Jaakko I. Partanen

Re-Evaluation of the Activity Coefficients of Aqueous Hydrochloric Acid Solutions up to a Molality of 2.0 Using Two-Parameter Hückel and Pitzer Equations. Part II. Results from 0 to 95°C

Simple two-parameter Hückel and Pitzer equations were used for the calculation of the activity coefficients of aqueous hydrochloric acid at temperatures 0–60°C up to a molality of 2.0 mol-kg−1. The data obtained by Harned and Ehlers(2,3) on galvanic cells without a liquid junction were used in the parameter estimations of these equations. These data consist of sets of measurements at the temperature intervals of 5°C. It was observed that all estimated parameters follow very simple equations with respect to temperature. They are either constant or depend linearly on the temperature. The values for the activity coefficient parameters calculated by these simple equations are recommended here. The recommended parameter values were tested by predicting the data of Gupta, Hills, and Ives,(5) consisting of cell measurements from 5 to 45°C and molalities up to 1.0 mol-kg−1, and the data of Bates and Bower,(4) which extend to 95°C but measurements were only made on molalities less than about 0.1 mol-kg−1. The activity coefficients obtained by the new equations were also compared to those calculated by the Pitzer equations with the parameter values determined by Saluja, Pitzer, and Phutela(6) from calorimetric data. The agreement observed was excellent up to a molality of 1.5 mol-kg−1 at temperatures from 0 to 60°C.

Equations for calculation of the pH of buffer solutions containing sodium or potassium dihydrogen phosphate, sodium hydrogen phosphate, and sodium chloride at 25°C

Published thermodynamic data measured in aqueous mixtures of sodium or potassium dihydrogen phosphate with hydrogen phosphate and chloride at 25°C were used to test recently developed methods for calculation of the pH of phosphate buffer solutions. Equations for ionic activity coefficients are used in these methods. It is shown that all data used in the tests up to an ionic strength of about 0.5 mol-kg-1 can be accurately predicted by the two methods recommended. In one of these methods, equations of the Hückel type are used for ionic activity coefficients and in the other equations of the Pitzer type. Several sets of phosphate buffer solutions are recommended,e.g., for calibrations of glass electrode cells. In the recommended sets, the pH of the buffer solutions can be calculated either by the Hückel or Pitzer method, and the pH predictions of these methods agree in most cases within 0.005 at least up to ionic strengths of about 0.2 mol-kg-1. The pH values of the two primary pH standards endorsed by IUPAC based on aqueous mixtures of KH2PO4 and Na2HPO4,i.e., pH values of 6.865 and 7.413, can also be accurately predicted by the equations recommended in this study.

Comparison of different methods for calculation of the stoichiometric dissociation constant of acetic acid from results of potentiometric titrations at 298.15 K in aqueous sodium or potassium chloride solutions

Abstract Single-ion activity coefficient equations were determined for the calculation of the molality-scale dissociation constants, Km, for acetic acid in aqueous NaCl or KCl solutions at 298.15 K. The salt alone determines the ionic strength, Im, of the solutions considered in this study. The activity coefficient equations are of the Huckel type, and Km can be calculated by those for a certain ionic strength from the thermodynamic dissociation constant. The data used for the estimation of the parameters for these equations were measured by potentiometric titrations in a glass electrode cell. Three different methods to calculate the experimental Km values from the titration data were considered. The activity parameters for the Huckel equation were determined from the Km values calculated by all of these methods. The parameters obtained by these methods are very consistent with each other and also with the Huckel parameters obtained previously for acetic acid from the literature data measured on Harned cells. The final activity parameters recommended in this study seem to be reliable. Despite the theoretical difficulties associated with the single-ion activity coefficients and the simplicity of the calculation method based on Huckel equations, Km can be obtained by this method almost within experimental error for acetic acid in NaCl and KCl solutions up to Im of about 1 mol kg−1. It was shown in this study, in addition, that the Km values obtained by the Huckel equations agree well also with those calculated by the Pitzer equations.

Activity Coefficients of Potassium Dihydrogen Phosphate in Aqueous Solutions at 25°C and in Aqueous Mixtures of Urea and this Electrolyte in the Temperature Range 20–35°C

Abstract Simple two-parameter Hückel and Pitzer equations were determined for the calculation of the activity and osmotic coefficients of aqueous solutions of potassium dihydrogen phosphate at 25°C up to a molality of the saturated solution (= 1.83 mol kg−1). The isopiestic data measured by Stokes (1945) were used in the parameter estimations. The resulting parameter values were tested with all thermodynamic data found in the literature for this electrolyte at this temperature. In these tests it was observed, that the Hückel equation applies to the data within experimental error up to a molality of 1.0 mol kg−1, and the Pitzer equation applies well to the data in the molality range 1.0–1.83 mol kg−1 but not very well in dilute solutions. Therefore, also a three-parameter Pitzer equation was determined that applies to all data. The activity and osmotic coefficients calculated by these three models were compared to the values suggested by Robinson and Stokes (1959) and to those calculated by the equations of Hamer and Wu (1972) and of Pitzer and Mayorga (1973) for this electrolyte. Solubility measurements of KH2PO4 at 20, 25, 30 and 35°C were made in aqueous urea solutions, and the molality of urea varied in these measurements from 0 to 2.5 mol kg−1. The thermodynamics of these studies were analyzed by using the Pitzer formalism. It was observed that only one interaction parameter between urea molecules and ions (this parameter is linearly dependent on the temperature) was needed to describe almost completely the new solubility data.

