 844.71 844.66
1.5 -2.8 0.7 0.6
3944.0 8178.8 19298
1949.9 4053.0 9634.5
986.40 885.05 760.80
-0.4 -0.5 0.3
3763.4 10611 22508
1451.1 4140.3 8957.8
760.20 593.95 495.32
1.4 0.8 -0.8
548.74 4344.8 15700
166.32 1327.4 4907.1
791.71 432.93 296.76
3.9 4.6 -2.3
672.89 672.96 672.89
400.65 1744.3 9798.6
105.26 457.77 2607.2
606.08 338.01 198.38
4.2 -16.1 5.2
713.79 2630.1 7206.4 17303
478.60 1763.8 4834.4 11616
1081.9 1035.1 977.06 908.86
0.2 -0.2 0.0 0.0
808.67 3910.4 9491.2 17018
559.23 2704.6 6566.4 11778
1067.5 1008.1 954.43 910.40
1.3 -0.2 -0.5 0.2
367 1.5 7577.8 15439 15439
2244.1 4635.7 9460.4 9460.4
1057.5 995.06 921.22 921.33
-0.2 0.0 -0.0 0.1
3520.3 9355.9 19787 19787
2003.3 5333.6 11315 11315
1068.5 960.24 864.18 864.11
-0.1 -0.2 0.1 0.0
3592.9 9534.0 17102 17102
1936.4 5149.2 9261.8 9261.8
1080.9 963.16 882.57 881.79
-1.0 -0.1 0.5 -0.3
3972.4 9654.3 18290
1962.5 4789.6 91 17.4
1026.9 903.96 807.98
-1.2 1.4 -0.5
4952.4 11041 23345
1926.9 4344.4 9352
754.46 628.17 526.94
-2.5 -0.1 0.7
T:K
’
NaBr 642.62 642.62 642.62 642.63 642.63
67.186 67.186 189.09 478.27 805.75
38.211 38.21 1 107.55 272.05 458.37
1187.7 1187.3 1170.8 1143.9 1121.3
648.88 648.87 648.88 648.88 648.87
66.020 66.020 199.30 481.89 768.35
35.569 35.569 107.38 259.67 414.07
1226.0 1226.6 1207.0 1177.2 1154.2
655.85 655.85 655.86 655.87
2 1.409 50.757 124.62 515.56
10.568 25.047 61.491 254.42
1273.5 1263.7 1246.9 1188.9
665.35 665.38 665.39 665.39
11.290 35.049 129.73 405.52 5.2538 17.732 54.550 149.45 1.0590 1.5211 20.937 99.734
4.3301 13.430 49.686 155.19 1.5905 5.3701 16.566 45.170
1329.3 1309.7 1239.2 1125.2 1348.9 1290.2 1193.0 1039.9 1342.3 1331.7 1161.6 900.74
669.80 669.83 669.86 669.87 672.94 673.04 672.99 672.88
0.27801 0.39615 5.4838 26.197
p = 28.01 MPa 0.3 642.63 -0.1 642.63 0.2 642.62 -0.1 642.63 -0.3 p = 28.05 MPa -1.4 648.88 -0.8 648.89 0.6 648.89 0.9 648.89 0.8 p = 28.00 MPa -1.2 655.88 -0.9 655.87 0.5 655.86 2.3 -0.4 665.38 3.7 665.38 -2.4 665.39 -2.2 7.9 669.87 -4.2 669.86 -3.2 669.86 -5.4
1.2 -2.7 -1.8 6.9 CsBr
604.58 604.58 604.59 604.58
91.325 91.325 183.57 470.1 1
61.232 61.232 123.08 315.21
1113.5 1113.6 1106.4 1091.7
p = 22.51 MPa -0.2 604.58 -0.1 604.58 -0.1 604.59 0.4 604.60
60 1.66 601.66 601.67 60 1.67
63.917 63.917 187.68 483.05
44.199 44.199 129.78 334.04
1100.3 1100.0 1091.2 1078.7
p = 28.00 MPa -0.7 60 1.67 -1.0 601.68 -0.3 60 1.68 1.3 60 1.69
63 1.63 631.62 63 1.62 63 1.62 631.62
38.059 38.059 106.77 269.06 445.39 28.772 28.772 108.86 268.30 441.51
1197.3 1196.3 1184.0 1164.0 1147.9
642.66 642.66 642.67 642.67 642.68
62.3 13 62.313 174.81 440.49 729.11 50.610 50.610 191.48 47 1.88 776.45
648.92 648.93 648.93 648.93 648.93
49.652 49.652 172.56 427.61 713.79
26.726 26.726 92.887 230.20 384.29
1285.7 1286.5 1267.5 1238.6 1213.6
655.87 655.87 655.86 655.86 665.45 665.28 665.25 665.23
24.200 48.717 155.03 579.33 18.994 47.366 142.37 420.82
11.938 24.033 76.462 285.91 7.2544 18.223 54.867 162.43
1317.5 1308.7 1283.2 1222.8 1340.4 1320.6 1265.0 1162.7
p = 28.01 MPa
1247.3 1247.5 1228.3 1201.2 1179.0
0.3 631.61 -0.7 631.61 0.0 631.61 0.2 631.61 0.3 -0.9 642.69 -0.6 642.69 0.9 642.70 0.7 642.70 0.3 p = 28.02 MPa -2.0 648.92 -1.2 648.91 1.2 648.90 1.6 648.90 1.2 p = 28.00 MPa 0.3 655.87 -0.1 655.87 -0.3 655.86 0.4 -3.5 665.21 0.4 665.22 1.4 665.23 3.5
J. Phys. Chem., Vol. 99,No. 29, 1995 11619
Conductance Measurements at High Temperatures TABLE 1 (Continued) c , 10-6 mol/dm3
m, moVkg
T," K
A, S cm2/mol
612, S cm2/mol
moVkg
c , 10-6 mol/dm3
A, S cm2/mol
611, S cm*/mol
m, T/K
CsBr p = 28.00 MPa
669.87 669.87 669.87 669.87
3.7158 9.2881 41.711 144.23
673.02 672.99 672.98 672.97
0.68786 2.1323 8.1970 40.923
1.1278 2.8072 12.635 43.701
1349.9 1331.2 1254.4 1092.7
-3.3 -1.7 6.3 0.9
669.87 669.86 669.87
542.60 4160.7 14235
164.20 1271.4 4433.1
839.59 472.79 329.55
-2.7 -0.1 0.3
0.17993 0.55742 2.1484 10.690
1372.5 1362.0 1311.1 1122.7
-6.6 0.2 6.3 2.3
672.97 672.95 672.95
300.43 2839.4 14541
78.663 745.18 3887.8
711.15 33 1.02 194.83
-1.7 -3.2 1.4
The temperature scale is the International Practical Temperature Scale of 1968.
distance 473. At least seven experimental (c, A) results were concentrations the Justice criterion is exceeded by up to 40%. available at each of the temperature and pressure conditions, Due to shifts in the cell constant with temperature changes, the and three parameters were obtained from the nonlinear regresaccuracy of A was about 1%. However, the precision of the measurements in a single run can be much higher. This is sion of eqs 1 and 2: &, K",, and J2. Although J2 can also be important because the value of K", does not change apcalculated from the Fuoss-Hsia-Femhdez-Prini (FHFP) preciably with small (1%) shifts in the cell constant provided model, it was treated as an adjustable parameter in order to the cell constant is constant for