F. J. Millero, G.K. Ward, F. K. bepple, and E. V. Hoff
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pressibility of Aqueous Sodium Chloride, wide, Sodium Sulfate, and Magnesium Sulfate Solutions fro
Frank ,J. Millero,* Gary K. Ward,lb Fred K. Lepple, and Edward V. Moff University of Miami, Rosenstiel School of Marine and Atmospheric Science, Miami. Florida 33749
(Received December 7, 1973)
(F'ubiicafion costs assisted by the Office of Naval Research and the National Science Foundation
The isothermal compressibilities (6's) of aqueous NaC1, Na2S04, MgS04, and MgClz solutions have been ineasuired at 0, 15, 30, and 45" by a piezometric technique. The compressibilities were determined at applied pressures P = 8.7, 16.8, and 25.7 bars and the data were extrapolated to 1 atm. The P's have been littrd iio an equation of the form, 6 = Po + AKC+ &e3", where Po is the compressibility of pure water, I: is the molar concentration, and AK and BK are temperature-dependent parameters. The equation fits bar-1 for all the salts. The apparent molal compressibilities, the compressibility data to k0.07 X I$K, have been calculated from the compressibility data. At high concentrations the concentration depens found to follow the equation, 4K = S K * I V I / ~where , $soand SK*are emdence of the ( $ ~ ) ' were 's pirical constants and I\- is the molar ionic strength. To obtain reliable infinite dilution ( 6 ~ ~ )(that ~ agree with values derived from sound velocity measurements) it was necessary to use the equation, i b = +KO 4- S&1/2 -!- b&, where $90 is the infinite dilution apparent molal compressibility, SK is the Debye -Huckel limiting law slope, and b K is a temperature-dependent parameter related to deviations horn the limiting law. The ( 4 ~ ~ from ) ' s all the electrolytes increase with increasing temperature and ap, a13 pear t o go through a maximum between 40 and 50". The deviations from the limiting law, b ~ are s positive at low temperature and decrease with increasing temperatures for all the salts. The ( 4 ~ ) 'are briefly discussed in terms of the ion-water and ion-ion interactions responsible for the observed behavior. V i e ($K)'s for MgS04 solutions have been analyzed by assuming the ion pair, Ev$gS04O, is formed. The for the formation of the ion pair and the $K of MgS04O have been calculated a t various concentraliorns and temperatures. The results are used to examine the structure of the ion pair.
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Introduction Although the isothermal compressibilities have been measured for various electrolytes by a number of worke r ~ ,the ~ , rermlts ~ are ,at high pressures ( P 9 100 bars) and for concentrated solutions ( m > 1.0). The pressure dependence of the compressibility, P, is such that 6 decreases most rapidly at low pressures, where it is most difficult to obtain accurate experimental results. The usual measurements involve determining the volume change due to an increase in pressure of the order of 200 to 1000 atm. The , are calculated apparent molal compressibilities, 4 ~which from the Compressibility data extrapolated to 1 atm, vary a good deal between different ~ t u d i e s . Thus, ~ , ~ there is a need for accurate 1-atm compressibilities for aqueous solutions of varioius electrolytes at low concentrations ( m < 1.0). Although &'s derived from sound speed data are normally more reliabie than those derived from direct measurements, the heat capacities and expansibilities necessary to convert the adiabatic to isothermal values are not readily avaiiable. This study deals with the precise determination of the isothermal compressibilities for four electrolytes, NaCl, MgS04, NaZSCI4, and MgC12, which were chosen because they are the four major sea salts in the oceans. The basic thermodynamic properties of these salts are of prime importance for various thermodynamic calculations in oceanography. One of the applications of the data obtained is the study of ion pair formation of MgSOqO. Although the compressibility changes for the ionization of weak acids and The Journal of Fhysicai Chemistry, Voi. 78. No. 16, 1974
bases have been studied by a number of ~ o r k e r s little ,~ attention has been paid to the compressiSiiity changes associated with the ion pair formation
M + + A - -- M A o 1) where M+ and A- are the free ions, and MAQis the ion pair. From the compressibility data in this study, one can ion calculate the A& for the formation of the I'gS04° pair and the $K for the ion pair by applying a method recently used to study the volume change for the formation of the ion pair using apparent molal volume d a h 5 Experimental Section The isothermal compressibility apparatus used in this study was originally described by Millero, Curry, and Drost-Hansen.6 The apparatus has been ~ h o w n to ~ .yield ~ results for the compressibility of water that agree with the results of Me11 and Whalley8 and Kei19 t o hO.07 x 106 bar-l from 0 to 65". The apparatus consists of three basic :inits, a piezometer, a pressure cell, and a constant temperature bath. A precision bore capillary is fitted to the bottom of the glass piezometer vessel, which has a volume of approximately 410 ml. The capillary is calibrated by weighing various lengths of mercury (measured with a cathetometer), yielding a cross-sectional area of 0.03246 f 0.00001 cm2. The piezometer is contained inside a pressure cell constructed of nickel-plated brass and a glass boiler tube which allows the viewing of the capillary stem. The boiler tube restricts
