The Hu ¨ckel equation is used to correlate the experimental activities of dilute NaCl and KCl solutions up to a molality of about 1.0 mol • kg -1 . The two parameters of this equation are dependent on the electrolyte and are B [which is simply related to the ion-size parameter (a*) in the Debye-Hu ¨ckel equation] and b 1 (which is the coefficient of the linear term in molality and related to hydration numbers of the ions of the electrolyte). In more concentrated solutions up the saturation for both electrolytes, an extended Hu ¨ckel equation was used, and it contains, additionally, a quadratic term with respect to the molality with parameter b 2 . The values of parameters B and b 1 for dilute KCl solutions were determined from the cell potential differences measured by Hornibrook et al. on concentration cells with transference (J. Am. Chem. Soc. 1942, 64, 513-516). With these values of KCl, the corresponding parameter values for NaCl solutions were determined from the isopiestic data of Robinson for NaCl and KCl solutions (Trans. R. Soc., N. Z., 1945, 75, 203-217). Only the data points for NaCl molalities less than 1.4 mol • kg -1 were included in this determination. The resulting parameter values were successfully tested with all reliable cell potential and isopiestic data in the literature for dilute NaCl and KCl solutions. For more concentrated solutions, new values of parameters b 1 and b 2 were determined for the extended Hu ¨ckel equations of NaCl and KCl, but the same values of parameter B were used as for dilute solutions. For these more concentrated NaCl solutions, the values of parameters b 1 and b 2 were determined from the vapor pressure data of Olynyk and Gordon (J. Am. Chem. Soc. 1943, 65, 224-226), which cover the molality range (2.3 to 6.1) mol • kg -1 . With these values for NaCl, the corresponding parameter values for more concentrated KCl solutions were determined from the isopiestic data of Robinson for this pair of electrolytes (see the citation above), where all experimental points were included in the determination. The resulting extended Hu ¨ckel equations were thoroughly tested with all reliable experimental data presented in the literature on the basis of electrochemical, isopiestic, and direct vapor pressure measurements. Most of these data can be reproduced within experimental error by means of the extended Hu ¨ckel equations up to the saturated solutions. Reliable activity and osmotic coefficients of NaCl and KCl can, therefore, be calculated by using the Hu ¨ckel and extended Hu ¨ckel equations determined in this study. The values obtained by these equations are probably the most accurate values available, and they have been tabulated at rounded molalities. The activity and osmotic coefficients obtained from the new equations were compared with the values suggested by Robinson (see citation above), with those calculated by using the Pitzer equations of Pitzer and Mayorga (J.

We present fully traceable two-parameter Hückel equations (with parameters B and b 1) for the activity coefficient of sodium chloride and for the osmotic coefficient of water in aqueous NaCl solutions at temperatures from (0 to 80) °C. These equations apply within experimental error to all thermodynamic data available for these solutions at least up a molality of 0.2 mol·kg–1. In our previous study (J. Chem. Eng. Data 2016, 61, 286–306), these equations were successfully tested against the literature results of electrochemical, isopiestic, and cryoscopic measurements usually in the temperature range from (0 to 25) °C. There, a constant value was employed for B, whereas a linear model with respect to the temperature was utilized for b 1. The linear model was determined from the values of b 1 at 0 °C and at 25 °C obtained from freezing-point depression data and from isopiestic and cell-potential difference data, respectively. In the present study, these two b 1 values are utilized alongside the constant value of parameter B but a new quadratic model is presented for the temperature dependence of b 1. The third data point required for this model is obtained from the direct vapor pressure measurements of Gibbard et al. (J. Chem. Eng. Data 1974, 19, 281–288) at 75 °C. The results obtained with this quadratic equation for b 1 agree well with the test results of the linear model in the previous paper (see the citation above) up to 25 °C. The most important new test results above that temperature are reported here. Our quadratic model has additionally been tested with all the high-precision calorimetric data available in the literature for NaCl solutions. In this first part (Part 1) of the study, the test results from the thermodynamic quantities associated with partial molar enthalpy are reported. In the forthcoming second part (Part 2) of the study, the results of the quantities associated with the heat capacity of NaCl solutions will be considered. In the tests of these two parts, all calculations dealing with calorimetric data are performed in a new way. Both the calorimetric data and the vapor pressure data (from both direct and isopiestic measurements) can be predicted using the new Hückel equations within experimental error in dilute NaCl solutions from (0 to 80) °C. For comparison, also other Hückel models are considered and at best these apply up to the molality of the saturated NaCl solution at various temperatures. Following the success of the new models, new values for the activity coefficients, osmotic coefficients, relative apparent molar enthalpies, and relative partial molar enthalpies for NaCl solutions at rounded molalities are reported at the end of this Article. We have good reasons to believe that the new values contain the most reliable ones available for the given thermodynamic quantities.