the whole run. The experimental obtain more reliable estimates of & and K",. accuracy of individual (c, A) results was mainly affected by The temperature and pressure drifts during one series of three factors in addition to the cell constant: (1) fluctuations measurements approached 0.26 K and 0.06 MPa in the worst of pressure caused by the pump and the back-pressure regulators, cases. The derivative of & and K", with respect to tempera(2) the magnitude of the solvent correction, and (3) possible ture at the pressure p = 28 MPa could be fairly accurately contamination of the samples. The latter two factors affect only determined from a preliminary analysis of the data. This the measurements of the most dilute solutions, whereas the first allowed corrections to be introduced into the fitting equation one is also important at high concentrations. All three factors to account for changes of these parameters caused by variations become increasingly more important at temperatures above 665 of temperature from its average value during a series of K because the compressibility of the fluid increases, and measurements. The procedure was to determine & and K", at measurements on more dilute solutions are necessary to obtain a mean temperature Tm by using eq 1 to calculate the reliable conductances at infinite dilution as the association conconductance at the actual temperature T of the measurement stant increases. In addition, at these temperatures, measurements with Ao(T,P) = &(Tm) (d&JdT)(T - Tm) and Pm(T =) of the very high resistances of the solvent (up to 6 MQ) were KB,(Tm) (dK",/dr)(T - Tm), where J2 was assumed constant less accurate due to the presence of the shunting resistor and because its temperature derivative is negligible and Tm is a an increased frequency dependence. As a result, the precision temperature close to the median of the experimental temperaof the measurements of A as estimated by the deviations from tures. Values of &(T,,,), Pm(Tm),and J2(Tm) were determined the fitting equation decreased with increasing temperature from by a least-squares fit of the results to eq 1 using these 0.1% at T = 600 K to about 1% at T = 673 K (d = 260 kg temperature corrections. The changes in the regressed values m-3). This is illustrated in Figure 3, where deviations of all of & and K", resulting from these corrections were signifithe measured equivalent conductances from eq 1 are plotted cantly lower than the 95% confidence level error estimates given against temperature. The scatter of the experimental points in Table 2. No corrections for the pressure variations were increases rapidly as the critical temperature is approached. The introduced because the derivatives of & and K", with respect unusually high scatter at 677 K (d = 230 kg m-3) may be caused to pressure could not be determined from the experiments by variation in the additional leakage path. The largest performed. Results at higher temperatures (Marshall, Franck) deviations from eq 1 are 4.8% for a moderately concentrated show that A0 is apparently independent of temperature, and Nal3r at 673 K and 5.5% for the most concentrated NaCl at K", is a weak function of temperature at constant density. 677 K. Several cases of deviations of about 2% occur for both Assuming that A0 and K", are only functions of density, and dilute and more concentrated solutions at 670 K and above. using the Hill equation of state for water, the correction resulting The average of the absolute value of the deviations in percent from the pressure variations was estimated to be even smaller is 0.06, 0.04, 0.03, 0.08, 0.05, 0.23, 0.44, 0.81, and 2.2 at the than that resulting from temperature variations. temperatures 602, 632, 643, 649, 656, 665, 670, 673, and 677 K, respectively, for all the measurements at 28 MPa. The values of &, K",, and J2 thus obtained together with their uncertainties and the standard deviations of the fits are There was a possibility that hydrolysis played a significant given in Table 2. The deviations of the experimental equivalent role in these solutions, so calculations were made for NaCl at conductances from those calculated from eqs 1-3 are listed in 656 K and above to estimate these effects. The applicable Table 1. equilibria are Several experimental points obtained at the highest concentrations do not fulfill the recommendation of Justice36that ~ 4 ~ a " ~ NaCl(aq) Na+(aq) Cl-(aq) 5 0.5. As a check on possible errors, the last point in the results for NaCl at T = 673 K was omitted, and this led to insignificant Cl-(aq) H 2 0* OH-(aq) HCl(aq) changes in & and K", and an increase of the uncertainties, although J2 became less negative. It was then decided to include H 2 0 * H+ OH-(aq) all the data in our fitting, even in the cases where at the highest
+
+
-
+
+
+
+
Zimmerman et al.