Compressibility of Aqueous NaCI, MgCI, Na2S04,and MgS04
the measurements to a maximum of 35 bars. The pressure inlet is fitted with a stainless steel Swagelok tee, and also serves as the mercury exchange port. The chamber between the capillary and the boiler tube is open to the main pressure cell, thus allowing equalization of the pressure inside and outside the piezometer. The interior of the main pressuie cell area i s filled with ethylene glycol which is circulated by a magnetic stirring bar. The entire pressure cell is submerged in a constant temperature bath, regulated to zkO.001" with a Nallikainen Thermotrol. The temperature inside the cell is monitored with a Hewlett-Packard quartz crystal thermometer, which was calibrated with a platinum resistance thermometer (traceable to the National Bureau of Standards) and a G-2 Mueller brid :e. The quartz crystal thermometer can detect ternperat ure changes of +0.0001" with an accuracy of k0.001" after calibration. The inside temperature fluctuates less than &O.NXX2" after thermal equilibrium is reached before and after compression, and it is expected that the fluctuations within the piezometer are even smaller than this value. The pressure chsinges are measured with a Texas Instrument Company's fused quartz precision gauge to a precision of AO.001 bar and an accuracy of h0.005 bar (traceable to the National Bureau of Standards) at the highest pressure differences measured. Since we are only concerned with pressure differences, the accuracy of the instrument is not a limiting factor. The change in volume of the solution In the piezometer, caused by a given pressure change (A$), was determined by measuring the change in height, Ah, of the mercury in the attached capillary. This height change was measured to kO.01 mm (&0.001%) with a Gaertner cathetometer. The height measurements were made at 0, 17, and 34 bars applied pressure. The piezom etnc compressibility apparatus was calibrated with water using the sound derived compressibilities of KeL9 'ii'he water used for both the calibration and the test soltiticlns "ai3 ion exchange (Millipore Super Q) 18 megohm water The densities of the solutions (used in some of the calculations) were measured on a magnetic float densimeterl0 and are given elsewhere.ll The sodium chloride and magnesium sulfate were anhydrous Baker analyzeld reagents, while the sodium sulfate was anhydrous Fisher Certified ACS grade. The solutions of these salts were made up by weight without further purification and analyzed by a quantitative evaporation technique. The magnesium chloride, MgC1.6H20, was" a Mallinckrodt Imalyti cal reagent, and the test solutions were analyzed by a gravimetric chloride titration. All the solutions were analyzed after each run to eliminate errors due to possible changes in concentration occurring during degassing of the samples prior to each experiment.
Results and ~ ~ I ~ u ~ ~ ~ ~ Q n s The isothermal compressibility, /3, of a liquid is defined by the equation
The total volume of the interior of the glass piezometer, V,, is given by
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V, V,i, i- V,, Ah (3) where V1iq is th'e volume of the test solution, and Vs9 + A h is the total volume of mercury, A represents the cross-
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sectional area of the capillary, and h is the height of mercury in the capillary measured from the reference mark. If eq 3 is differentiated with respect to pressure and we include the effect of pressure on glass,12J3a we obtain
where Pc is the isothermal compressibility of glass, /3~, is the compressibility of mercury, /3 is the compressibility of the test solution, and Ah is the change in height of the mercury in the capillary for a given change in applied pressure, AP. Since the volumes of liquid and mercury used in the test solution runs and the water calibration run were nearly equal, the differences between /3 of the test solution and Po (compressibility of pure water) can be calculated in a manner which is independent of the values selected ~ . subtracting eq 4 for water from eq 4 for for PG and ( 3 ~ By the test solution, we obtain
(0 - Po)
= (AAh/VAP)li, - @Ah/VAP)x2o (5)
