Curvature invariants, differential operators and local homogeneity

We first prove that a Riemannian manifold with globally constant additive Weyl invariants is locally homogeneous. Then we use this result to show that a manifold whose Laplacian commutes with all invariant differential operators is a locally homogeneous space.

     

Thermodynamics of electrolyte solutions. The system HCl + CaCl2 + H2O at 298.15°K

Activity coefficients of hydrochloric acid have been determined from electromotive-force measurements of cells containing mixtures of hydrochloric acid and calcium chloride at constant total ionic strengthsI=0.1, 0.5, 1.0, 2.0, and 3.0 mole-kg^–1 at 298.15°K. Interpretations based on Scatchard's and Pitzer's equations indicate that Pitzer's equations probably provide a more convenient guide to the thermodynamic properties of the mixed-electrolyte solutions. Activity coefficients for calcium chloride were derived from these equations.     

Flow injection analysis methods for determination of diffusion coefficients

Two flow injection analyses (FIA) methods for the determination of diffusion coefficients in a straight single tube FIA system were developed. Based on the analytical solution of the convection-diffusion equation, linear relationships of the logarithmic values of the dispersion coefficient (D) and the half-peak width (W_1/2) with the diffusion coefficient (D_m) were obtained. Experiments were designed to verify these methods. For example, for potassium hexacyanoferrate (III) a D_m value of 0.72 × 10⁵ cm² s⁻¹ was found versus a literature value of 0.76 × 10⁵ cm² s⁻¹ (error, 5%). For potassium hexacyanoferrate (II) a D_m value of 0.67 × 10⁵ cm² s⁻¹ was obtained versus a literature value of 0.63 × 10⁵ cm² s⁻¹ (error, 6%). The diffusion coefficients of some important biomedical compounds, such as dopamine, epinephrine, norepinephrine and ascorbic acid, were then determined. The values of 10⁵ D_m/cm² s⁻¹ are 0.60 ± 0.03, 0.44 ± 0.02, 0.60 ± 0.01 and 0.68 ± 0.06, respectively.     

Liquids and liquid mixtures: Deduction of the BGY equation considering the angular distribution function

The Born→Green→Yvon equation for molecular fluid has been deduced considering the orientational distribution functions. The isotropic and anisotropic parts of the distribution function have been separated. The expressions deduced can be used in the case of mixtures and for the non-central type of intermolecular potential energy.     

Activity coefficients of electrolytes from the E.M.F. of liquid membrane cells. II - multicharged electrolyte solutions

The activity coefficients of Co(en)₃Cl₃ and K₂SO₄ were measured by means of a cell with ion-exchange liquid membranes following the method described in paper I. The results prove that this method is even more valuable with multicharged salts than with 1-1 electrolytes. The values obtained are precise and reliable down to dilution limits never before accessible, e.g., 4×10^–5 mol-kg^–1 in Co(en)₃Cl₃. High dilution levels are of particular importance when dealing with highly charged electrolytes since the trend at higher concentrations often leads to errors both in extrapolation to infinite dilution and in the absolute activity coefficients. As an application, the activity coefficients of [Co(en)₃]₂(SO₄)₃-suspected to be wrongly evaluated in past literature-were measured, and their values at low concentrations were actually lower than those quoted before.     

Diffusion in aqueous copper sulfate and copper sulfate-sulfuric acid solutions

Diffusion coefficients of copper sulfate-water and copper sulfate-sulfuric acid-water solutions have been determined at 25°C using conductimetric and diaphragm-cell techniques. The ternary diffusion measurements indicate that diffusion of sulfuric acid can produce large counterflows of copper sulfate and vice versa. If diffusion of copper sulfate in aqueous sulfuric acid solutions is treated as a binary process, the measured apparent diffusivities of copper sulfate can be 1 to 8% lower than the salt's true diffusivity. Equations are developed to predict transport coefficients from the concentrations and mobilities of the diffusing species.     