11620 J. Phys. Chem., Vol. 99, No. 29, 1995
TABLE 2: Parameters of Eq 1: Equivalent Conductance at Infinite Dilution &, Equilibrium Constant for Dissociation and J2; s is the Standard Deviation of the Experimental Points from Eq 1 (Numbers in Parentheses Are the Uncertainties of the Last Dieit)
e:
T,b K
K", x 103
P,MPa
Ao, S cm2/mol
579.47 604.57 601.73 631.69 642.57 648.91 655.89c 655.91' 665.47 670.09 673.10 677.20
9.8 22.47 28.01 27.99 28.00 28.00 28.00 28.00 28.00 28.00 28.00 28.00
1042.6(12) 1068.2(10) 1052.4(19) 1153.6(22) 1210.3(15) 1255.2(13) 1297.0(9) 1284.7(9) 1336(5) 1305(22) 1349( 13) 1290(46)
112( 13) 74(7) 90(16) 32.6(28) 18.3(7) 14.1(4) 7.85(12) 7.9(3) 1.44(6) 0.28(4) 0.064(4) 0.0162(28)
604.58 601.69 631.66 642.64 648.91 655.84 665.36 669.55 672.89
22.50 28.01 28.00 28.01 28.00 27.95 28.00 28.00 28.00
1029.0(5) 1012.3(7) 1121.7(7) 1179.0(3) 1222.0(12) 1266.9(6) 1309(4) 1325(5) 1327(22)
W3) 87(6) 30.9(7) 18.35(13) 14.6(4) 8.11(9) 1.54(5) 0.327(10) 0.082(11)
601.66 631.62 642.63 648.88 655.86 665.38 669.85 672.94
28.02 27.99 28.01 28.05 28.00 28.00 28.00 28.00
1046.1(13) 1151.8(8) 1208.2(3) 1250.8(22) 1290.0(23) 1350(5) 1371(13) 1359(19)
100(15) 37.0(12) 21.52(17) 17.0(9) 9.7(3) 1.91(7) 0.36(3) 0.114(12)
604.58 601.67 631.62 642.68 648.92 655.87 665.27 669.87 672.98
22.51 28.00 28.01 28.01 28.02 28.00 28.00 28.00 28.00
1129.9(3) 11 13.5(14) 1213.8(5) 1266.4(9) 1308.0(19) 1333.8(16) 1372(5) 1374(7) 139l(9)
75.9(20) 95(12) 36.3(7) 21.6(5) 17.5(8) 10.15(26) 2.20(11) 0.448(22) 0.137(8)
-log
K",
J2
x
dm9'2/mo13'zS cm2/mol
s, S cm2/mol
NaCl
1.1 1 .o 1.5 1.6
0.95(5) 1.13(4) 1.05(7) 1.49(4) 1.737(17) 1.852(13) 2.105(7) 2.101( 17) 2.841( 17) 3.55(6) 4.20(3) 4.79(7)
0.040(6) 0.058(9) 0.046(13) 0.107(20) 0.165(18) 0.247(17) 0.420(19) 0.2(3) 1.4(3) 5(8) -11(17) -3(400)
0.8 0.6 2.6 11 5.9 12
1.108(19) 1.06(3) 1.510(10) 1.736(3) 1.836(16) 2.091(5) 2.813( 14) 3.486(13) 4.09(5)
0.056(3) 0.042(5) 0.097(5) 0.1643(3) 0.257(15) 0.441(15) 1.39(22) 2.8(18) 2(45)
0.4 0.6 0.6 0.2 0.8 0.6 3.5 2.4 12
l.OO(6) 1.431( 14) 1.667(3) 1.770(23) 2.014(14) 2.719(17) 3.44(3) 3.94(4)
0.043(11) 0.098(6) 0.155(3) 0.23(3) 0.40(3) 1.45(21) 1(4) 5(29)
1.0 0.6 0.2 1.6 1.4 2.6 6.3 9.5
1.1 19(12) 1.02(5) 1.441(8) 1.665(9) 1.756(18) 1.994(1 1) 2.658(20) 3.349(21) 3.864(25)
0.0542(25) 0.047(10) 0.103(4) 0.166(7) 0.255(21) 0.406(24) 1.55(20) 4.4(19) 6(10)
0.2 1 .o 0.4 0.7 1.4 1 .o 2.9 3.9 5.1
1.1
1.o
LiCl
NaBr
CsBr
Standard state is a hypothetical solution with composition mo = 1 mol kg-'. This is the median temperature where A0 and K", were determined. The temperature scale is the International Practical Temperature Scale of 1968. Measurements at this temperature were done twice: once by G.H.Z. and then later by M.S.G. after a new assembly of the cell and a new determination of the cell constant. Also, the ranges of concentrations were different, as shown in Table 1. The limiting conductances obtained differ by 0.96% and the equilibrium constants by 0.64%. The differences in & presumably reflect changes in the cell constant with time and temperature cycling.
