Partial Molal Volumes of Electrolytes in Sodium Chloride 1737 The Partial Molal Volumes of Electrolytes in 0.725 zyxw m Sodium Chloride Solutions at 25 OC Frank J. Millero,' Arthur L. Laferrlere, and Peter V. Chetlrkln The Rosenstiel School of Marine and Atmospheric Science, University of Miami, Mlami, Fiorida 33 149 (Received February 22, 1977) Publication costs assisted by the National Science Foundation and the Office of Naval Research zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQ The apparent molal volumes of zyxwvut 29 electrolytes have been determined in the medium 0.725 zyxw m NaCl from precise density measurements at 25 "C. The values of 9~ have been extrapolated to infinite dilution by using a least-squares fit of the data and by using Young's rule. The two methods yield values of Po in 0.725 zy rn NaCl that agree to within 0.2 cm3mol-l. The experimentallydetermined values of zyxw Y*O are compared zy to those predicted from binary solution data by using the ionic strength principle, Young's rule, and the specific interaction model. The values of Po predicted by using the specific interaction model and Young's rule are similar and in better agreement (f0.3 cm3 mol-') with the experimentalresults than those predicted by using the ionic strength principle (f0.4 cm3mol-'). For electrolyteswithout a common cation (Na+) or anion (Cl-),the specific interaction model gives the best estimates. The volumes of mixing the electrolytes with a common cation (NaX zyx + NaC1) and anion (MC1+ NaC1) at I = 0.725 determined from our results correlate very well with the enthalpies of mixing and various properties of the uncommon ion (M+and X-). Introduction In recent years a number of workers have de~elopedl-~ and used6-11 various ionic interaction models to estimate the activity coefficients of electrolytes in various ionic media (e.g., seawater). Progress has also been made in using these models to estimate the effect of pressure on the activity coefficients or the partial molal volumes of electrolytes in ionic media.12-17 Owen and BrinkleyI2 estimated the partial molal volumes (n of electrolytes in seawater by assuming the Ps were equivalent to the values in binary solutions at the ionic strength of seawater (-0.725 m). They defined 0.725 m NaCl as being equivalent to "sea salt" and estimated the P of electrolytes in sea salt from the measurements of Wirth." In recent years, we have examined the Ps of electrolytes in 0.725 m NaC113-15 and seawater,13-15 by using a simple hydration rn0de1.l~ We have interpreted the deviations from this model in terms of ion pairing.13-15 Leelghas measured the Ps of electrolytes in NaCl solutions and also showed how Young's ruleBVu could be used to estimate the partial molal volumes. Leyendekker~'~ has recently used these methods to estimate the partial molal volumes of electrolytes in seawater. In a recent paper, we hav? used the specific interaction modeP to estimate the V of electrolytes in NaCl and seawater solutions. At present it is difficult to state with certainty which of these methods gives the most reliable estimates for the partial molal volumes of elec- trolytes in an ionic media because of the paucity of reliable experimental data. In the present paper we will present our experimental results for measurements of 29 electrolytes in 0.725 m NaCl. We will use these experimental results to examine the most reliable method that can be used to estimate the partial molal volumes of electrolytes in an ionic media. Experimental Section The density measurements were made with a vibrating densimeter that is described in detail elsewhere.25 The densimeter measures the relative densities of aqueous solutions zyxwvutsrq (d - do) to a precision of *3 x 10-6 g cm-3.25726 The densimeter was calibrated by using ion-exchanged water and dry nitrogen. The reliability of the densimeter was checked by measuring the densities of standard seawater solutions weight evaporated or diluted with water. The measured densities agree on the average to f2 ppm26 with the values calculated from the equation of state of seawater.27 The temperature of the densimeter is controlled to fO.OO1 "C and set to h0.005 "C with a platinum resistance thermometer (calibrated by the National Bureau of Standards on the 1968 IPTS temperature scale) and a G-2 Mueller bridge. All of the salts used were Baker reagent grade. The salts that did not decompose were heated in vacuo at 110 OC for at least 1 h. Stock solutions of these salts (KBr, LiCl, RbC1, CsC1, NaI, KI, NaBr, KC1, NaN03, KNOB, Na2C03, K2C03, Na2S04, K2S04, NaF, KHCO3, NaHC03,NH4C1, and NH,Br) were made by weight in 0.725 m NaC1. Approximately 1 m stock solutions of the electrolytes that could not be dried (HC1, NaOH, KOH, KF, MgC12, CaC12, SrC12, and BaC12) were made. The molalities of these solutions were determined by measuring the density (HC1, NaOH, KOH, MgSO,, and KF) or by titrating with AgN03 (MgC12, CaC12,SrC12, and BaC12). The NaCl was added to these solutions to make them 0.725 m NaCI. Dilute solutions of the salt mixtures (salt and NaC1) were pre- pared by adding a weighted amount of 0.725 m NaC1. Duplicate density measurements were made on most of the solutions. The two measurements agreed on the av- erage to h3.5 ppm which represents the precision of the measurements. The density of the NaCl medium for all of the experiments was 1.025810 zyx f 0.0000025 g mL-'. This density is equivalent to a molality of 0.72525 h 0.00006 mol (kg of H20)-' as determined from the relationship 103(d - do) = 1.011 + 38.227 m (valid from 0.7 to 0.8 m). The combined error in density was -6 ppm. This error is equivalent to an error of f0.006 cm3 mol-' at 1.0 m and k0.06 cm3 mol-' at 0.1 m in the apparent molal volumes of the electrolytes. Results and Calculations The densities at 25 "C for the various electrolytes (NaF, KF, HC1, LiC1, NaCI, KC1, RbCl, CsC1, NH4C1, MgClz CaC12,SrC12, BaC12,NaBr, KBr, NH4Br NaI, KI, NaOH, KOH, NaN03, KNOB, NaHC03, KHC03, Na2C03, K2CO3, Na2S04,K2S04, and MgSO,) at various molalities (m3) in The Journal of Physical Chemistry, Vol. 81, No. 18, 1977