Thermodynamically Traceable Calorimetric Results for Dilute Aqueous Potassium Chloride Solutions at Temperatures from (273.15 to 373.15) K. Part 1. The Quantities Associated with the Partial Molar Enthalpy

In our previous study (Partanen, J. I.; Partanen, L. J.; Vahteristo, K. P., J. Chem. Eng. Data 2019, 64, 16−33), we presented a fully traceable two-parameter Hückel equation with parameters B and b1 for activity and osmotic coefficients in dilute KCl(aq) in the temperature range of (273.15 to 383.15) K. This equation applies within experimental error to almost all thermodynamic data in the literature at least up to a molality of 0.2 mol·kg−1. In our Hückel model, parameter B is treated as a constant, whereas parameter b1 depends quadratically on the temperature. In the present study, the same model is applied to the molar enthalpies of the components in KCl solutions. No new parameter estimations are necessary for the treatment of these calorimetric data. We also extend now the previous enthalpy results for dilute NaCl solutions (see Partanen, J. I.; Partanen, L. J.; Vahteristo, K. P., J. Chem. Eng. Data 2017, 62, 2717−2632) up to 373 K because in that study the treatment of calorimetric data was limited only up to 353 K. In a future publication (Part 2 of this study), it will be shown that this Hückel model applies additionally well to the heat-capacity literature available for dilute KCl solutions. Here, we also consider a second parametrization of the Hückel equation for KCl solutions obtained in a previous work (Partanen, J. I., J. Chem. Eng. Data 2016, 59, 286−306). This is seen to apply better to enthalpy data in less dilute KCl solutions up to the saturated solutions in the range of (298 to 303) K. However, the alternative parametrization is not fully traceable and not as accurate as our primary one. Following the success of these Hückel models, we supplement the thermodynamic tables for KCl solutions with the relative apparent and partial molar enthalpies of KCl in these solutions from (273.15 to 373.15) K. We also give here the values of these quantities for NaCl in dilute aqueous NaCl solutions at 373.15 K. We have good reason to believe that the new tables contain the most reliable values available for the enthalpy quantities of dilute NaCl and KCl solutions. ■ INTRODUCTION The two-parameter Hückel equation with parameters B and b1 has been previously proven to be useful when the thermodynamic properties of dilute solutions of pure electrolytes are predicted at the normal reference temperature of 298.15 K. In recent studies, it has been additionally observed that it applies within experimental error to the thermodynamic properties of sodium and potassium chloride solutions at least up to a molality of 0.2 mol·kg−1 in the temperature range of (273 to 383) K. In ref 22, the following approach (parametrization PI) was presented for the determination of the temperature dependence of the parameters in the Hückel equations of NaCl and KCl. (1) At 298.15 K, the parameter values from ref 3 were utilized. (2) At 273.15 K, the parameter values from ref 19 were utilized. These values were determined from the existing freezing-point-depression data. (3) The parameter values for NaCl solutions at 348.15 K were determined in ref 20 from the vapor pressure data of Gibbard et al. (4) Because parameter B had the same value for both NaCl and KCl in operations 1, 2, and 3, these values are accepted, and they are used in all temperatures. These values are BNaCl = 1.4 (mol·kg −1)−1/2 and BKCl = 1.3 (mol· kg−1)−1/2. For NaCl at temperatures other than the three that were mentioned, a quadratic equation was Received: January 11, 2019 Accepted: April 9, 2019 Published: April 18, 2019 Article pubs.acs.org/jced Cite This: J. Chem. Eng. Data 2019, 64, 2519−2535 © 2019 American Chemical Society 2519 DOI: 10.1021/acs.jced.9b00031 J. Chem. Eng. Data 2019, 64, 2519−2535 This is an open access article published under a Creative Commons Attribution (CC-BY) License, which permits unrestricted use, distribution and reproduction in any medium, provided the author and source are cited. Dow nloa ded by AA LTO UN IV a t 04 :45: 22:0 65 o n Ju ly 0 1, 2 019 from http s://p ubs .acs .org /doi /10. 