The molalities of all species in these equilibria were calculated with and without hydrolysis using the equilibrium constants from this study for NaCl, the expression given by Frantz and Marshalltgfor HC1, and the equation recommended by Marshall and Francks8 for the self-dissociation of water. The lowest composition at each temperature was used, since this is where hydrolysis effects would be maximized. The amounts of C1assuming hydrolysis and no hydrolysis differed at most by about 3% at the highest temperature where the effect was largest. Considering the inherent uncertainty of the composition in these very dilute solutions, and the fact that the conductance of NaCl is not drastically different from that of NaOH (at most 25% using the equation for NaOH of Quist and Marshall),26the effect of hydrolysis was estimated to be negligible. Conductance measurements at room temperature have shown that triple ions can form when the dielectric constant of the solvent is less than They have also been proposed to occur at high temperature and pressure.65 The existence of triple ions
is exhibited by a minimum in a plot of A against concentration. There is no evidence for triple ion formation in these new measurements. At concentrations higher than the present measurements it is expected that triple ions would be found. VII. Discussion The measurements for NaCl near 579.47 K and 9.8 MPa were compared with the results of Noyes66 after minor corrections for the small differences in temperature and pressure. The two results agreed to within less than 1%. A similar comparison with the results of Pearson et al.67at 65 1.15 K and d = 525 kg m-3 showed reasonable agreement (< 1.5%) considering the temperature and pressure differences. Samoilov and Manshikova6*report agreement with the results of Noyes and Pearson et al. for NaC1, but they report only a graph of their results. One of the main advantages of the new flow apparatus in comparison to the static cells used before is an extended concentration range where reliable measurements can be made.
J. Phys. Chem., Vol. 99, No. 29, 1995 11621
Conductance Measurements at High Temperatures TABLE 3: Solvent Specific Conductances Measured before Starting a Series of Conductance Measurements at All the Temperature and Pressure Conditions Included in Table 2 KS,
T/K
P,MPa
NaCl
579.5 604.6 601.7 631.7 642.6 648.9 655.g6 655.9b 665.5 670.1 673.1 677.2
9.8 22.5 28.0 28.0 28.0 28.0 28.0 28.0 28.0 28.0 28.0 28.0
3.38 2.60 3.27 1.87 1.30 1.12 0.66 0.69' 0.15 0.12 0.035 2.06
S cm-l
LiCl
NaBr
CsBr
2.55 3.08 1.81 1.25 1.06 0.72
3.05 1.67 1.26 1.02
2.49 2.97 1.75 1.37 1.36
0.65 0.16 0.12 0.O4lc
0.61 0.21 0.062 0.037
0.20' 0.058 0.044
0.001 0.002
a The temperature scale is the International Practical Temperature Scale of 1968. Measurements for NaCl at this temperature were done twice: once by G.H.Z. and then later by M.S.G. after a new assembly of the cell and a new determination of the cell constant. Also, the ranges of concentrations were different, as shown in Table 1. The limiting conductances obtained differ by 0.96%, and the equilibrium constants by 0.64%. 'This value is an average of two or three measurements.
0.02
0.04
0.06
c1/2/ ( m o l dm-3) 112 Figure 4. Equivalent conductance, A, of CsBr at T = 673.15 K and d = 260 kg m-3 as a function of the square root of concentration: (0) experimental results; (-) eq 1 with coefficients from Table 2; (- - -), Onsager limiting law. The insert shows a blowup of the dilute region inside the rectangle.
6 0
2W
0.003
416001500
c
d I
\\a
22
0
-"[
1
0
-4
300
400
500
600
700
d/kg In-3
Figure 3. Percent deviations from eq 1, lOO{Ao(expt) - Ao(fit)}/Ao(fit), of all experimental points as a function of density. The average of the absolute value of the deviations is 2.2, 0.81, 0.44, 0.23, 0.05, 0.08, 0.03, 0.04, 0.04, 0.06, and 0.08 at densities (kg mT3)of 230, 260, 300, 380, 490, 540, 570, 610, 670, 690, and 700, respectively.
