Experimental Osmotic Coefficients Research Articles

Isopiestic Studies of H3PO4(aq) at Elevated Temperatures

Isopiestic molalities of aqueous solutions of phosphoric acid have been measured at 383.15 to 523.15 K. NaCl(aq) served as the isopiestic standard for the calculation of osmotic coefficients. The ion-interaction model gave an excellent fit to the experimental osmotic coefficients by treating H3PO4(aq) as a 1–1 weak electrolyte. Activity coefficients, both real and stoichiometric, were also obtained from the analysis of the isopiestic results. As expected, the ionization of H3PO4(aq) decreased with increasing temperature. However, at higher molalities, the ionization increased with increasing molality (reionization).

Osmotic coefficient data for NaOH–NaCl–NaAl(OH) 4–H 2O system measured by an isopiestic method and modeled using Pitzer's model at 298.15 K

Osmotic coefficient data were obtained for the aqueous solutions of NaOH–NaCl–NaAl(OH) 4. The solutions were prepared by dissolving AlCl 3·6H 2O in aqueous NaOH solutions. The osmotic coefficients of the solutions were measured by an isopiestic method at 25°C. The osmotic coefficient data were used to evaluate the unknown binary and mixing parameters of Pitzer's model for the aqueous NaOH–NaCl–NaAl(OH) 4–H 2O system. The binary Pitzer's parameters, β (0), β (1), and C φ , for NaAl(OH) 4 were found to be −0.0083, 0.0710, and 0.00184 respectively. These binary parameters were obtained from the data on the ternary system. This was necessary since it was not possible to prepare a single (NaAl(OH) 4) solution. The mixing parameters, Θ OH −Al(OH) − 4 , Θ Cl −Al(OH) − 4 , Ψ Na +OH −Al(OH) − 4 , and Ψ Na +Cl −Al(OH) − 4 were found to be −0.2255, −0.2430, −0.0388, and 0.2377 respectively. The experimental osmotic coefficient data were correlated well with Pitzer's model using the parameters obtained.

Activity coefficients of Al(ClO4)3 in aqueous solutions: a reexamination

A reexamination of the published activity coefficients of Al(ClO4)3 in aqueous solutions (E. Kalman, G. Horn, K. Schwabe, Z. Phys. Chem. (Leipzig), 244 (1970) 106) is given. A procedure for the estimation of activity coefficients of electrolytes is proposed. The method combines experimental osmotic coefficients and a theory based on the primitive model. This strategy provides suitable results, especially for asymmetrical electrolytes.

Osmotic coefficient data for Na 2SiO 3 and Na 2SiO 3–NaOH by an isopiestic method and modeling using Pitzer's model

Osmotic coefficient and water activity data for Na 2SiO 3 and mixed Na 2SiO 3–NaOH aqueous solutions were obtained at 25°C by employing the isopiestic method. The binary Pitzer's parameters, β (0), β (1), and C φ , for Na 2SiO 3 and the mixing parameters, θ OH −SiO 2− 3 and Ψ Na +OH −SiO 2− 3 were estimated using the osmotic coefficient data. The experimental osmotic coefficient data were correlated well with Pitzer's model. Mean activity coefficients of Na 2SiO 3 and NaOH for the solutions were predicted by Pitzer's model with the parameters obtained. Finally, the presence of metasilicic species, when sodium metasilicate (Na 2SiO 3·9H 2O) is dissolved in aqueous alkaline solution, was established by titration with hydrochloric acid.

An isopiestic study of aqueous solutions of the alkali metal bromides at elevated temperatures

Isopiestic molalities of aqueous solutions of the alkali metal bromides have been measured atT=383.15 K toT=498.15 K. Aqueous NaCl served as the isopiestic standard for the calculation of osmotic coefficients. The ion-interaction model gave an excellent fit to the experimental osmotic coefficients and provided parameters for the calculation of activity coefficients. Osmotic and activity coefficients both decrease with increasing temperature in this temperature range. A simple model is presented from which activity and osmotic coefficients (atpsat) can be calculated as a function of molality forT=273.15 K toT=523.15 K. Comparison of the stoichiometric activity coefficients with those of the corresponding alkali metal chlorides reveals quite complicated relative behavior.