102 1/ac s.jc ed.9 b00 031 . determined in ref 20 for the temperature dependence of parameter b1 using the three b1 values. (5) For KCl solutions, the value of parameter b1 at 353.15 K was determined in ref 20 from the isopiestic data ofMoore et al. against NaCl solutions using the quadratic equation for b1,NaCl. (6) In ref 22, a quadratic equation of b1 for KCl solutions was determined using the values of this parameter at 273.15, 298.15, and 353.15 K. The resulting equations from this six-step approach were tested in refs 20, 21, and 22 against all existing thermodynamic data for NaCl solutions and in ref 22 against the thermodynamic data obtained at equilibrium in a constant or in an almost constant temperature for KCl solutions. In these tests, it was observed that this fully traceable approach applies to dilute solutions of both electrolytes at temperatures extending up to 383 K. In the present study, we show that the suggested approach also applies to all enthalpy data measured for dilute KCl solutions up to 373 K. In a forthcoming study, the experimental heat-capacity data for KCl solutions will be investigated in the same way. In the second calculation method considered in ref 19 and identified here and previously as parametrization PII, the BNaCl and BKCl values were identical to those used in PI. In PII, the quadratic temperature dependence of parameter b1 was mainly determined from the amalgam-cell data of Harned and Nims and Harned and Cook for NaCl and KCl solutions, respectively. These electrochemical data cover the temperature range from (273.15 to 313.15) K and extend at each temperature up to a molality of 4.0 mol·kg−1. Because amalgam-electrode data are not as accurate as the data used in the estimations of PI, the resulting models are less reliable than those based on PI. However, it was observed in refs 19 and 20 that PII applies quite well at temperatures up to 353 K also to more concentrated NaCl and KCl solutions. In this article, both PI and PII are thoroughly tested against the heats of dilution and solution available in literature for KCl solutions and also against other literature values of the quantities associated closely with these heats. The calorimetric tests of this study are analogous to those presented in ref 20 for NaCl solutions. Also for NaCl(aq), some previous and new results are considered here to make comparisons and to extend the previous results up to 373 K because in ref 20 the treatment of calorimetric data were limited only up to a temperature 353 K. As in ref 21 for NaCl solutions, the wide amount of the heatcapacity data for KCl solutions will be later considered in a separate study. ■ THEORY In our previous studies, the following Hückel equations i k jjj y { zzz z z I


■ INTRODUCTION
The two-parameter Huckel equation with parameters B and b 1 has been previously proven to be useful when the thermodynamic properties of dilute solutions of pure electrolytes are predicted at the normal reference temperature of 298.15 K. 1−18 In recent studies, 19−22 it has been additionally observed that it applies within experimental error to the thermodynamic properties of sodium and potassium chloride solutions at least up to a molality of 0.2 mol·kg −1 in the temperature range of (273 to 383) K. In ref 22, the following approach (parametrization PI) was presented for the determination of the temperature dependence of the parameters in the Huckel equations of NaCl and KCl.
(1) At 298. 15  In these tests, it was observed that this fully traceable approach applies to dilute solutions of both electrolytes at temperatures extending up to 383 K. In the present study, we show that the suggested approach also applies to all enthalpy data measured for dilute KCl solutions up to 373 K. In a forthcoming study, the experimental heat-capacity data for KCl solutions will be investigated in the same way.
In the second calculation method considered in ref 19 and identified here and previously 20−22 as parametrization PII, the B NaCl and B KCl values were identical to those used in PI. In PII, the quadratic temperature dependence of parameter b 1 was mainly determined from the amalgam-cell data of Harned and Nims 25 and Harned and Cook 26 for NaCl and KCl solutions, respectively. These electrochemical data cover the temperature range from (273.15 to 313.15) K and extend at each temperature up to a molality of 4.0 mol·kg −1 . Because amalgam-electrode data are not as accurate as the data used in the estimations of PI, the resulting models are less reliable than those based on PI. However, it was observed in refs 19 and 20 that PII applies quite well at temperatures up to 353 K also to more concentrated NaCl and KCl solutions.
In this article, both PI and PII are thoroughly tested against the heats of dilution and solution available in literature for KCl solutions and also against other literature values of the quantities associated closely with these heats. The calorimetric tests of this study are analogous to those presented in ref 20 for NaCl solutions. Also for NaCl(aq), some previous and new results are considered here to make comparisons and to extend the previous results up to 373 K because in ref 20 the treatment of calorimetric data were limited only up to a temperature 353 K. As in ref 21 for NaCl solutions, the wide amount of the heatcapacity data for KCl solutions will be later considered in a separate study.