Results at low concentrations are important if accurate values of limiting equivalent conductances are to be obtained when ion association is extensive. In Figure 4 the experimental conductance results for CsBr solutions at T = 673 K and at solvent density d = 262 kg m-3 are plotted against the square root of concentration together with eq 1. The most rapid decrease of the equivalent conductance with concentration due to ion pairing takes place in the range 10-6-10-4 mol dm-3. At these (and higher) concentrations the equivalent conductances do not obey the Onsager limiting law. (The limiting slope is shown in Figure 4 as a straight line.) Measurements in this concentration range are necessary to test the conductance theories used to extrapolate A to infinite dilution and to obtain accurate dissociation equilibrium constants. However, conductance measurements at lower concentrations and at high temperatures in static cells are very difficult, and the results often have large inaccuracies due to (1) adsorption of the solute on the walls of the cell, (2) inaccurate solvent corrections, and (3) impurities from corrosion of the apparatus. It is evident from Figure 4 that limiting conductances at low densities may
d/kg m-3 Figure 5. Equivalent conductance, &,at infinite dilution as a function of density of the solvent for the four salts investigated. The experimental points shown are the results of this work in order of increasing limiting conductance at low densities: 0, LiCl; 0, NaCl; 0, NaBr; 0, CsBr. The bending lines are smoothed experimental results: .**, LiCl; -, NaC1; - - -,NaBr; - * -,CsBr. The straight lines are eqs 4 and 5; bending lines represent our results.
depend on the extrapolation method chosen if all measurements are made at concentrations higher than mol dm-3. To circumvent this difficulty, Quist and M a r ~ h a l lestimated ~~,~~& at low densities using an empirical extrapolation. They found that & was a linear function of density independent of temperature at temperatures from 673 to 1073 K and densities from 400 to 700 kg-3. For NaCl and NaBr they proposed A,,(NaCl) = 1876 - 1.160d
(4)
A,,(NaBr) = 1880 - 1.180d
(5)
as an average value from all of their experiments. By assuming that eqs 4 and 5 are valid at slightly lower temperatures, Figure 5 compares relationships 4 and 5 with the present results for all four salts. There is reasonable agreement with eqs 4 and 5 at densities higher than 500 kg m-3 but
11622 J. Phys. Chem., Vol. 99, No. 29, 1995
Zimmennan et al. T/K 1000900 800 700
16001
600
c; I
rl
8 3 0
1400
4 1300
. Q
a
m
E
g:
1200
1100 L
1000
200
300
400
500
600
700
d/kg m-3 Figure 6. Equivalent conductance, Ao, at infinite dilution for NaCl and NaBr as a function of density of the solvent. Experimental results: this work -, 0, NaCl; - - -, dotted 0, NaBr; Fog0 et al.',2 for NaCl recalculated using FHFP theory at (0)T = 651, 656, and 666 K and (crossed 0 ) T = 661 K; x, Fog0 et al.' for NaCl as reported by the for NaCI; A, Lukashov et authors at T = 661 K; 0, Pearson et al.69for NaCI; V, Martynova et al.'O for NaC1. The straight lines are eqs 4 and 5 for (-), NaCl and (- - -), NaBr. The dotted line (.-*), and stars (a) represent the Oelker and Helgeson7' correlation evaluated at our experimental densities.
deviation from the straight-line equation of Quist and Marshall at lower densities. A similar dependence of & on density was obtained for all the salts in the present investigation. The results from other laboratories are in reasonable agreement with the present results. Figure 6 shows the results obtained by Fog0 et al.,2 Pearson et al.,67Lukashov et al.,69 and Martynova et The temperatures of these experiments are not very different, so the comparison should accurately reflect the differences. The agreement is very good at densities higher than 500 kg m-3 with the exception of the data of Lukashov, which are up to 7% higher, and those of Martynova, which are up to 20% higher. At lower densities the straight-line equations proposed by Quist and Marshall overestimate the experimental limiting equivalent conductances. Between 200 and 300 kg m-3 the uncertainties of the limiting conductances that can be obtained from the literature data are estimated to be 10-50% depending on density. The uncertainties of the present results at the densities 260 and 230 kg m-3 are estimated to be less than 3%. It is interesting to note that the limiting conductances obtained by Fog0 et alS2at T = 661 K using the Shedlovsky method of extrapolation increase linearly with decreasing density, and the slope is roughly the same as that obtained by Quist and Marshall, who also used Shedlovsky's method. However, Figure 6 shows that our calculations using the same experimental results with the FHFP equation give much more scattered limiting conductances which, when taken together with complementary results obtained in the same laboratory at higher densities,66 are in agreement with the present results within experimental uncertainties. Also included in Figure 6 are limiting equivalent conductances for NaCl calculated from the correlation given by Oelkers and Helgeson." This correlation, based on an equation analogous to the Arrhenius equation for chemical reaction rate constant, gives values of & close to the present experimental results (with differences up to 6%.) As seen in Figure 6, this correlation deviates significantly from the straight lines given by Quist and Marshall in the low-density region, in a way similar to the present results.
