Ion Association and Hydration in Aqueous Solutions of Nickel(II) and Cobalt(II) Sulfate

Aqueous solutions of nickel(II) and cobalt(II) sulfate have been investigated at 25 ^∘C by dielectric relaxation spectroscopy (DRS) over a wide range of frequencies (0.2 ≤ ν (GHz) ≤ 89) and salt concentrations (0.025 ≤ c(mol-L⁻¹) ≤ 1.4). The spectra indicate, as for MgSO₄(aq) studied previously, the simultaneous presence of double solvent-separated, solvent-shared and contact ion pairs in both NiSO₄(aq) and CoSO₄(aq). The stepwise formation constants for each ion-pair type and the overall association constant, obtained from the data are in good agreement with ultrasonic relaxation and other estimates. The DR spectra at higher concentrations (c ≥ 0.5 mol-L⁻¹) suggest the existence of a nonlinear triple ion M₂SO₄²⁺(aq). Consistent with the very strong hydration of the salts, which have ‘effective’ hydration numbers approaching 27 at infinite dilution, there are no significant differences in any of the relaxation or thermodynamic parameters for NiSO₄(aq) and CoSO₄(aq), except that the triple ion appears to be somewhat more stable for the latter.     

Bestimmung der Aktivitätskoeffizienten im chromatographischen Modell „binärer Lösungen“

An explanation is given for the two possible ways of determination of the activity coefficients of solutes, when applying a new thermodynamic model of adsorption and partition chromatography, i. e. the binary solutions model.

     

Concentrated electrolyte solutions at high temperatures and pressures

A survey is given of recent experimental results obtained from high-temperature, high-pressure investigations with water, aqueous solutions, and ionic fluids. Data on the static dielectric constant of water to 550°C and 5 kbar are given and discussed with respect to their relation to water structure. Infrared and Raman spectra of HDO in pure water have been obtained to 400°C and 4 kbar, which give information on hydrogen bonding. Xe–H₂O and CO₂–H₂O mixtures were investigated in the infrared. Ni(II) and Cu(II) complexes were investigated by absorption spectroscopy in aqueous solutions of high chloride content to 350°C and 2–6 kbar. The gas-liquid critical point of ammonium chloride was found at 880°C and 1635 bars. This fluid appears to be predominantly ionic even in the critical region. The possibility of converting pure polar fluids such as ammonia and water into concentrated ionic solutions by self-ionization at very high pressures is mentioned.This paper was presented at the symposium, The Physical Chemistry of Aqueous Systems, held at the University of Pittsburgh, Pittsburgh, Pennsylvania, June 12–14, 1972, in honor of the 70th birthday of Professor H. S. Frank.     

定标粒子理论计算非水溶液的盐效应常数

本文应用定标粒子理论计算了非电解质溶质在盐(NaI、或KI)和环丁砜组成的非水电解质溶液中溶解度的盐效应常数。硬球作用项采用Masterton-Lee的方法。软球作用项采用胡英等的径向分布函数处理方法, 并考虑进了偶极-偶极、偶极-诱导偶极、电荷-偶极和电荷-诱导偶极等相互作用。分子的硬球直径σ和能量参数∈/k由经验方程计算。由理论值和实验结果比较得出: 当σ_2取0.563 nm、离子半径取电子密度标度时, 理论值与实验值符合得较好。     

Long-range dispersion coefficients for like centrosymmetric linear molecules and an application to H2-H2

The real spherical tensor theory of long-range intermolecular coefficients developed in previous papers is applied to derive explicit formulae for the first three dispersion coefficients for like centrosymmetric linear molecules. The expansion of angle-dependent coefficients in associated Legendre polynomials allows one to identify the isotropic and anisotropic components of the dispersion interaction in terms of London dispersion constants, the treatment of higher coefficients being simplified by the coupling of the elementary (l, l′)-polarizations to resultant angular momenta L_A and L_B onto each molecule. The contributions from all coupling schemes are given explicitly for C₆, C₈, C₁₀, and numerical results are presented for H₂-H₂ using two-term reduced spectra values from the Kaiserlautern group.     

Thermodynamics of multicomponent electrolyte solutions: Aqueous mixtures of two salts from among NaCl,KCl, NaH2PO4, and KH2PO4 at 25° C

Five of the six possible aqueous two-salt mixtures from among NaCl, KCl, NaH₂PO₄,and KH₂PO₄ have been studied by the isopiestic method at 25°C. The sixth mixture, NaCl–KCl, has been studied previously. The deviations from ideal mixing behavior are described by a series of coefficients which were found by regression analysis. The coefficients were used to calculate the excess Gibbs energies of mixing for equal ionic strength fractions of each salt and the trace activity coefficient of each salt at an ionic strength of 2 mode-kg^–1. The cross-square mixing rule is obeyed within experimental uncertainty for the excess Gibbs energies of mixing.     

求解张量随机互补问题的光滑牛顿算法

近年来, 越来越多的人意识到随机互补问题在经济管理中具有十分重要的作用。有学者已将随机互补问题由矩阵推广到张量, 并提出了张量随机互补问题。本文通过引入一类光滑函数, 提出了求解张量随机互补问题的一种光滑牛顿算法, 并证明了算法的全局和局部收敛性, 最后通过数值实验验证了算法的有效性。     

Existence and Uniqueness of Solutions to Time-delays Stochastic Fractional Differential Equations with Non-Lipschitz Coefficients

In this paper, we consider the existence and uniqueness of solutions to time-varying delays stochastic fractional differential equations (SFDEs) with non-Lipschitz coefficients. By using fractional calculus and stochastic analysis, we can obtain the existence result of solutions for stochastic fractional differential equations.     

Products and transforms of white-noise functionals (in general setting)

Some sharp results about Weiner and Wick products of whitenoise functionals are obtained. Using the inequality of Wick products we show to what extent scaling transformations, translations, and Sobolev differentiations can be performed on white-noise functionals.This work was supported by the National Natural Science Foundation of China. This paper is an enlargement and revised version of the paper entitled Products and Transforms of White-Noise Functionals (preprint, 1990).     

The nearest neighbor random walk on subspaces of a vector space and rate of convergence

LetX be the collection ofk-dimensional subspaces of ann-dimensional vector spaceV _n overGF(q). A metric may be defined onX by letting