■ THEORY
In our previous studies, 2−22 the following Huckel equations  (2) have been used for the mean activity coefficient (γ) of the electrolyte and for the osmotic coefficient (φ) of water in aqueous solutions of many electrolytes at least up to an ionic strength (I m ) of 1 mol·kg −1 . In eqs 1 and 2, m is the molality, m°i s 1 mol·kg −1 , z + is the charge number of the cation, and z − is that of the anion, and the electrolyte-dependent parameters are B and b 1 . The values of the Debye−Huckel parameter α at 101.325 kPa and at various temperatures are given in Table 1 of ref 20 and  were taken from ref 27. For a 1:1 electrolyte such as KCl, |z + z − | is 1 and I m is the same as molality m. The excess Gibbs energy of the system (G ex ) on the molality scale in salt solutions is related to the activity and osmotic coefficient by equation where T is the temperature in Kelvin. For all further energy quantities, the molality scale is used and the mass of water is considered to be 1 kg. The apparent molar enthalpy of salt (symbol 2) is H app,2 and it is now defined by equation where H is enthalpy of the system, H m,1 * is the molar enthalpy of pure water (symbol 1), H 1 * is enthalpy of the mass of 1 kg water (= w 1 ), M 1 is the molar mass of water (= 0.018015 kg·mol −1 ), and in the last term "kg" is omitted from the unit for simplicity (as now generally) because the molality scale is always used. The relative apparent molar enthalpy (ΔH app ) of salt in these solutions is associated with the excess Gibbs energy by the following thermodynamic identity where H m,2 ∞ is the partial molar enthalpy of the salt at infinite dilution. In this presentation, we simplify and make clearer the previous notations, and quantity H app,2 is now exactly the same as ΔH ex /m in ref 20 where T 0 is 273. 15    were determined at many rounded molalities from (0.001 to 1.0) mol·kg −1 in the following way: First, after Huckel parameter b 1 was obtained from eq 7 or 9 for a certain temperature, the molar excess Gibbs energies (ΔG ex /m) were calculated for these series of different molalities from eqs 1, 2, and 3. These calculations were performed at all temperatures from (273.15 to 353.15) K in intervals of 5 K in the same way as in ref 20 for NaCl. To study ΔG ex at different temperatures at a given molality, next, a quadratic equation of type where T 0 = 273.15 K, was fitted to these results. The resulting values of parameters u, v, and w are given for parametrizations PI and PII at the different molalities in Tables 1 and 2, respectively. For PI, they have been determined using the temperature values from (273.15 to 353.15) K in intervals of 5 K and for PII the same intervals were used but for the range of (273.15 to 313.15) K. To describe the quality of the fit, the standard deviation about regression is included in both tables for each molality. The relative apparent molar enthalpy of the salt can be calculated from the values of parameters u, v, and w given in Tables 1 and 2 using equation Sample enthalpies are presented in Table 3 for 298.15 K. The symbol for the relative apparent molar enthalpy obtained, for example, by parametrization PI is ΔH app,PI throughout this article. Table 3 also shows the absolute apparent molar enthalpies based on the relative values calculated using PI and the value of 17241 J·mol −1 presented by Kilday 28 for the partial molar enthalpy of KCl at infinite dilution. The relationship between the resulting ΔH app values and the molality was then determined by fitting these points with a function of the following type where a 1 , a 2 , and a 3 are the fitting parameters. The theoretical value based on the Debye−Huckel theory was used for the coefficient of the square root term (i.e., for α T ). These α T values were taken from ref 27 and are given in Table 4. For parametrization PI, the parameter values of a 1 , a 2 , and a 3 for eq 12 at all considered temperatures are also collected in this table. For PII, these values are given in Table 5. The standard deviation about regression is provided for each fit in both tables. At 298.15 K, the relative apparent enthalpies calculated by PI and PII and those predicted by eq 12 with the parameter values in Table 4 and in Table 5, respectively, are also displayed as errors in Table 3. The quality parameters in Tables 3, 4, and 5 are all close to each other for PI and PII.