1
1
1.2
1.4
1.6
1000K/T Figure 7. pK8, for NaCl as a function of 1OOOT'. The dashed line is the p = 28 MPa isobar where most of the present measurements were made. The continuous lines represent eq 6 at densities decreasing from bottom to top of the diagram from 700 to 200 kg m-3 at intervals of Quist and Marshall at densities 100 kg m-3. Experimental points: decreasing from bottom to top of the diagram from 700 to 300 kg m-3 at intervals of 100 kg m-3;23 V, Franck;6 Fog0 et aL2 for NaCl recalculated using FHFP theory at (0)T = 651, 656, and 666 K and (crossed 0 ) T = 661 K; 0, Pearson et al.;67 A, Lukashov et al.;69 V, Martynova et al.'O The dotted lines connect the results from the same source at constant density. The results of Quist and Marshall, Franck, Fog0 et al., Pearson et al., Lukashov et al., and Martynova et al.'O are at the densities d = 700, 600, 500, 400, and 300 kg m-3, d = 700, 500, and 300 kg m-3, d = 400,380,360,340,320,290,260,230, and 200 kg m-3, d = 712, 667, 591, 525,447, and 399 kg m-3, d = 700, 600, 500, 400, and 230 kg m-3, and d = 700, 600, and 500 kg m-3, respectively.
*,
Figure 7 shows experimental -log K", results for NaCl solutions as a function of T ' and density. The dashed line represents the p = 28 MPa isobar where most of present results were obtained. The results of Franck,6 Quist and Marshall,23 Pearson et al.,67 Lukashov et al.,69 and Martynova et a1.,7O as well as those obtained using the results of Fog0 et aL2 and eqs 1-3, are shown. The dotted lines connect the data of Quist and Marshall at constant densities, showing the dependence of -log K", on temperature. In order to get a preliminary comparison of these results, we assumed that the dependence of the equilibrium constant on T ' is linear, with a constant slope (independent of density). The value of the slope was set equal to that of the lines representing the results of Quist and Marshall at intermediate densities (500-650 kg m-3). At low densities the slope from Quist and Marshall's results becomes more negative, but Quist and Marshall noted that this effect may be due to larger uncertainty of K", at high temperatures and low densities. This slope is certainly not accurate, but the temperature dependence is probably small, so that comparisons over a small temperature range are reasonable. To establish the dependence of the equilibrium constant on density, only the present results were fit to a simple function of density d with the above temperature dependence. The result was -log
e
+
= 2.887 - 1.647 x lOP3d 910.16'
+ 1200T' (6)
where d is the density in kg m-3. In order to compare the results, Figure 8 shows the difference between the experimental
J. Phys. Chem., Vol. 99, No. 29, 1995 11623
Conductance Measurements at High Temperatures
u
1 t
'3
Oe2 i 0
a
I
T
U
1
*
-o-2 -0.4
*
I 200
300
400
500
600
700
d/kg In-3 Figure 8. Difference between pK", calculated using eq 6 and that obtained from experimental results: 0, present results. All other symbols are the same as in Figure 7: t,Quist and Marshall at 673 K;23Fog0 et al.z for NaCl recalculated using FHFP theory at (0)T = 651, 656, and 666 K and (crossed 0 ) T = 661 K; 0,Pearson et al.;67 A, Lukashov et The results of Martynova et al.'O are 0.7-1.0 log units higher than the present results.
values of -log K", and those calculated using eq 6. The symbols are the same as in Figure 7. The results of Quist and Marshall were included only at 673.15 K, and the results of Franck at 823.15 K were not included because the comparison is reasonable only near the temperatures of our measurements. Very close to the critical point eq 6 will probably fail due to critical point effects. The error bars represent the uncertainties reported by the authors or, in case of the results of Fog0 et al., the uncertainty at the 95% confidence level obtained from our fit of the data to eqs 1-3. The worst agreement between present results and literature results can be observed at high densities (650-750 kg m-3). The results of Quist and Marshall are over 0.4 log units lower, while those of Pearson et al. and Lukashov et al. are 0.28 log units higher than present results. The results of Martynova et aL70 (not included in Figure 8) are 0.7-1.0 log units higher than the present results. These differences where association is small are due mainly to the conductance model chosen. For example, when the present results for NaCl at 579 K were fit to the Shedlovsky model, the resulting equilibrium constant was 0.3 log units lower than that using eqs 1-3. In addition, very accurate conductance measurements are needed when association is small. (At a density of 700 kg m-3 the salt is less than 10% associated at concentrations up to 0.02 mol dm-3.) The best agreement occurs at densities 450550 kg m-3. At 400 kg m-3 and lower densities both Pearson et al. and Fog0 et al. observed changes of the experimental equilibrium constants with temperature that are 3-5 times larger than those obtained by Quist and Marshall at slightly higher temperature. The dependence of the equilibrium constant on temperature in this region should be investigated further to see whether this change of slope is real. Taking into account the difficulty of measurements at the conditions close to the critical point of water, the agreement with present results is reasonably independent of whether the change in slope is real. At low densities, the discrepancies are caused by difficulties in obtaining accurate limiting conductivities from data at concentrations where association is still extensive. Very recent results of Ho et al.72 using a modified version of Marshall's apparatus are closer to the present results than those of Marshall and Quist. Oelkers and H e l g e ~ o nrecalculated ~~ the dissociation constants using their values of Ao7' and the A values of Quist and