The Hückel equation used in this study to correlate the experimental activities of dilute LiCl solutions up to a molality of about 1.0 mol·kg−1 contains two parameters being dependent on the electrolyte: B [that is related closely to the ion-size parameter (a*) in the Debye−Hückel equation] and b 1 (this parameter is the coefficient of the linear term with respect to the molality, and this coefficient is related to hydration numbers of the ions of the electrolyte). In more concentrated solutions up to a molality of 6.0 mol·kg−1, an extended Hückel equation was used. It contains additionally a quadratic term with respect to the molality, and the coefficient of this term is the parameter b 2. The values of parameters B and b 1 for dilute LiCl solutions were determined from the isopiestic data measured by Robinson and Sinclair for KCl and LiCl solutions (J. Am. Chem. Soc. 1934, 56, 1830−1835) by using the Hückel parameters determined recently by Partanen and Covington for dilute KCl solutions (J. Chem. Eng. Data 2009, 54, published ASAP July 24, 2008). The resulting parameter values were tested with the sparse cell potential and isopiestic data existing in the literature for dilute LiCl solutions. In more concentrated solutions, new values of parameters b 1 and b 2 were determined for the extended Hückel equation of LiCl but the same value of parameter B was used as for dilute solutions. The values of b 1 and b 2 for LiCl were determined from the isopiestic data measured by Robinson for NaCl and LiCl solutions (Trans. Faraday Soc. 1945, 41, 756−758) by using the extended Hückel equation determined recently by us for concentrated NaCl solutions (see the citation above). The resulting extended Hückel equation was tested with all reliable experimental data presented in the literature on the basis of electrochemical, isopiestic, and direct vapor pressure measurements. Most of these data can be reproduced within experimental error by means of the extended Hückel equation up to a molality of 6.0 mol·kg−1. Reliable activity and osmotic coefficients for LiCl solutions can, therefore, be calculated by using the new Hückel equations, and they have been tabulated here at rounded molalities. The activity quantities obtained from these equations were compared to the values suggested by Robinson and Stokes (Trans. Faraday Soc. 1949, 45, 612−624), to those calculated by using the Pitzer equations of Pitzer and Mayorga (J. Phys. Chem. 1973, 77, 2300−2308), of Kim and Frederick (J. Chem. Eng. Data 1988, 33, 177−184), and of Marshall et al. (J. Chem. Eng. Data 1995, 40, 1041−1052), and to those calculated by using the extended Hückel equation of Hamer and Wu (J. Phys. Chem. Ref. Data 1972, 1, 1047−1099).

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The Hückel equation used in this study to correlate the experimental activities of dilute RbCl and CsCl solutions up to a molality of about 3.5 mol·kg−1 contains two parameters being dependent on the electrolyte: B [that is related closely to the ion-size parameter (a*) in the Debye−Hückel equation] and b 1 (this parameter is the coefficient of the linear term with respect to the molality, and this coefficient is related to hydration numbers of the ions of the electrolyte). In more concentrated solutions up to the saturated molality of RbCl (= 7.78 mol·kg−1) and up to a molality of about 8 mol·kg−1 for CsCl, an extended Hückel equation was used. It contains additionally a quadratic term with respect to the molality, and the coefficient of this term is parameter b 2. All parameter values for the Hückel equations of RbCl were determined from the isopiestic data measured by Rard for NaCl and RbCl solutions (J. Chem. Eng. Data 1984, 29, 443−450) and all parameters for CsCl from the isopiestic data measured by Rard and Miller for NaCl and CsCl solutions (J. Chem. Eng. Data 1982, 27, 169−173). In these estimations, the Hückel parameters determined recently for NaCl solutions (J. Chem. Eng. Data 2009, 54, 208−219) were used. The resulting parameter values were tested with the cell potential, vapor pressure, and isopiestic data existing in the literature for RbCl and CsCl solutions. Most of these data can be reproduced within experimental error by means of the extended Hückel equation up to a molality of about 8.0 mol·kg−1. Reliable activity and osmotic coefficients for RbCl and CsCl solutions can, therefore, be calculated by using the new Hückel equations, and they have been tabulated here at rounded molalities. The activity and osmotic coefficients obtained from these equations were compared to the values suggested by Rard (RbCl, see citation above), Rard and Miller (CsCl, see citation above), and Robinson and Stokes (Electrolyte Solutions, 2nd ed.; Butterworths Scientific Publications: London, 1959). These values were also compared to those calculated by using the Pitzer equations with the parameters of Pitzer and Mayorga (J. Phys. Chem. 1973, 77, 2300−2308) and Pitzer (Activity Coefficients in Electrolyte Solutions, 2nd ed.; CRC Press: Boca Raton, 2000; pp 100−101) and to those calculated by using the extended Hückel equation of Hamer and Wu (J. Phys. Chem. Ref. Data 1972, 1, 1047−1099).