Tests of the New Equations for the Apparent Molar Enthalpy with the Heat-of-Dilution Data. The most extensive measurements for heats of dilution of aqueous KCl have been carried out by Lange and Leighton 29 at 285.65 and 298.15 K. Both of those sets contain more than 20 points in the molality range of (0.00025 to 0.5) mol·kg −1 . The details of these data are given in Table 6 and as can be seen, the data contain several repeat determinations. In these data, the molar heats of dilution (=ΔH m,dil ) are reported for several initial concentrations (denoted here as m initial = m i ) and final concentrations (m final = m f ) of KCl. (To be precise, Lange and Leighton used molarities instead of molalities as the composition variable but the correction between these quantities is not important for the dilute solutions considered in the article.) These data are used here as the corresponding data of Robinson 30 in Table 6 of ref 20 for NaCl solutions and the experimental heats were predicted using parametrizations PI and PII. The molar heat of dilution can be calculated from the apparent molar enthalpies of the final and initial solutions by The apparent enthalpies are obtained using eq 12 with the parameters given either in Table 4 or in  (14) in which the predicted value is generally obtained by PX where PX is PI or PII. According to Table 6 where these errors are presented for PI and PII, the heat-of-dilution data from Lange and Leighton 29 can be predicted quite well using these parametrizations, but the former applies slightly better to these heats. In more concentrated KCl solutions, calorimetric dilution experiments were carried out by Richards and Rowe, 31 Wood et al., 32 Leung and Millero, 33 and Mayrath and Wood. 34 In the first 31 of these studies four points were measured at 293.15 K with m i = 2.2204 mol·kg −1 , and in the second, 32 seven points were measured at 298.15 K. In those, m i was either 1.0 or 3.0 mol·kg −1 . In the third, 33 the initial molality was 1.03081 mol·  The value of 17241 J·mol −1 from Kilday 28 was used in eq 5 for the partial molar enthalpy of KCl at infinite dilution as well as the relative value obtained by parametrization PI. b m°= 1 mol·kg −1 . c The amount of water giving the molality in question. d The difference between the suggested and predicted value.  Table  S1. This table is given in the Supporting Information of the present study, and the acronym used for each data set is explained in footnote a to this table. For the data of Richards and Rowe, 31 Table S1 also includes the NaCl results from these authors, and the symbol of this NaCl set is RiRo20NaCl. Also for the other NaCl sets in this table, the same notation logic is used. For the NaCl sets, the PI and PII parameters presented in ref 20 (taken there from Table 4 or 5) were used when possible.

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The data from the two old data sets of ref 31 in Table S1 can be predicted well only using parametrization PII. As mentioned above and observed in ref 20, PII applies better than PI to less dilute solutions at or close to 298 K as also observed in this case for the sets containing not dilute solutions. The same is also true concerning the PI and PII predictions for the data of set WRB25 in this table. The heat-of-dilution data from Wood et al. 32 at m i = 1.0 mol·kg −1 can be predicted well only using PII and the two points where m i = 3.0 mol·kg −1 are predicted relatively well with this parametrization. In the same way, the high-precision data of set LeMi30 support satisfactorily only PII because this set contains data from less dilute solutions only. The data from set MaWo100 support quite well the PI parameters up to 0.1244 mol·kg −1 but not above 0.25 mol·kg −1 . In Table S1, we included the NaCl results of Mayrath and Wood 35 Table 4 of the present study. At the former temperature, these heats support PI very satisfactorily up to 0.5 mol·kg −1 . At the latter temperature, the agreement for these NaCl solutions is close to that of KCl solutions in this table.   The values of α T are given in Table 4. b Standard deviation about the regression. Tests of the New PI Equations for the Apparent Molar Enthalpy with the Heat-of-Solution Data. The dissolution of crystalline KCl into water has been used for many years as an important reference reaction for endothermic solution calorimetry. In 1980, the National Bureau of Standards published an article 28 in which Kilday recommends that the enthalpy of solution of the reference material of SRM 1655 of crystalline KCl at 298.15 K is (17584 ± 17) J for the solution that contains an amount of 1 mol of KCl and that of 500 mol of water. The dilution ratio is thus 1/500 and the molality of such solution is 0.11102 mol·kg −1 . In the paper of Kilday, extensive studies were performed to obtain the molar enthalpy for this solution and for other corresponding reference values in the temperature range of (296 to 358) K. Many data sets from this research were used here in the testing of parametrization PI. At temperatures close to 298.15 K, Kilday measured 26 points using different experimental methods to treat the crystalline reference material. All of these points were used in the present tests without any correction. It is a general definition in thermodynamics that the molar solution enthalpy is the same as the apparent molar enthalpy for the solute (i.e., H app,2 in eq 4). The test results are shown as an error plot in graph A of Figure 1. In this plot, the error defined by

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is presented as a function of the molality. In the calculation of the relative values required in eq 15, we used the value for the partial molar enthalpy of KCl at infinite dilution (i.e., for H m,2 ∞ ) that gives the best fit in the error plot. This value is 17177 J·mol −1 . The value suggested by Kilday for this quantity is 17241 J·mol −1 . The latter was based on the recommended NBS-solutionenthalpy at m = 0.11102 mol·kg −1 and some additional calorimetric information from more concentrated KCl solutions. While this value is close to ours, we think that ours is superior as it utilizes (in addition to the high precision data measured by Kilday) all thermodynamic data for dilute KCl solutions reported in the literature for this temperature.
