Determination of the contribution of pair, triplet, and higher-order multiplet interactions to the excess free energy of mixing in mixed electrolyte solutions

Leifer, Leslie; Wigent, Rodney J.

doi:10.1021/j100248a013

Cited by 16 publications

(20 citation statements)

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“…The b23 term has not been included by most workers. However, Leifer and Wigent (26) argue that it should be included since, like b03 and b 13, it is necessary to fully account for four-ion interactions.…”

Section: Calculations and Discussionmentioning

confidence: 99%

Isopiestic determination of the osmotic and activity coefficients of aqueous mixtures of sodium chloride and magnesium chloride at 25.degree.C

Rard¹,

Miller²

1987

J. Chem. Eng. Data

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The osmotic and activity coefficlents of aqueous mixtures of NaCl and MgCi, have been determined at 25 OC by uslng the isoplestic method. These measurements extend from low concentrations to the crystallization l i m b of the mixtures. They are critically compared to published Isopiestic, dlrect vapor pressure, and emf data for this system. Our data agree well with prevlous isoplestic data and two seis of emf values, but dlrect vapor pressure data are slgnlficantiy discrepant. Osmotlc and activity coefficients for NaCI-MgCI, mixtures are fairly reliably represented by both PHzer's equations and Scatchard's neutral electrolyte equations.The osmotic coefficients of aqueous La( NO3), have been measured from 1.3435 to 8.4591 mol-kg-' at 25 O C by using the isopiestic method. Some earlier osmotic coefficients for this salt are too high, apparently due to a stock solution concentration error, and have been normailzed to the present results. These comblned data and other activlty data were then used to generate recommended values for the osmotic coeff icients, water activities, and mean molal activlty coefficients of La (N03)3. The solubility of La(NO,),.BH,O(cr) was determined to be 4.6147 f 0.0056 mol-kg-' by the isoplestlc method; this Is in excellent agreement with the IUPAC recommended value of 4.610 f 0.005 mol-kg-'. Denslty data were measured for aqueous Eu(NO,), from 0.03996 to 1.1014 mol-kg-' at 25 OC by uslng pycnometry. These results are in fairly good agreement with published low-concentration densities measured with a magnetic float.

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Section: Calculations and Discussionmentioning

confidence: 99%

Isopiestic determination of the osmotic and activity coefficients of aqueous mixtures of sodium chloride and magnesium chloride at 25.degree.C

Rard¹,

Miller²

1987

J. Chem. Eng. Data

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“…We preferred to analyze the osmotic coefficients of these mixtures by using the virial coefficient approach of Pitzer . It should be pointed out here that Leifer and co-workers in the past, have successfully employed the Scatchard−Rush−Johnson equations to analyze the osmotic coefficients of the cluster forming electrolyte mixtures. The Scatchard−Rush−Johnson equations provide a more accurate description of thermodynamics of electrolytes at the expense of a large number of parameters. ,,, In the Pitzer theory, a combination of the Debye−Huckel and virial coefficient terms is used to describe the thermodynamic properties of electrolyte solutions.…”

Section: Resultsmentioning

confidence: 99%

Ionic Interactions from the Mixing of NaCl with the Acetate, Nitrate, Perchlorate, and Sulfate Salts of Guanidinium in Water

Kumar

2003

J. Phys. Chem. B

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Ionic interactions have been investigated from the experimental isopiestic osmotic coefficient measurements on the mixing of NaCl with several guanidinium (Gn) salts, like CH 3 COOGn, GnNO 3 , GnClO 4 , and Gn 2 SO 4 , up to high ionic strengths. Analysis of osmotic coefficient data by the Pitzer theory offers valuable information on the mixing of ions of like and unlike charges of hydrophilic and hydrophobic nature. The mixing effects arising out of symmetrical and unsymmetrical mixing of ions are computed by the Pitzer theory in these systems. The excess Gibbs free energies of mixing, ∆ m G E have been analyzed by the Friedman theory of cluster integral expansion. The ∆ m G E values display very interesting features with respect to the ionic strength fraction of the acetate, nitrate, and perchlorate salts of guanidinium. The minima in the ∆ m G E values are noted in the NaCl-rich mixtures, and the addition of these guanidinium salts slowly enhances ∆ m G E , passing through zero to positive values. The mixing of NaCl with Gn 2 SO 4 offers negative ∆ m G E throughout the mixture composition. Although binary interactions are nearly absent in the NaCl-CH 3 COOGn mixtures, the ternary and quaternary interactions are noted to be important in the mixtures of NaCl with other guanidinium salts. The ∆ m G E values of the mixture containing Na + , Gn + , Cl -, and SO 4 2ions (where binary interactions are important) can be estimated by Young's cross square rule (YCSR) with confidence. The YCSR is not obeyed when NaCl is mixed with CH 3 COOGn, GnNO 3 and GnClO 4 , where ternary and quaternary interactions are dominant over the binary interactions.