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 (

The Hückel equation used in this study to correlate the experimental activities of dilute alkali metal bromide solutions up to a molality of about 1.5 mol·kg−1 contains two parameters that are dependent on the electrolyte: B [that is related closely to the ion-size parameter (a*) in the Debye−Hückel equation] and b 1 (this parameter is the coefficient of the linear term with respect to the molality, and this coefficient is related to hydration numbers of the ions of the electrolyte). In more concentrated solutions up to a molality of about 5 mol·kg−1, an extended Hückel equation was used, and it contains additionally a quadratic term with respect to the molality, and the coefficient of this term is parameter b 2. All parameter values for the Hückel equations of LiBr, KBr, RbBr, and CsBr were determined from the isopiestic data measured by Robinson for solutions of these salts against KCl solutions (J. Am. Chem Soc. 1935, 57, 1161−1165), and all parameters for NaBr were determined from the isopiestic data measured by Robinson for KCl and NaBr solutions (Trans. Faraday Soc. 1939, 35, 1217−1220). In these estimations, the Hückel parameters determined recently for KCl solutions (J. Chem. Eng. Data 2009, 54, 208−219) were used. The resulting parameter values were tested with the cell potential, vapor pressure, and isopiestic data existing in the literature for alkali metal bromide solutions. Most of these data can be reproduced within experimental error by means of the extended Hückel equations up to a molality of about 5.0 mol·kg−1. Reliable activity and osmotic coefficients for alkali metal bromide solutions can, therefore, be calculated by using the new Hückel equations, and they have been tabulated here at rounded molalities. The activity and osmotic coefficients obtained from these equations were compared to the values suggested by Robinson and Stokes (Electrolyte Solutions, 2nd ed.; Butterworths Scientific Publications: London, 1959), to those calculated by using the Pitzer equations with the parameter values of Pitzer and Mayorga (J. Phys. Chem. 1973, 77, 2300−2308), and to those calculated by using the extended Hückel equations of Hamer and Wu (J. Phys. Chem. Ref. Data 1972, 1, 1047−1099).

Parameter-free activity coefficient equations were tested in addition to those containing one, two, three or four electrolyte-dependent parameters with the experimental activity coefficients obtained from the literature data for aqueous solutions of the following electrolytes at 298.15 K: KCl, NaCl, RbCl, KBr, RbBr, CsBr, KI, RbI, KNO 3 , and KH 2 PO 4 . The experimental activity coefficients of each electrolyte considered can be reproduced within the uncertainty of the measurements up to the molality of the saturated solution by using a three-parameter equation of the extended Hückel type. The best Hückel equations are given for all electrolytes in question. The results from the present studies reveal that the parameterfree equations can be reliably used in thermodynamic studies only for very dilute electrolyte solutions. On the other hand, in most cases, a good agreement with the experimental data is obtained with the one-parameter equations of Bromley [14] and Kusik and Meissner [13], with the two-parameter equation of Bretti et al. [15], and with the three-or four-parameter equation of Hamer and Wu [19] in addition to the three-parameter Pitzer equation [23], with almost all parameter values suggested in the literature. In several cases, these equations seem to apply to much higher molalities than those used in the parameter estimations. Therefore, the best of these equations may have important applications in calculations associated with the dissolution and crystallization processes of these salts.