The new value determined here is also presented in Table S2 in the same way as all H m,2 ∞ values employed now in the calculations of the heat-of-solution data. This table is given in the Supporting Information of the present study. The error plot for this data set in graph A of Figure 1 is completely random and thus supports parametrization PI excellently. It is interesting to observe that the largest absolute errors in graph A are an order of about 150 J·mol −1 . These errors are clearly larger than the errors obtained using the heat-of-dilution data (for example, see Table  6). Indicating that the heats of dilution can be measured more accurately than the heats of solution.
Sanahuja and Cesari 36 have also reported heats for dissolution of small amounts of solid KCl into water in experiments that lead to dilute aqueous solutions at 298.15 K. In the prediction of these experimental ΔH app values, the value of H m,2 ∞ was taken to be 17206 J·mol −1 following their paper. Our fitted PI value for this quantity agrees closely to this original value. The resulting error plot for this set is shown in graph A of Figure 1. Evidently, the data from this set support PI as well as the data of Kilday in this graph.
At 298.15 K, Zverev and Krestov, 37 Abrosimov and Krestov, 38 Dadgar and Taherian, 39 and Bazlova et al., 40 have additionally reported heats of solution for dilute KCl(aq). These data were predicted here using parametrization PI. The H m,2 ∞ values for these data are given in Table S2, and the resulting error plots are in graphs B and C of   Benjamin 41 were not considered in our previous calorimetric article 20 for NaCl solutions. All calculations for the NaCl solutions were performed using parametrization PI determined in ref 20. In graph B of Figure 1, the dilute-solution data from the group of Krestov 37,38 support parametrization PI very well for KCl solutions as also the results of numerous determinations at m = 0.27755 mol·kg −1 . This molality corresponds to the dilution ratio of 1/200. On the other hand, all four KCl points from Dadgar and Taherian 39 do not agree in graph C with the predictions obtained by using PI. These points are probably not reliable. In contrast, the NaCl data of this group seem to be accurate in graph B and the H m,2 ∞ value estimated from these points (i.e., the value of 3833 J·mol −1 in Table S2) is very close to the value recommended in ref 20 for this quantity (i.e., close to 3824 J·mol −1 in Table 7 of that reference). Bazlova et al. 40 have determined heats of solution in more concentrated NaCl and KCl solutions than those considered above, and the results are shown in graph C for both cases. Their KCl data can be predicted quite satisfactorily using parametrization PI but the H m,2 ∞ value presented for this set in Table S2 (i.e., 17349 J·mol −1 ) is not very close to the value obtained from the more accurate sets. The NaCl data of this group do not agree well with the predictions obtained by PI and are thus probably not reliable. Plot of e H,app (eq 15), the deviation between the suggested relative apparent molar enthalpy for KCl or NaCl solutions and that predicted using parametrization PI or PII of the present study (see text) at 298.15 K as a function of molality m. The suggested values have been calculated from the heats of solution or dilution by Kilday, 28 Sanahuja and Cesari, 36 Zverev and Krestov, 37 Abrosimov and Krestov, 38 Dadgar and Taherian, 39 Lange and Monheim, 43 Bazlova et al., 40 Benjamin, 41 Wust and Lange, 44 and Hubert et al. 42 Also the smoothed values from Parker 45   The 23 experimental points from Benjamin 41 for NaCl solutions belong to a high-precision set up to a molality of 0.72 mol·kg −1 . As mentioned, the less dilute solutions from this set are considered in graph C, and they can be predicted very well using PI. Also the absolute errors for this set in the dilute solutions of graph A are very small. The errors in graph A were used in the determination of the H m,2 ∞ value for  42 have determined heats of solution mainly for less dilute NaCl solutions. (Actually, the measurement temperatures were 297.6, 317.5, and 332.4 K but these data can be predicted using the activity models at these rounded Celsius temperatures of 25, 45, and 60°C because the enthalpy data are not very precise.) The data for less concentrated solutions were predicted using parametrization PI for NaCl solutions, and the parameters for eq 12 are given in Table 4 Table S2. The resulting error plots for 298 K are presented here in graph C of Figure 1. All data at 298 K were predicted using PII with the parameters given in Table 5 of ref 20 and the results are shown in graph D of this figure. The data for the other two temperatures of 318 and 333 K were predicted here using only PI. The results at 318 K from dilute solutions are given in graph A of Figure 2, and all results containing also those from less dilute solutions at this temperature are given in graph B of this figure in addition to the results obtained at 333 K. All the data from this source except the most concentrated points at 333 K in graph B support at least very satisfactorily the PI parameters of NaCl determined in ref 20.