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“…Scatchard's neutral-electrolyte model equation for the osmotic coefficient of a mixture of two electrolytes [3], with additional terms as described by Leifer and Wigent [7] for quadruplet and higher-order ionic interactions, can be written in the form: The equation that was generally used by Scatchard and by Rush [3,4] to represent the osmotic coefficient of a solution of a single electrolyte i can be re-written in the equivalent form:…”

Section: Scatchard's Neutral-electrolyte Model Equationmentioning

confidence: 99%

“…Wigent and Leifer [6] and Leifer and Wigent [7] give equations relating Friedman's g n mixing coefficients to those of Scatchard's neutral-electrolyte model and generalized the mixing terms of the neutral-electrolyte model to include higher-order interactions [7]. Blandamer et al [8] have summarized some additional mixing equations with an emphasis on mixing relations for water activities.…”

Section: Introductionmentioning

confidence: 99%

“…Because the neutral-electrolyte model uses a very flexible combination of mixing terms with five [3] or more [7] mixing parameters, it is capable of accurately representing thermodynamic activity data for ternary solutions to very high ionic strengths. However, although five or six of these mixing parameters may be required for some electrolyte mixtures, in other cases such as when the ionic strength range is more limited or when the electrolytes are common-ion mixtures of the same charge type, fewer parameters may be needed.…”

Section: Introductionmentioning

confidence: 99%

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Conversion of Parameters Among Variants of Scatchard’s Neutral-Electrolyte Model for Electrolyte Mixtures that Have Different Numbers of Mixing Terms

Rard

Wijesinghe

2008

J Solution Chem

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Various model equations are available for representing the excess Gibbs energy properties (osmotic and activity coefficients) of aqueous and other liquid mixedelectrolyte solutions. Scatchard's neutral-electrolyte model is among the simplest of these equations for ternary systems and contains terms that represent both symmetrical and asymmetric deviations from ideal mixing behavior when two single-electrolyte solutions are mixed in different proportions at constant ionic strengths. The usual form of this model allows from zero to six mixing parameters. In this report we present an analytical method for transforming the mixing parameters of neutral-electrolyte-type models with larger numbers of mixing parameters directly to those of models with fewer mixing parameters, without recourse to the source data used for evaluation of the original model that was applied by them to binary systems. It was found that the use of this approach with a constant ionic-strength cutoff of I ≤ 6.2 mol·kg -1 (the NaCl solubility limit) yielded parameters for the NaCl + SrCl 2 + H 2 O and NaCl + MgCl 2 + H 2 O systems that predicted osmotic coefficients φ in excellent agreement with those calculated using the same sets of parameters whose values were evaluated directly from the source data by least-squares, with root mean square differences of RMSE(φ) = 0.00006 to 0.00062 for the first system and RMSE(φ) = 0.00014 to 0.00042 for the second. If, however, the directly evaluated parameters were based on experimental data where the ionic strength cutoff varied with the ionic-strength fraction, i.e. because they were constrained by isopiestic ionic strengths (MgCl 2 + MgSO 4 + H 2 O) or solubility / oversaturation ionic strengths (NaCl + SrCl 2 + H 2 O and NaCl + MgCl 2 + H 2 O), then parameters converted by this approach assuming a 2 constant ionic-strength cutoff yield RMSE(φ) differences about an order of magnitude larger than the previous case. This indicates that for an accurate conversion of model parameters when the source model is constrained with variable ionic strength cutoffs, an extension of the parameter conversion method described herein will be required.However, when the source model parameters are evaluated at a constant ionic strength cuttoff, such as when source isopiestic data are constrained to ionic strengths at or below the solubility limit of the less soluble component, or are Emf measurements that are commonly made at constant ionic strengths, then our method yields accurate converted models.

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Determination of the contribution of pair, triplet, and higher-order multiplet interactions to the excess free energy of mixing in mixed electrolyte solutions

Cited by 16 publications

References 0 publications

Isopiestic determination of the osmotic and activity coefficients of aqueous mixtures of sodium chloride and magnesium chloride at 25.degree.C

Isopiestic determination of the osmotic and activity coefficients of aqueous mixtures of sodium chloride and magnesium chloride at 25.degree.C

Ionic Interactions from the Mixing of NaCl with the Acetate, Nitrate, Perchlorate, and Sulfate Salts of Guanidinium in Water

Conversion of Parameters Among Variants of Scatchard’s Neutral-Electrolyte Model for Electrolyte Mixtures that Have Different Numbers of Mixing Terms

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