Determination of the Glass Electrode Parameters by Means of Potentiometric Titration of Acetic Acid in Aqueous Sodium or Potassium Chloride Solutions at 25°C

Single-ion activity coefficient equations are presented for the calculation of stoichiometric (molality scale) dissociation constants Km for acetic acid in aqueous NaCl or KCl solutions at 25°C. These equations are of the Pitzer or Hückel type and apply to the case where the inert electrolyte alone determines the ionic strength of the acetic acid solution considered. Km for a certain ionic strength can be calculated from the thermodynamic dissociation constant Ka by means of the equations for ionic activity coefficients. The data used in the estimation of the parameters for the activity coefficient equations were taken from the literature. In these data were included results of measurements on galvanic cells without a liquid junction (i.e., on cells of the Harned type). Despite the theoretical difficulties associated with the single-ion activity coefficients, Km can be calculated for acetic acid in NaCl or KCl solutions by the Pitzer or Hückel method (the two methods give practically identical Km values) almost within experimental error at least up to ionic strengths of about 1 mol-kg−1. Potentiometric acetic acid titrations with base solutions (NaOH or KOH) were performed in a glass electrode cell at constant ionic strengths adjusted by NaCl or KCl. These titrations were analyzed by equation E = Eo + k(RT/F) ln[m(H+)], where m(H+) is the molality of protons, and E is the electromotive force measured. m(H+) was calculated for each titration point from the volume of the base solution added by using the stoichiometric dissociation constant Km obtained by the Pitzer or Hückel method. During each base titration at a constant ionic strength, Eo and k in this equation were observed to be constants and were determined by linear regression analysis. The use of this equation in the analysis of potentiometric glass electrode data represents an improvement when compared to the common methods in use for two reasons. No activity coefficients are needed and problems associated with liquid junction potentials have been eliminated.

Calculation of stoichiometric dissociation constants of monoprotic carboxylic acids in dilute aqueous sodium or potassium chloride solutions and p[m(H+)] values for acetate and formate buffers at 25°C

Equations are given for calculation of the stoichiometric (molality scale) dissociation constants, K(m), of weak acids in dilute aqueous electrolyte solutions at 298.15 K from the thermodynamic dissociation constant, K(a), of the acid and the ionic strength, I(m), of the solution. The equations for K(m) were based on the single-ion activity coefficient equations of the Hückel type. The equations were tested with the conductivity data for formic, acetic, propionic, n-butyric, lactic, chloroacetic, alpha-crotonic and cyanoacetic acids, and with data measured by Harned cells for formic, acetic, propionic, n-butyric and glycolic acids. These data were taken from the literature. According to these tests, K(m) can be obtained by the Hückel method within experimental error at least up to I(m) of about 0.1 mol kg(-1). On the basis of the equations for K(m), it is suggested p(m(H)) values {p(m(H))=-lg[m(H(+))/(mol kg(-1))] where m refers to the molality} for buffer solutions containing acetic or formic acid. A new calibration method is suggested for glass electrode cells, and this method is based on the p(m(H)) values instead of pH values (pH=-lg[a(H(+))] where a refers to the activity).

Determination of Stoichiometric Dissociation Constant of Ammonium Ion in Aqueous Potassium Chloride Solutions at 298.15 K

Abstract Equations were developed for the calculation of the stoichiometric (molality scale) dissociation constants, Km, of ammonium ion in aqueous KCl solutions at 298.15 K from the thermodynamic dissociation constant, Ka, of this acid and the ionic strength, Im, of the solutions. Excess KCl was used in the solutions considered so that this salt in practice determined the ionic strength of these solutions. Equations for Km were based on the single-ion activity coefficient equations of the Hückel type. Potentiometric titration data measured with a glass electrode cell were used in the estimation of the parameters for the Hückel equations. By means of the calculation method suggested in this study, Km can be obtained almost within experimental error up to Im of 1.0 mol kg−1 for KCl solutions. The Km values obtained by this method were compared to the literature results obtained from the Harned cell data of Bates and Pinching (1949) and from the concentration cell data of Everett and Wynne-Jones (1938) measured with hydrogen electrodes on cells containing two liquid junctions.

Determination of Stoichiometric Dissociation Constants of Glycolic Acid in Dilute Aqueous Sodium or Potassium Chloride Solutions at 298.15 K

Equations were determined for the calculation of the stoichiometric (molality scale) dissociation constant, Km, of glycolic acid in dilute aqueous NaCl and KCl solutions at 298.15 K from the thermodynamic dissociation constant, Ka, of this acid and from the ionic strength, Im, of the solution. The salt alone determines mostly the ionic strength of the solutions considered in this study, and the equations for Km were based on the single-ion activity coefficient equations of the Hückel type. The data measured by potentiometric titrations in a glass electrode cell and the literature data obtained by Harned cells were used in the estimation of the parameters for the Hückel equations of glycolate ions. By means of the calculation method based on the Hückel equations, Km can be obtained almost within experimental error at least up to Im of about 0.5 mol kg-1 for glycolic acid in NaCl and KCl solutions.

Modelling of crystal growth in multicomponent solutions

Abstract The crystal growth model was derived from Maxwell-Stefan equations for the diffusioncontrolled growth regime. As a model system, the ternary potassium dihydrogen phosphate (crystallizing substance)-water (solvent)-urea (foreign substance) system was employed. The thermodynamic model for the present system was successfully derived by the Pitzer method and allowed calculating activity coefficients of each component. The resulting activity-based driving force on each component and other solution properties; mass transfer coefficient, concentration of each component and solution density, were introduced to the Maxwell-Stefan equations. The crystal growth rates were successively determined by solving the Maxwell-Stefan equations. The model was evaluated from single crystal growth measurements. The urea concentrations, supersaturation level and solution velocity were varied. The results showed that experimental and predicted growth rates are in acceptable agreements.