Tests of the New Values for Relative Apparent Molar Enthalpy with Those Presented in the Literature. Lange and Monheim 43 and Wust and Lange 44 have reported apparent molar enthalpies for KCl solutions at 298.15 K on the basis of their heat-of-dilution experiments. We predicted these data using parametrizations PI and PII. The results obtained using PI for the dilute solutions at 298.15 K from the set of Lange and Monheim 43 are given as an error plot in graph A of Figure 1. These results support the parametrization excellently. More concentrated solutions from this set are treated with PI in graph C and all solutions from this set using PII in graph D of this figure. In both of these graphs, the agreement is good throughout. The set of Wust and Lange 44 consists of ΔH app values for more concentrated solutions than those given in ref 43 starting at a molality of 0.28 mol·kg −1 and extending up to 4.7 mol·kg −1 . The PI errors for this set in the five most dilute points are shown in graph C, whereas all PII errors are given in graph D of Figure 1. Graph C shows that PI applies satisfactorily to these data up to 0.6 mol·kg −1 as well as graph D shows that PII applies to the data of all molalities reported in refs 43 and 44. The most likely cause of the quite large systematic error in the plot for the latter data 44 in graph D is the fact that the value of H m,2 ∞ obtained here from ref 43 (see Table S2) was used in the calculations instead of the fitted value. Most of the dilute-solution points from ref 43 were omitted from graph D because of clarity, and the omitted errors are all close to those in graph C for PI.
PI and PII at 298.15 K were also tested against the ΔH app values reported by Parker. 45 The errors of the former parametrization are shown in graphs B and C and those of the  Table 7 for these data. , and some partial molar enthalpies of the salt at infinite dilution are given in Table 7. b The values have been calculated using parametrization PI (see text). c m°= 1 mol·kg −1 . d Unit is J·mol −1 and the value is given at temperature T expressed in parentheses as (T − 273.15)/K. Finally, we compared predictions from PI and PII to the ΔH app data that can be obtained from the Pitzer equations determined by Pabalan and Pitzer 46 for KCl solutions at rounded molalities at 298.15 K. In the determination of these Pitzer equations, thermodynamic data apart from calorimetric data was also employed, as usually for these multiparameter treatments. The multiparameter equations determined by Archer 47 are also available in the literature for KCl solutions, and these equations were considered previously in ref 19. As before, the errors from dilute solutions up to 1.5 mol·kg −1 for ref 46 are presented for PI in graph C and the errors from all data for PII in graph D of Figure 1. Because the Pitzer equation follows exactly the enthalpies of Parker, 45 also these smoothed values agree quite well with the predicted ones in the graphs. All symbols for ref 46 are not discernible from those of ref 45 in these graphs.

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As the data of Herbert et al. 42   , and some partial molar enthalpies of the salt at infinite dilution are given in Table 7. b The values have been calculated using parametrization PI (see text). c m°= 1 mol·kg −1 . d Unit is J·mol −1 and the value is given at temperature T expressed in parentheses as (T − 273.15)/K. , and some partial molar enthalpies of the salt at infinite dilution are given in Table 7. b The values have been calculated using parametrization PI (see text). c m°= 1 mol·kg −1 . d Unit is J·mol −1 and the value is given at temperature T expressed in parentheses as (T − 273.15)/K.   , and some partial molar enthalpies of the salt at infinite dilution are given in Table 7. b The values have been calculated using parametrization PI (see text). c m°= 1 mol·kg −1 . d Unit is J·mol −1 and the value is given at temperature T expressed in parentheses as (T−273.15)/K.

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Article are often expressed as the partial molar enthalpies of the solute. These partial enthalpies can be easily calculated using eq 6 from the polynomials given in eq 12 with the parameter values given in Tables 4 and 5. Both PI and PII were tested here against the relative partial molar enthalpies suggested in the literature. In these tests, the reported ΔH m,2 values are compared to the predicted ones, and the resulting errors are defined by  Table S2 in the Supporting Information) for 285.65 and 298.15 K, respectively. The results of these tests are given as error plots in graph A of Figure 3. According to this graph, both parametrizations apply well to all of these data. At 285.65 K, however, PI seems to apply slightly better.