Isopiestic molalities for aqueous solutions of the alkali metal hydroxides at elevated temperatures

Isopiestic molalities of aqueous solutions of the alkali metal hydroxides have been measured atT=(383.25, 413.12, and 443.09) K. The isopiestic standard for calculation of osmotic coefficients was NaCl(aq). The ion-interaction model gave an excellent fit with the experimental osmotic coefficients and provided parameters for the calculation of activity coefficients. Osmotic and activity coefficients both decrease with increasing temperature in this temperature range. As atT=298.15 K, the order of the results is the reverse of that for the alkali metal chlorides. The model of Simonsonet al. (J. Chem. Thermodynamics1989, 21, 561–584) is an excellent predictor of the experimental results for NaOH(aq). A simple model is presented from which activity and osmotic coefficients (atpsat) can be calculated as a function of molality forT=273.15 K toT=523.15 K.

Isopiestic determination of the osmotic and activity coefficients of Cu(NO3)2(aq) at the temperature 298.15 K

The four previous isopiestic investigations of Cu(NO3)2(aq) at the temperature 298.15 K exhibit a remarkable lack of agreement. Consequently, isopiestic vapor-pressure measurements were performed for Cu(NO3)2(aq) solutions atT=298.15 K both at the Texas Christian University and the Lawrence Livermore National Laboratory. These measurements extend from molalitym=(0.0638 to 6.9235) mol·kg−1. Under the conditions typically used for isopiestic experiments, it is found that solutions of Cu(NO3)2(aq) at higher molalities lose HNO3into the vapor phase, resulting in a gradual increase in the extent of hydrolysis of their solutions as the samples are re-equilibrated. This produces a progressive downward drift in the apparent osmotic coefficients. Consequently, most previous higher-molality isopiestic results for this system are believed to be unreliable. Experiments were performed to quantify and to minimize the effect of this hydrolysis on the resulting osmotic coefficients. These experiments indicate that the error in the osmotic coefficient from this HNO3loss is insignificant at lower molalities of Cu(NO3)2(aq); atm=4 mol·kg−1it is ≤0.2 per cent, but abovem≈5 mol·kg−1it can become quite significant. Recommended values of the osmotic coefficients, water activities, and mean activity coefficients of Cu(NO3)2(aq) are presented up tom=3.00 mol·kg−1, the maximum molality where we consider them to be completely accurate, and, with slightly lower accuracy, up tom=6.9235 mol·kg−1. Pitzer's equation was found to represent reliably the experimental osmotic coefficients provided the third virial coefficient was ionic-strength dependent.

Osmotic Coefficient of Methanol + LiCl, + LiBr, and + LiCH3COO at 25 °C

The osmotic coefficients of methanol + LiCl, + LiBr, and + LiCH3COO were determined by the isopiestic method at 25 °C. NaI in methanol solutions up to 4.33 mol·kg -1 were used as the isopiestic reference with osmotic coefficients calculated from vapor pressure data reported by Barthel and Tomasula. Experimental osmotic coefficient data are reliably represented by the Pitzer model with and without the β(2) term. The parameters for these equations, along with the corresponding standard deviations, are presented for these systems. The set of Pitzer parameters b = 3.2, α1 = 2.0 may be used. Including the β(2) term with α2 = 1.4 improves the fit for all of the investigated solutes, so that the standard deviations reduce from 0.015 to 0.006 for LiCl, from 0.009 to 0.005 for LiBr, and from 0.005 to 0.004 for LiCH3COO in methanol solutions at 25 °C.