1
,
1.0
1.2
1.4
1.6
IOOO.K.T-~ Figure 9. K", for LiCl as a function of 100OT'. The dashed line is the p = 28 MPa isobar where most of our measurements were made: 0, present results; x, points on the isobar corresponding to densities from 700 to 300 kg m-3 at intervals of 50 kg m-3 interpolated from the present results. Other experimental points are (V) Franck6and (A) Lukashov et al.69The dotted lines connect the results at constant density
including those interpolated from our results. The results of Franck are at the densities d = 700, 500, and 300 kg m-3, and those of Lukashov et al. are at d = 700,600,500,400, and 230 kg m-3. Higher values of -log K", correspond to lower densities. Marshall. The dissociation constants obtained were practically identical with those reported by Quist and Marshall, so they are not included in Figure 7. Similar observations can be made about experimental equilibrium constants in aqueous solutions of NaBr and LiC1. (No literature data are available on CsBr.) As shown in Figure 9, analogous to Figure 7, -log K", results of Lukashov et al.69for LiCl deviate from the present results in a way similar to the case of NaC1. The results of Franck6 are higher than ours at the density of 300 kg m-3 and lower at 700 kg m-3 with a good agreement at 500 kg m-3. These comparisons support the conclusion that using the FHFP model (eqs 1-3) to obtain & and K", results in values of K", which are more accurate than those obtained from the Shedlovsky equation. The values of K", obtained by Franck and by Quist and Marshall at 300 kg m-3 deviate from the present results, whereas the values calculated from the data of Fog0 et al. (obtained 40 years ago) recalculated using the FHFP theory are in reasonable agreement with the present results, although the uncertainties are much higher. The FHFP theory describes well the dependence of the equivalent conductance of the dilute 1:1 electrolytes on concentration when J 2 is treated as an adjustable parameter. Calculating J 2 using the equations given by Femhdez-Prini gives increasingly worse residuals as the density of the solvent decreases and association increases. At the temperatures from 580 to 665 K the ionic radii obtained from the regressed J 2 coefficients are 0.7-1.3 nm, in good agreement with the respective Bjerrum distances. At higher temperatures the uncertainties increase very rapidly so that at T = 673 and 677 K determining the parameter J 2 from FHFP theory by fitting our experimental data is practically impossible as the uncertainties in J 2 are larger than 5 2 itself. Fitting the data of Fog0 et al. leads to similar results. There are a few scattered reports of conductance measurements of supercritical aqueous NaCl which indicate phase separation up to 16 K above the critical p ~ i n t ' ~ - 'determined ~ by normal phase equilibrium studies. Corwin and Owen76
Zimmerman et al.
11624 J. Phys. Chem., Vol. 99, No. 29, 1995
v)
& 0.08
-4
3,
5 0.06.
a
o? N
.
@
4 ,0.04
150
*
* *
1100
* . O'
200
2 X
.*
c
0.021
@
B
300
400
500
d I kg.11~3
6 0 0 * ';'a0
'
Figure 10. Values of Aovo (cm2 S mol-' Pa s) and Nex for NaCl(aq) as a function of density. 0, at 28 MPa (T = 579-677 K); 0, &vo at T = 1073 K from Quist and Marshall;23 Ner at 28 MPa from Majer et a1.;53.55 indicate experimental points; indicate extrapolated values assuming the direct correlation function integral well behaved. Nex and the isothermal compressibility KT are roughly proportional to each other in this region.
*
*, *
1.0 nm).s5 Closer to the critical point the long-range solvation must have a large effect, but at 28 MPa the drop in &qo is due to short-range solvation. The fact that the Stokes radius is so small (0.2-0.4 nm) confirms the conclusion that short-range solvation is involved and indicates that on average very few water molecules are carried along by the ion. Using the friction coefficient point of view, it is quite remarkable that all of the univalent ions have approximately the same AO at high temperatures even though the ionic radii vary by more than a factor of 3 in going from Lif to Br-. A sound theoretical approach must include dielectric f r i ~ t i o n ~and ~ - ~the~ effects of the large changes in density and viscosity near the ions6 that arise from the high compressibility of the solvent. Acknowledgment. The authors thank Robert L. Kay for pointing out the importance of reducing adsorption errors when making measurements at low concentrations and Joseph Morello for constructing the containment chamber, heater boxes, and preheating system. This research was supported by the National Science Foundation under Grants CHE9011866 and CHE9340740. References and Notes (1) Fogo, J. K.; Benson, S. W.; Copeland, C. S. Rev. Sci. Instrum. 1951, 22, 765.
