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.
In this article we show how to calculate free energies for atmospherically relevant complexes when multiple conformers and/or isomers are present. We explain why the thermal averaging methods used in several published works are incorrect. On the basis of our two sample cases, the sulfuric acid-pinic acid complex and the (HSO)(NH)(HO) cluster, we provide numerical evidence that the use of these incorrect formulas can result in errors larger than 1 kcal/mol. We recommend that if vibrational frequencies and thus Gibbs free energies of the individual conformers are unavailable, one should not attempt to correct for the presence of multiple conformers and instead use only the global minimum conformers for both reactants and products. On the contrary, if the free energies for the conformers are calculated for both reactants and products, their effect can be accounted for by the statistical mechanical methods presented in this article.
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.
We investigate kinetic barriers for the oxygen evolution reaction (OER) on singly and doubly nitrogen-doped single-walled carbon nanotubes (NCNTs) using the climbing image nudged elastic band method with solvent effects represented by a 45-water-molecule droplet. The studied sites were chosen based on a previous study of the same systems utilizing a thermodynamic model which ignored both solvent effects and kinetic barriers. According to that model, the two studied sites, one on a singly nitrogen-doped CNT and the other on a doubly doped CNT, were approximately equally suitable for OER. For the four-step OER process, however, our reaction barrier calculations showed a clear difference in the rate-determining *OOH formation step between the two systems, with barrier heights differing by more than 0.4 eV. Thus, the simple thermodynamic model may alone be insufficient for identifying optimal OER sites. Of the remaining three reaction steps, the two H2O forming ones were found to be barrierless in all cases. We also performed solvent-free barrier calculations on NCNTs and undoped CNTs. Substantial differences were observed in the energies of the intermediates when the solvent was present. In general, the observed low activation energy barriers for these reactions corroborate both experimental and theoretical findings of the utility of NCNTs for OER catalysis.
We present fully traceable two-parameter Huckel 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 (353.15 to 383.15) K. In our most successful parametrization of these equations, parameter B is treated as a constant whereas b 1 is a quadratic function of the temperature. The new calculations extend the tables presented up to 353.15 K in our previous study (
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