Harned and Cook 26 thermodynamically determined partial molar enthalpies from their results of the amalgam-cell measurements at temperatures from (273 to 313) K using intervals of 5 K. Up to a molality of 1.0 mol·kg −1 , these data are considered in graphs B and C of Figure 3. Graph B shows the , and some partial molar enthalpies of the salt at infinite dilution are given in Table 7. b The values have been calculated using parametrization PI (see text). c m°= 1 mol·kg −1 . d Unit is J·mol −1 and the value is given at temperature T expressed in parentheses as (T−273.15)/K. results for parametrization PI, and graph C shows those for PII at all investigated temperatures. The errors support at least satisfactorily both of these parametrizations at all temperatures but PI applies in general slightly better to the data. In graph D, the more concentrated solutions of Harned and Cook have been used in the testing of parametrization PII up to 4 mol·kg −1 . Only the results at temperatures 298, 303, 308, and 313 K were included in the graph, because those at the lower temperatures do not show even a satisfactory agreement that can be observed at these four temperatures. Like the two sets of Monheim and Lange, 43 the set of Wust and Lange 44 at 298.15 K similarly consists of both apparent and partial molar enthalpies. This set reports values mainly for the less dilute solutions and the partial enthalpies were used here in the testing of PII at these higher concentrations with a value of H m,2 ∞ = 17216 J·mol −1 (see Table  S2). These results are displayed in graph D of Figure 3, and are seen there to support PII better than the amalgam-cell results.
Determination of the Partial Molar Enthalpy for KCl at Infinite Dilution at Various Temperatures from the Heats of Solution Measured using Dilute KCl Solutions. Vasil'ev and Lobanov 49 have determined many values for the heat of solution for KCl(aq) where the molality of the salt was close to a value of 0.12335 mol·kg −1 at 291. 15, 298.15, 308.15, 313.15, 328.15, 343.15, and 358.15 K. This molality corresponds to the dilution ratio of 1/450. These data were used here with parametrization PI to determine the partial molar enthalpies of KCl at infinite dilution at the seven temperatures. The experimental heats were predicted using PI together with the value of H m,2 ∞ that gives the best fit at each temperature. The errors are shown in Figure 4 as a function of the temperature. The exact molalities used in our calculations are provided by the original paper. 49 They are all, however, very close to 0.12335 mol·kg −1 . The resulting values for H m,2 ∞ are reported in Table 7. The error plot in Figure 4 verifies that the agreement between the measured and predicted heats of solution is very good throughout.
For determination of H m,2 ∞ values at various temperatures, the apparent molar enthalpies given by Kilday 28 can also be used. In addition to wide heat-of-solution data reported in her study at 298.15 K (see Figure 1A), she also determined one ΔH app value  , and some partial molar enthalpies of the salt at infinite dilution are given in Table 7. b The values have been calculated using parametrization PI. c m°= 1 mol·kg −1 . d Unit is J·mol −1 and the value is given at temperature T expressed in parentheses as (T − 273.15)/K.  Table 7.

Journal of Chemical & Engineering Data
The agreement between the H m,2 ∞ values from different sources in Table S2 and Table 7 is quite good at 298.15 K but not at the higher temperatures. The largest discrepancy between the analogous values in Table 7 is observed at 343.15 K where the absolute difference is over 150 J·mol −1 . This implies that only two digits in the limiting value are reliable. According to the present study, for example, the relative enthalpy values are known in dilute solutions to a much higher accuracy. Therefore, it is not reasonable to tabulate absolute enthalpies as recommended values but instead to tabulate those of the relative enthalpies.