(2) Fogo, J. K.; Benson, S. W.; Copeland, C. S. J. Chem. Phys. 1954, pointed out that if these results are correct, the measurements 22, 212. of Fog0 et al.'g2 are in the two-phase region. Fog0 et al.7s (3) Franck, E. U. Z. Phys. Chem. (Munich) 1956, 8, 92. responded that phase equilibrium studies quite conclusively put (4) Franck, E. U. Z. Phys. Chem. (Munich) 1956, 8, 107. their measurements in the one-phase region. The fact that our ( 5 ) Franck, E. U. Z. Phys. Chem. (Munich) 1956, 8, 192. (6) Franck, E. U. Angew. Chem. 1961, 73, 309. recalculation of the results of Fog0 et al. gives values of & (7) Franck, E. U. The Physics and Chemistry of High Pressures; Papers and K", in agreement with the present results indicates that the Symp.: London, 1962; pp 19-24. two-phase behavior reported previously is probably an experi(8) Franck, E. U. Z. Phys. Chem. (Leiprig) 1988, 269, 1107. mental artifact which could be due to either corrosion or the (9) Franck, E. U.; Hartmann, D.; Hensel, F. Discuss. Faraday SOC. 1965, 39, 200. presence of nitrogen in the cell. The present measurements (10) Franck, E. U.; Savolainen, J. E.; Marshall, W. L. Rev. Sci. Instrum. show no indications of the drift with time or other erratic 1962, 33, 115. behavior expected if two phases were present in the input stream. (1 1) Hartmann, D.; Franck, E. U. Ber. Bunsen-Ges. Phys. Chem. 1969, 73, 514. (The cylindrical axis of the cell is horizontal in our experiment.) (12) Hensel, F.; Franck, E. U. Z. Naturforsch. 1964, 19A, 127. One of the great puzzles inherent in the high-temperature (13) Mangold, K.; Franck, E. U. Ber. Bunsen-Ges. Phys. Chem. 1969, results is that, as Quist and Marshall showed,23& is a simple 73, 21. function of density with very little temperature dependence, (14) Renkert, H.; Franck, E. U. Ber. Bunsen-Ges. Phys. Chem. 1970, 74, 40. whereas &qo is not.23,79,s0One would expect from simple (15) Ritzert, G.;Franck, E. U. Ber. Bunsen-Ges. Phys. Chem. 1968, 72, continuum theory that the Walden product, &qo, would be a 798. slowly varying function of temperature and density.s' Figure (16) Dunn, L. A.; Marshall, W. L. J. Phys. Chem. 1969, 73, 723. (17) Frantz, J.; Marshall, W. L. In Water and Steam-Their Properties 10 shows that &qo drops sharply with decreasing density at and Current Industrial Applications; Straub, J., Scheffler, K., Eds.; Ninth 28 MPa but shows more normal behavior at high temperatures. Intl. Conf. Prop. Steam, Munich, Germany, Sept 10-14, 1979; Pergamon Using the more sophisticated Hubbard-Onsager t h e ~ r yand ~ ~ , ~ ~Press: Oxford, 1979. taking into account friction coefficientss4 does not change the (18) Frantz, J. D.; Marshall, W. L. Am. J. Sci. 1982, 282, 1666. (19) Frantz, J. D.; Marshall, W. L. Am. J. Sci. 1984, 284, 651. qualitative picture. The drop in &qo (or equivalently the (20) Quist, A. S. J. Phys. Chem. 1970, 74, 3396. friction coefficient increase) indicates that the size of the (21) Quist, A. S.; Franck, E. U.; Jolley, H. R.; Marshall, W. L. J. Phys. hydration sphere that is dragged along by the ion when it moves Chem. 1963,67, 2453. in an electric field is increasing as the density decreases. The (22) Quist, A. S.; Marshall, W. L. J. Phys. Chem. 1966, 70, 3714. (23) Quist, A. S.; Marshall, W. L. J. Phys. Chem. 1968, 72, 684. Stokes law radius R,of the Na+ and C1- increases from 0.2 nm (24) Quist, A. S.; Marshall, W. L. J. Phys. Chem. 1968, 72, 1545. at d = 700 kg m-3 to 0.4 nm at d = 230 kg m-3.81 One finds (25) Quist, A. S . ; Marshall, W. L. J. Phys. Chem. 1968, 72, 2100. a sharp increase in long-range hydration as the critical point is (26) Quist, A. S.; Marshall, W. L. J. Phys. Chem. 1968, 72, 3122. a p p r o a ~ h e d but , ~ ~this is not the reason for the observed drop (27) Quist, A. S.; Marshall, W. L. J. Phys. Chem. 1969, 73, 978. (28) Quist, A. S.; Marshall, W. L. J. Chem. Eng. Data 1970, 15, 375. in &qo. If the effect were due to the long-range hydration, it (29) Quist, A. S., Marshall, W. L.; Jolley, H. R. J. Phys. Chem. 1965, should correlate with the excess number of water molecules 69, 2726. around the ion, Nex = e*J(g - 1 ) 4 d dr, where e* is the bulk (30) Wood, R. H. Thermochim. Acta 1989, 154, 1. (31) Christensen, J. J.; Hansen, L. D.; Eatough, D. J.; Izatt, R. M.; Hart, number density of water and g is the ion-water pair correlation R. M. Rev. Sci. Instrum. 1976, 47, 730. function. Figure 10 shows the Nex determined by volumetric (32) Christensen, J. J.; Hansen, L. D.; Izatt, R. M.; Eatough, D. J.; Hart, measurements peaks sharply at 150 water molecules at d = 300 R. M. Rev. Sci. Instrum. 1991, 52, 1226. kg m-3 and 28 MPa, while it is only about 25 water molecules (33) Wormald, C. J.; Colling, C. N. In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S . A,, Ed.; ACS Symposium at d = 500 kg m-3 and 28 MPa. In this region &qo drops by Series 133; American Chemical Society: Washington, DC, 1980; Chapter about 30% while Nex increases by 700%.53,55Comparison of 30, p 435. simulations and experimental data has previously shown that (34) Wormald, C. J.; Colling, C. N. J. Chem. Thermodyn. 1983, 15, 725. most of the excess water molecules are far from the ion ( r >
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