Thermodynamic Properties of Aqueous Sodium Sulfate Solutions at 40°C

We report osmotic and activity coefficients of aqueous sodium sulfate solutions. The osmotic coefficients were determined at 40°C by the isopiestic method. Sodium chloride served as the isopiestic standard. The molality ranges covered in this study correspond to about 0.2–3.0. The activity coefficients were calculated from the parameters obtained by fitting the Hamer–Wu and Pitzer equations to the experimental osmotic coefficients.

Measurements of Solubilities of Two Amino Acids in Water and Prediction by the UNIFAC Model

The solubility of an amino acid in an aqueous solution containing another amino acid was measured at 298 K. The measured amino acid pairs were dl-alanine/dl-serine and dl-alanine/dl-valine. The invariant eutectic compositions of these pairs of amino acids were also determined. In addition, a prediction model of solubility for such a system was developed on the basis of solid−liquid equilibria. To represent more accurately the activity coefficient of amino acids and homopeptides by Larsen's UNIFAC model, new assignments of UNIFAC groups were proposed and their interaction parameters were determined from experimental osmotic coefficient data. Finally, the prediction of solubilities of mixed solid amino acids was made and the results were compared with experimental data.

Least-Squares Analysis of Osmotic Coefficient Data at 25 .degree.C According to Pitzer's Equation. 1. 1:1 Electrolytes

Pitzer ion-interaction parameters for 93 1:1 electrolytes have been calculated by least-squares analysis of published experimental osmotic coefficient data at 25 °C. The quality of the resulting fit of these data, expressed as the sum of squared residuals, the standard errors in the least-squares estimates, and the variation of the residuals with electrolyte concentration, is shown to be consistently superior to that obtained with the use of parameters taken from previous publications. The discrepancies between the present estimates of the Pitzer parameters and the published values are mainly concentrated in β (1) . The relative standard error in this parameter depends strongly on the maximum molality represented in the data and is typically at least 1 order of magnitude greater than the relative standard errors in the other parameters. This observation is interpreted by examining the contours of the sum of squared residuals in parameter space. Trends in the quality of fit for different classes of electrolytes are also described.

Salting out of aqueous proteins: Phase equilibria and intermolecular potentials

AbstractSalting‐out phase equilibria are reported for lysozyme and α‐chymotrypsin from concentrated ammonium‐sulfate solutions. Supernatant and dense‐phase protein concentrations and the resulting protein partition coefficients are given as a function of solution pH and ionic strength. Phase equilibria with a trivalent salt (sodium citrate) confirm that ionic strength, rather than salt concentration, is the appropriate variable describing phase equilibria. The salting‐out behavior of a mixture of an aqueous lysozyme and α‐chymotrypsin is independent of the presence of the other protein.Parameters for a molecular‐thermodynamic description of salting‐out behavior are obtained from low‐angle laser‐light scattering (LALLS). Osmotic second virial coefficients from LALLS are reported over a range of pH for dilute chymotrypsin concentrations in aqueous electrolyte solutions at 0.01 and 1.0 M ionic strengths. Effective Hamaker constants, regressed from experimental osmotic second virial coefficients, are determined for models of the protein – protein potential of mean force. In addition to excluded volume, dispersion, and shielded charge – charge potentials, the description of protein ‐ protein interactions includes attractive charge – dipole and dipole – dipole potentials as well as an osmotic‐attraction potential that becomes important at high salt concentrations. Protein dipole – dipole potentials are required to account for the observed pH dependence of osmotic second virial coefficients, especially at low ionic strength.

Modification of the Pitzer equations for application to electrolyte + polar non-electrolyte mixtures

The fitting of experimental osmotic and activity coefficient values to Pitzer equations requires the use of a large number of adjustable parameters when polar neutral species are present in the system. This is because the Pitzer equations consider the λ ion—neutral and λ neutral—neutral as constant interaction parameters for the fitting. The modification of the original Pitzer equations, by considering the dependence of these binary interaction parameters concerning the polar neutral components, on both the ionic strength and the neutral species concentration in the system, leads to a considerable improvement in these fittings. To test the applicability of these modified Pitzer equations, they were used to fit several series of data from the literature, related to pure aqueous solutions of different amino acids, or urea, as well as aqueous mixtures of an electrolyte plus an amino acid, or urea.