The use of parametrization PI enables us to suggest a new calibration method for calorimetric heat measurements at 298.15 K and possibly also at other temperatures. For this purpose, Table 1 shows at 298.15 K the molar solution enthalpies and the amounts of water for the solutions where the dilution ratio is close to the calorimetric calibration value of 1/ 500 suggested by Kilday 28 Tables 6 and 7 in the text  and Table S1 in the Supporting Information), the experimental data available in the literature for dilute KCl solutions from (273 to 333) K can often be predicted within experimental error using the new Huckel equations at least up to a molality of 1 mol·kg −1 . In the upcoming Part 2 of this study, it will be shown that this conclusion applies also to the heat capacities in dilute KCl solutions. Completely traceable thermodynamic quantities can be obtained using parametrization PI at least up to 0.2 mol·kg −1 in the temperature range of (273 to 373) K. Recommended traceable activity coefficients and osmotic coefficients in KCl solutions up to 383 K have already been tabulated in ref 22. To supplement the tables with the calorimetric properties, we present here new values for the relative apparent and partial molar enthalpies (i.e., for ΔH app and ΔH m,2 ) in the dilute KCl solutions at rounded molalities on the basis of the used model. We have collected the values for apparent molar enthalpies (ΔH app ) in Tables 8, 9   We have also examined these enthalpies for more concentrated solutions than those considered in Tables 8−15. Up to 333.15 K and at least up to 1.0 mol·kg −1 , the relative apparent molar enthalpies are reported in Tables 16−18 on the basis of parametrization PI. The reported values for these less dilute solutions are not as accurate as those in Tables 8−11. For concentrated solutions above 1 mol·kg −1 , parametrization PII gives a better agreement than PI in the interpretation of the existing calorimetric data in the temperature range of (298 to 303) K. These ΔH app values based on PII are reported in Table  17 for temperatures 298.15 and 303.15 K up a molality of 5 mol· kg −1 . At these two temperatures and in the molality range of about (0.7 to 1.2) mol·kg −1 , the ΔH app values are close to zero and parametrizations PI and PII suggest slightly different values. At the moment, it is not possible to recommend convincingly either of those, and so the relative values at the rounded molalities have been set in Table 17 simply to be zero.

■ CONCLUSIONS
On the basis of the extensive testing against the existing highquality enthalpy data presented in this communication, against heat-capacity data presented in a future communication (Part 2 of this study), and against the other thermodynamic data presented in our previous studies, 19,20,22 we conclude that the experimental data for dilute KCl solutions can often be predicted within experimental error up to 1.0 mol·kg −1 in the temperature range of (273 to 373) K with a simple reparametrization of the Huckel equation. Completely traceable thermodynamic quantities can be obtained using the new Huckel parametrization at least up to 0.2 mol·kg −1 in all of these temperatures. These main results for KCl solutions are analogous to those obtained in refs 20−22 for NaCl solutions. In the present part (Part 1) of the calorimetric KCl study, new values of the relative apparent and partial molar enthalpies, that is, of ΔH app and ΔH m,2 for which 2 refers to the solute, have been tabulated for dilute solutions on the basis of our simple model. The corresponding values for the activity coefficient of KCl and osmotic coefficient of water in KCl solutions have been tabulated in ref 22. In the second part (Part 2) of this study, we will give in the near future, accordingly, the values for the relative apparent and partial molar heat capacities, that is, for ΔC app and ΔC m,2 , in these solutions. The tabulated values are congruent with all the available high-quality experimental data, and represent the most accurate values determined for this system up to date.
For molalities larger than 1 mol·kg −1 in the temperature range from (298 to 303) K, a previously suggested alternative parametrization yields better agreement with experiments than the parametrization that resulted to completely traceable values of these thermodynamic quantities. Concurrently, this alternative parametrization was employed in the prediction of enthalpy values of KCl solutions at these higher molalities in the tables for 298.15 and 303.15 K. Even though this parametrization lacks traceability and the values it predicts are generally less reliable than the ones recommended for more dilute solutions, they are still useful for applications because the existing experimental data are often well reproduced.
The dissolution of crystalline KCl into water has been used for many years an important reference reaction for endothermic solution calorimetry. In 1980, the NBS published a paper 28 where Kilday recommends that the enthalpy of solution of the reference material of SRM 1655 of crystalline KCl at 298.15 K is (17584 ± 17) J for a solution that contains an amount of 1 mol of KCl and that of 500 mol of water. Table 1 in the present study shows alternative suggestions for dilution ratios of this standard enthalpy at 298.15 K. In this table, we give the molar solution enthalpies and the amounts of water for the solutions where the amount of KCl is 1 mol and the dilution ratio is close to the calorimetric calibration value of 1/500 suggested by Kilday. 28 These enthalpies have been calculated using our traceable parametrization (PI) with the Kilday's value for H m,2 ∞ (=17241 J· mol −1 ). Each of these solution enthalpies is, according to our understanding, as reliable as the value recommended by Kilday for the dilution ratio of 1/500. The values in Table 3 (as well as the corresponding values calculated using PI for other reasonable dilution ratios than those shown in the table) apply probably to the use as the reliable calorimetric standards at 298.15 K.

* S Supporting Information
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.9b00031.
Heat-of-dilution data existing in the literature for KCl solutions at various temperatures and the results obtained with these data using the thermodynamic parametrization considered in the present study; partial molar enthalpies of KCl at infinite dilution determined from the existing heats of solution (PDF)