Mean Activity Coefficients and Osmotic Coefficients in Dilute Aqueous Sodium or Potassium Chloride Solutions at Temperatures from (0 to 70) °C

Abstract

Two-parameter Huckel equations have been determined for the activity coefficient of the salt and for the osmotic coefficient of water in aqueous NaCl or KCl solutions at 0 °C from the highly accurate freezing point data of Scatchard and Prentiss (J. Am. Chem. Soc. 1933, 55, 4355−4362), and points were taken in the estimation up to a molality of 0.5 mol•kg −1 . This molality is the upper limit for the use of the data from this method without any corrections to determine thermodynamic activity values for a constant temperature of 0 °C. The electrolyte parameters of the Huckel equation are B and b 1 , and the value obtained for parameter B in the case of both salts is closely the same as that determined in a previous NaCl and KCl study (Partanen, J. I.; Covington, A. K. J. Chem. Eng. Data 2009, 54, 208−219) from the isopiestic and cell potential difference (cpd) data at 25 °C. The resulting parameters were tested with the other precise freezing point data existing in the literature for these salts and with the cpd data existing for 0 °C. The tests using the latter data reveal that the new parameters apply up to a molality of 1.0 mol•kg −1 . Using the parameter values obtained here for b 1 at 0 °C and in the previous study at 25 °C (see the citation above), a linear dependence of the temperature was determined for this parameter for solutions of both salts. The resulting parameters for B and b 1 were tested with the cpd and isopiestic data existing for NaCl and KCl solutions at the temperatures other than 0 and 25 °C, and they were observed to be reliable up to a molality of 1.0 mol•kg −1 in this temperature range. Above 25 °C, however, these simple temperature dependences for b 1 are probably not sufficient. For a wider range, a quadratic temperature dependence of this parameter was determined for both salt solutions, and these models apply quite well up to 70 °C in these dilute solutions. These b 1 models were mainly determined from the concentration cell data of Harned and Nims (

Traceable Values for Activity and Osmotic Coefficients in Aqueous Sodium Chloride Solutions at Temperatures from 273.15 to 373.15 K up to the Saturated Solutions

“…It is important to emphasize the fully traceable and transparent nature of the best parametrization presented here and in our previous studies, − in addition to its ability to predict experimental results. A critical reader can reproduce all calculations using the presented results with the appropriate literature data.…”

“…Our recent NaCl studies show that an extended version of the simple Hückel equation applies well to experimental data from various sources in the temperature range from 273.15 to 373.15 K. − With our best parametrization for the temperature dependence, the extended Hückel equation could predict all calorimetric data reported in the literature up to 373 K for dilute NaCl solutions, even though these data were not included in the parameter estimation. In the present study, we demonstrate that by extending our parametrization with a quadratic molality term, we can predict all the thermodynamic properties of NaCl solutions from 273.15 to 373.15 K at all temperatures up to the saturated solutions.…”

“…For dilute NaCl solutions, we have observed in our previous studies that the constant value of 1.4 (mol·kg –1 ) −1/2 generally applies for parameter B at all temperatures from 273 to 500 K. ,− In our most successful parametrization of the Hückel equation, the following quadratic equation was determined for parameter b 1 (see ref ): This equation was obtained from the following three values for b 1 ( T ): b 1 (273.15 K) = 0.0077 (determined in ref ), b 1 (298.15 K) = 0.0716 (ref ), and b 1 (348.15 K) = 0.105 (ref ). With this parametrization, our Hückel equation can explain the existing thermodynamic data for dilute NaCl solutions within experimental error at least up to 0.2 mol·kg –1 in the temperature interval of (273, 383) K. For the more concentrated solutions considered in this study, we retained eq for b 1 to preserve the excellent agreement with experimental results in dilute solutions.…”

“…In aqueous solutions of many salts at least up to an ionic strength ( I m ) of 1 mol·kg –1 , the following extended Hückel equations can be used to predict the mean activity coefficient (γ) of the salt and the osmotic coefficient (ϕ) of water: , − where for the standard Hückel equation the parameter b 2 is set equal to zero. In eqs and , m is the molality, m o is 1 mol·kg –1 , z + and z – are the charge numbers of the cation and anion, respectively, α is the Debye–Hückel parameter, and B , b 1 , and b 2 are electrolyte dependent parameters.…”

“…To tackle this issue, we have previously determined traceable and highly accurate activity and osmotic coefficients for solutions of the common reference electrolytes NaCl and KCl at 298.15 K . These values have been utilized in all our subsequent studies containing isopiestic data − including this one. Due to the abundance of theoretical models, we mainly compare our results against different types of experimental data and reserve alternative activity models for future publications.…”