Isopiestic measurements at high temperatures: I. Aqueous solutions of LiCl, CsCl, and CaCl2 at 155�C

Isopiestic measurements have been made for LiCl (aq) and CsCl (aq) at a temperature of 155°C. Equilibrium molalities ranged up to 21 mol-kg−1. MgCl2(aq) was chosen as the reference electrolyte. The apparatus used for the isopiestic experiments is an enhanced version of that developed by Grjotheim and co-workers. To test its precision osmotic coefficients of CaCl2 (aq) have also been determined and compared with previously reported vapor pressure measurements at high concentrations. The results show a very good coincidence. The data can be described by the ion interaction model of Pitzer. The resulting set of parameters allows a fit of the experimental osmotic coefficients with a standard error of 0.0078 and 0.0114 for LiCl(aq) and CsCl (aq), respectively. The osmotic coefficients of LiCl are consistent with data at lower molalities, but there are discrepancies for the CsCl solutions.

Representation of excess properties of electrolyte solutions using a new equation of state

AbstractA new equation of state for electrolyte solutions has been developed from an expression of the Helmholtz free energy containing a nonelectrolyte part and a part relative to ions. The nonelectrolyte part is taken from the equations of state (EOS) of Schwartzentruber et al. (1989). The ionic part is composed of an MSA long‐range term to account for electrostatic interactions and a short‐range interaction term specific to ions. Using correlations between parameters and experimental ionic diameters, the model reduce to a one‐parameter model. It has been applied to numerous strong electrolyte systems and extended to ternary systems to test its predictability without mixing parameters for ions. Its results compare well to the results reported for other one‐parameter models (electrolyte EOS). Furthermore, it was found that the cation‐anion interaction parameter could also be correlated to experimental ionic diameters. Then, the osmotic coefficients of 28 alkaline and alkaline‐earth halide systems may be represented with a root mean square relative deviation of 2.9% using only six correlation parameters. This result has been extended to other systems, with the conclusion that the model with all parameters correlated may also be applied to systems other than halide solutions. The resulting model is predictive. The quality of the prediction was tested by determining osmotic coefficients relative to six systems without any parameter adjustment. The deviations of the predicted values range from 2.0 to 5.4%. The quality of the representation of mixed salts systems without mixing parameters was evaluated using experimental osmotic coefficients of 30 ternary systems.

Isopiestic determination of the osmotic and activity coefficients of {(1 − y)H 2SO 4 + yNa 2SO 4}(aq) at 298.15 K I. Results for y = 0.5 (NaHSO 4) and y = 0.55595, 0.70189, and 0.84920

Isopiestic vapor-pressure measurements were made for {(1 − y)H 2SO 4 + yNa 2SO 4}(aq) with y = 0.5 (NaHSO 4) from 0.23 mol · kg −1 and with y = 0.55595, 0.70189, and 0.84920 from 0.16 mol · kg −1 up to the crystallization limits of the mixtures (4.6057 to 10.681 mol · kg −1) at 298.15 K. Experimental water activities are much higher than predicted by Zdanovskii's empirical rule; this difference is consistent with extensive HSO 4 −(aq) formation. If osmotic coefficients are calculated by using the stoichiometric molalities of Na 2SO 4 and H 2SO 4 and assuming that they behave as 1–2 electrolytes, then osmotic coefficients for the mixtures fall considerably below values predicted from the Scatchard neutral-electrolyte binary-solution mixing approximation. In fact, for ionic-strength fractions of Na 2SO 4 greater than 0.7, the experimental osmotic coefficients fall below those of both limiting binary solutions over most of the molality range. However, if these values are recalculated by treating NaHSO 4 as a 1-1 electrolyte that does not dissociate with changes in molality, then deviations of experimental results from the Scatchard neutral-electrolyte binary-mixing approximation are much smaller and usually negative for osmotic coefficients. The limited number of previous isopiestic values for {(1 − y)H 2SO 4 + yNa 2SO 4} are critically compared with our new experimental results.