Enthalpic interaction coefficients of formamides dissolved in N,N-dimethylformamide

Enthalpies of dilution of formamide, N-methylformamide, N-ethylformamide, N-propylformamide, N-butylformamide, N-pentylformamide, N,N-diethyl-formamide, N,N-dipropylformamide, N,N-dibutylformamide, and N,N-dipentyl-formamide dissolved in N,N-dimethylformamide as solvent have been measured calorimetrically at 25°C. The results are interpreted in terms of the McMillan-Mayer theory. Enthalpic interaction parameters are obtained for pairs, triplets, and in some cases, quadruplets of solute molecules. In general, the enthalpic pair interaction coefficients are negative, whereas the triplet coefficients are positive. The interaction enthalpies are positive only for N-methylformamide and formamide. The magnitudes of the enthalpic pair and triplet interaction coefficients increase with increasing number of C atoms in the N-alkyl groups. The results for the formamides presented in this paper are compared with those for corresponding acetamides published earlier. Although the trends are comparable, distinct differences are observed. The contribution of the -CH₃ group at the CO side of the dialkylacetamides to the enthalpic interaction coefficients appears to be negligible. The same is true for -CH₂ groups at the NH side of a number of amides and related compounds. The enthalpic pair interaction coefficients of the mono-N-alkylsubstituted formamides show a shift of about 100 J-kg-mol^–2 as compared with isomeric N-alkylacetamides. This is discussed in terms of the difference in proton donating and accepting ability of several types of amide molecules. It is concluded that substitution effects should be incorporated in additivity models for these type of systems.     

Thermodynamics of mixed electrolyte solutions. XI. An isopiestic study of the quaternary system NaCl−KCl−CaCl2−H2O at 25°C

Osmotic and activity coefficients in the aqueous quaternary system sodium chloride-potassium chloride-calcium chloride were derived from isopiestic measurements at 25°C. The isopiestic data were treated by the various procedures of Scatchard, Friedman, and Reilly, Wood, and Robinson. The results obtained showed good agreement with those obtained by pseudo-ternary transforms. Interaction parameters obtained indicated the preponderance of pairwise interactions. Excess Gibbs free energies of mixing were calculated.     

Side effects in measurements of selectivity coefficients of solid state ion selective electrodes

The influence of various factors such as solubility, the oxidation of the membrane, and the contamination of the solution, on the experimental values of the selectivity coefficients of solid state sulphide ion selective electrodes is discussed. A new method for the evaluation of very small selectivity coefficients, based on the addition of reagents forming complexes or insoluble salts with the main ion, is proposed. By means of this method, selectivity coefficients for silver, copper, cadmium and lead ion selective electrodes have been determined, which are in far better agreement with thermodynamic values than those described in the literature.     

Determination of partition behavior of organic surrogates between paperboard packaging materials and air

The suitability of recycled paperboard packaging materials for direct food contact applications is a major area of investigation. Chemical contaminants (surrogates) partitioning between recycled paper packaging and foods may affect the safety and health of the consumer. The partition behavior of all possible organic compounds between cardboards and individual foodstuffs is difficult and too time consuming for being fully investigated. Therefore it may be more efficient to determine these partition coefficients indirectly through experimental determination of the partitioning behavior between cardboard samples and air. In this work, the behavior of organic pollutants present in a set of two paper and board samples intended to be in contact with foods was studied. Adsorption isotherms have been plotted and partition coefficients between paper and air have been calculated as a basis for the estimation of their migration potential into food. Values of partition coefficients (Kpaper/air) from 47 to 1207 were obtained at different temperatures. For the less volatile surrogates such as dibutyl phthalate and methyl stearate higher Kpaper/air values were obtained. The adsorption curves showed that the more volatile substances are partitioning mainly in air phase and increasing the temperature from 70 to 100 degrees C their concentrations in air (Cair) have almost doubled. The analysis of surrogates was performed with a method based on solvent extraction and gas chromatographic-flame ionization detection (GC-FID) quantification.