when ( V H ~ ) H= ~O (vHg)llq, vn20 = vi^, and (Ah/AP)H,o and (Ah/AP)llq are compared at the same applied 'pressure. The precision of the term, (AAh/Vl,,AP), is 10.025 x 10-6 bar-1 and, therefore the precision of @, determined by our apparatus, is 10.05 X bar-I with an bar-I. accuracyof A0.07 X The quantity ( P - Po) for various concentrations of aqueous NaC1, MgS04, NaZS04, and MgClz solutions at 0, 15, 30, and 45" is given in Table I.I3b The values of (0 - P O ) given in Table I are the average values determined from the compressions (AAhIAP) a t the average pressures of 8.9 (Ah from 0 to 17 bars), 16.8 (Ah from 0 to 34 bars), and 25.7 (Ah from 17 to 34 bars). We have reported the average value of ((3 - Po) since there appears to be no regular pressure dependence of the (@ - Po) term and deviations from the average are within our experimental error.14 Since the pressure dependence of (@- 6 0 ) is small, we have equated the average values to the 1-atm values. Thus, we are assuming that the compressibilities of salt solutions have the same pressure dependence as water ( i e . , within the experimental error). The compressibilities of the solutions have been fitted to equations of the formaa
p = Po
+
AKc
+
BKc"'
(6)
where AK and BK are temperature-dependent parameters and c is the molar concentration, c = 1000dom/(lOOO $vmdo) [do is the density of pure water, m is the molality, and $\, is the apparent molal volume11]. The AK term is related to infinite dilution ion-water interactions ( lo3& = +KO - P 0 $ 1 ~ O ) and the B term is related to ion-ion interactions (iO3BK = S K * - /30Sv*).Plots of (@ - p'J),lc us. for the various salts are given in Figures 1-4.13b The constants AK and BK for the salts at various temperatures are given in Table II.I3a The average deviations between the experimental values and those calculated from eq 6 b a r 1 over the entire temperaare within 10.07 X ture and concentration range (which represents our experimental error). An attempt was made to fit the data to an equation similar to eq 6 by using molal concentrations (which are more convenient to use); however, the errors were much larger (A0.15 X bar-I) and required an
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The Journalof Physical Chemistry, Vol. 78,No. 16, 1974
F. J. Millero, G. K. Ward, F. K. Lepple, and E. V. Hoff
1638
additional term. The compressibility of all the solutions decreases with increasing concentration. If we assume that the size of the ion is not pressure dependent and the electrostricted water is already compressed to its maximum extent by t h e charge on the ions, we can assume (as will be discussed later) that the compressibility of a solution is mainly due to the effect of pressure on the bulk (unhydrated) water molecules. As the concentration of the electrolyte incrteases and a larger portion of the water molecules are electrostricted, the amount of bulk water decreases causing the compressibility to decrease. For electrolytes with large hydration numbers, such as MgS04 and" Na2S04, one would expect ap/ac to be much more negative than electrolytes such as NaCl with small hydrais would indicate that the concentration dependence of 8 becomes greater as the number of water molecules affected by the ions increase. As predicted, our data indicate that --(a/3/dc) is directly related to the hydration number of the salts. The magnitude of ap/ac at 0" follows the order Na2S04 > MgSO4 > MgClz > NaCl which holds for the hydration numbers (determined later in the paper). The temperature dependence of /3, a/3/aT, is also negative for all the solutions studied below 25". The compressibility of water also decreases with temperature to a minimum /3 value near 46". A number of have postulated that this is due to the existence of two structural typos of water aggregates at a given temperature (a structured form and a nonstructured or less-structured form). The 8/3/8T term for the structured form is negative, while it is positive for the less-structured form. A t low temperaturies, this structured form is the predominant species while at high temperatures, the nonstructured form predominates. In dilute electrolyte solutions (Figure 5 )?13b the compressibility decreases with temperature to a minimum also near 46". The value of 8/3/87', hoRevm, i s imuch less negative in dilute solutions than in water, indicating an increasing importance of a structure-breakin;: effect due to the presence of ions. As concentration increases, dp/aT becomes less negative and the minimum occurs at lower and lower temperatures (Rgure 5 ) . In a 4 r n NaCl solution, the minimum occurs at 29". One possible explanation is that the ions enhance the nonstructiired form causing this form to become the predominant facttm aLtincreasingly lower temperatures. The apparent mold compressibility is defined as @I
22-24 is given in Table V. The sound-derived (high concentyatiom) results of Allam and Lee2b are in good agreement with our results (from eq 10) for NaC1, MgC12, and MgS0.L. The values given by Owen and BrinkleyZ2for MgSCla and NazS04 appear to be too high when compared to our values. The low concentration s o ~ n d - d e r i v e d " , ~(4K0)'s ~ . ~ ~ for NaCl are in good agreement with oiir values obtained from eq 11. The temperature behavior of the &O'S of NaCl, MgC12, Na&O4, and MgSO
