Comment on "Dynamic ion association in aqueous solutions of sulfate" [J. Chem. Phys. 123, 034508 (2005)

The "dynamic exchange" model of ion association proposed by Watanabe and Hamaguchi, [J. Chem. Phys.123, 034508 (2005)] for aqueous solutions of MgSO4 is shown to be inconsistent with the extensive information available from Raman, relaxation, and thermodynamic studies, all of which can be explained by the Eigen equilibrium model.     

A critical review of methods for obtaining ionic volumes in solution

The various major methods for obtaining individual or “absolute” ionic standard partial molar volumes V‡(ion) from whole electrolyte data in both aqueous and nonaqueous solutions are critically reviewed. A number of undetected errors in previous analyses are pointed out, and it is demonstrated that the reported agreement amongst the various methods in aqueous solution is largely fortuitous. All methods are shown to be unsatisfactory to varying degrees, with the reference electrolyte approach, using an electrolyte such as tetraphenylarsonium tetraphenylborate, appearing to be the least objectionable of those currently available. It is recommended that, subject to future theoretical and experimental developments, the assumption that, at 25‡C: - V‡(Ph₄As⁺) - V‡(BPh₄) = 8 cm³-mol^-1, or its equivalent: V‡(Ph₄P⁺) - V‡(BPh ₄ ^- ) = 2 cm³-mol^-1 be used in all solvents.     

A Potentiometric Study of the Association of Copper(II) and Sulfate Ions in Aqueous Solution at 25 °C

A study of the association between copper(II) and sulfate ions in aqueous solution has been made using copper ion-selective electrode potentiometry at constant ionic strengths (I) of 0.05, 0.1, 0.25, 0.5, 1.0, 3.0 and 5.0 mol·L^?1 in NaClO₄ media at 25 °C. Only one complex was detected, corresponding to the equilibrium: \( {\text{Cu}}^{ 2+ } ({\text{aq}}) + {\text{SO}}_{4}^{2 - } ({\text{aq}}) \rightleftarrows {\text{CuSO}}_{4}^{0} ({\text{aq}}). \) No higher order complexes were detected even at sulfate/copper(II) concentration ratios of up to 1,000. The present potentiometric values of log₁₀ K ₁(I) are shown to be consistently higher than those obtained by UV–Vis spectrophotometry because of the failure of the latter technique to detect all of the solvent-separated ion pairs present. Extrapolation of log₁₀ K ₁(I) to infinite dilution using an extended Guggenheim equation yielded a standard state value of log₁₀ \( K_{1} \{ {\text{CuSO}}_{4}^{0} ({\text{aq}})\} = 2.32 \pm 0.09 \) , which is in excellent agreement with a recent IUPAC-recommended value.     

Entire Solutions of One Linear Implicit Differential-Difference Equation in Banach Spaces

Ukrainian Mathematical Journal - We establish the existence and uniqueness conditions for the solution for the initial problem $$ {Bu}^{\prime }(z)= Au\left(z+h\right)+f(z),\kern1em z\in...     

Regularity Properties for Solutions of Infinite Dimensional Kolmogorov Equations in Hilbert Spaces

Potential Analysis - In this article we establish regularity properties for solutions of infinite dimensional Kolmogorov equations. We prove that if the nonlinear drift coefficients, the nonlinear...     

Association of ionic liquids in solution: a combined dielectric and conductivity study of [bmim][Cl] in water and in acetonitrile

Ion association of the ionic liquid [bmim][Cl] in acetonitrile and in water was studied by dielectric spectroscopy for salt concentrations c ≤ 1.3 M at 298.15 K and by measurement of molar electrical conductivities, Λ, of dilute solutions (c ≤ 0.006 M) in the temperature range 273.15 ? T/K ≤ 313.15. Whilst acetonitrile solutions of [bmim][Cl] exhibit moderate ion pairing, with an association constant of K°(A) ≈ 60 M(-1) and increasing with temperature, [bmim][Cl] is only weakly associated in water (K°(A) ≈ 6 M(-1)) and ion pairing decreases with rising temperature. Only contact ion pairs were detected in both solvents. Standard-state enthalpy, entropy and heat capacity changes of ion association were derived, as well as the activation enthalpy of charge transport and the limiting conductivity of the cation, λ(∞)?([bmim](+)). These data, in conjunction with effective solvation numbers obtained from the dielectric spectra, suggest that the solvation of [bmim](+) is much weaker in water than in acetonitrile.     

Use of lithium perchlorate media in the study of protolytic equilibria

A study of the H⁺/F^– system by fluoride ion-selective electrode potentiometry over a range of ionic strengths in LiClO ₄ gives protolysis constants which differ markedly from those obtained in other media such as NaClO ₄ . This is shown to be consistent with the competitive complexation of the fluoride ion by the lithium ion. An examination of literature data indicates that lithium ion complexation is a general phenomenon and supports the conclusion that LiClO ₄ is not preferable to NaClO ₄ as a swamping electrolyte for the study of protolytic equilibria as has previously been thought.     

Fluoride complexes of the alkali metal ions

Measurements by fluoride ion-selective electrode potentiometry on the very weak monofluoride complexes of the alkali metal ions in aqueous solution at 25°C and an ionic strength of 1M indicate their stability constants lie in the order Li⁺ > Na⁺ > K⁺ > Rb⁺ ? Cs⁺. Data at varying ionic strengths and temperatures were used to calculate infinite dilution stability constants and enthalpies and entropies of complexation for LiF and NaF.     

Association constants for the NaSO(4)(-) ion pair in concentrated cesium chloride solutions

Values of the association constant, beta(NaSO(4)(-)), for the weak ion-pair formed by sodium and sulfate ions in aqueous solution have been determined at 25 degrees C by high precision sodium ion-selective electrode potentiometry in solutions of ionic strength ranging from 0.50 to 7.00 M in CsCl media and in 1.00 M Me(4)NCl. The data in CsCl media were fitted to an extended form of the Debye-Hückel equation which yielded log beta(NaSO(4)(-))(0)=0.834+/-0.005 at infinite dilution. Evidence is also presented for the formation of very weak ion-pairs between Cs(+) and SO(4)(2-).     

A potential for the description of alpha-alpha interactions

In an investigation into the α-α and α-nucleus interaction the former is studied employing for the effective interaction a potential with a repulsive core embedded into a long range attractive part. Calculations with this potential reproduce the energies and widths of the levels of the α-α system⁸Be and the phases for α-α scattering quite well thus pointing to an applicability of the model to α-α and α-nucleus scattering for light nuclei.