Potentials of average force for an interaction site model of aqueous alcohols: a molecular model for the hydrophobic bond

An interaction site model with simple square-well potentials of average force is shown, to accurately fit experimental second osmotic virial coefficients for a number of aqueous alcohol systems. The model takes into account the nonspherical structure of the alcohol molecules, includes all important orientational effects, and considers all interactions of the sites

Isopiestic studies of aqueous solutions at elevated temperatures VI. LiCl and CsCl

Isopiestic measurements have been made for LiCl(aq) and CsCl(aq) over the temperature range 382.96 to 473.61 K. NaCl(aq) served as the reference electrolyte for the calculation of osmotic coefficients and the molalities ranged from about 0.6 to 6 mol kg −1, for NaCl(aq). An ion-interaction model gave an excellent fit to the experimental osmotic coefficients with a standard error of fit ranging from 0.0004 to 0.0016 in the osmotic coefficient. Parameters obtained from the fit were used to calculate the activity coefficients. The osmotic and activity coefficients both decreased with increasing temperature over this temperature range. LiCl(aq) is somewhat unusual among the alkali-metal chlorides in that the osmotic (and activity) coefficient is much more dependent on molality at the higher molalities and there is no maximum between 273.15 and 373.15 K in the osmotic coefficient as a function of temperature. For both LiCl(aq) and CsCl(aq) there is an excellent correlation between the isopiestic results and the vapor pressures of Lindsay and Liu. Existing electrochemical results between 283.15 and 343.15 K are consistent with our calculated activity coefficients for CsCl(aq).

Electrochemical properties of spherical polyelectrolytes: I. Impermeable sphere model

The Poisson-Boltzmann equation was numerically solved to obtain the electrostatic potential in the vicinity of spherical polyelectrolyte particles at finite concentration and low ionic strength, using the cell model. The polyelectrolyte particles were treated as impermeable spheres having a uniform surface charge density. The electrostatic potential was studied as a function of surface charge density, concentration of added salt, and particle size. The osmotic coefficient, Δp K, and the local ion concentrations were computed from the electrostatic potential. The computational results were compared with experimental ionic activities and osmotic coefficients for micelles of ionic detergents. Excellent agreement was obtained between the experimental and computed osmotic coefficients for micelles of sodium dodecyl sulfate and potassium laurate, but not for the cationic detergents dodecylpyridinium chloride and dodecylammonium chloride. The reason for the disagreement is unknown. The present calculations at finite particle concentration are compared with the electrostatic potential tables of Loeb et al. (“The Electrical Double Layer around a Spherical Colloid Particle,” M.I.T. Press, Cambridge, Mass., 1961), which were computed for the special case of infinite dilution or high ionic strength in order to show the range of applicability of those tables. Detailed comparison requires the specification of all parameters; for the particular parameters used in this paper it was found that for particles having the radius of detergent micelles (∼18 Å), the presence of 0.1 M salt was required to give good agreement (within 1.5%) between the surface potential computed by the present method and the infinite-dilution method, whereas only 10 −4 M salt was needed to give similarly good agreement for particles having the radius of phospholipid vesicles (∼300 Å).

The thermodynamics of mixed electrolyte solutions III. The aqueous system (C 3H 7) 4NCl + NaCl at 298.15 K

The excess Gibbs free energy changes on mixing aqueous solutions of tetrapropylammonium chloride and sodium chloride were determined at 298.15 K by the gravimetric isopiestic method. The experimental osmotic coefficients were treated by the Scatchard and Friedman procedures to yield the excess free energy of mixing ΔG ex and the free energy interaction parameters g 0 and g 1. Results obtained are discussed in terms of self interaction of tetrapropylammonium cations as indicated by positive values of g 0.