Apparent molal volume densities

Interesting is a comparison of the volumes occupied by individual complexes in solution and in the solid state. The partial molal volumes can be obtained from precise measurements of the solution densities of the complexes as a function of concentration [177]. These values may be subsequently compared with the unit cell volumes per complex molecule derived from the crystal structure. For Fe[HB(pz)3]2, the apparent molal volume in tetrahydrofuran solution was determined as 340.9 em mol Taking into account that the complex in solution forms an equilibrium between 86% LS and 14% HS isomers and employing the volume difference between the two spin states AF° = 23.6 cm mol S the volume of the LS isomer was calculated as 337.6 cm mol This value agrees closely with the volume of 337.3 cm mol for the completely LS complex in solid Fe[HB(pz)3]2 [105]. 

Phase equilibria in water have been described by Kelly, who studied the effect of hexoses, sucrose, and inorganic salts on each other. The conclusion was reached that, for sucrose, the solubility of the second solute influences the composition at the invariant point, but for D-fructose, this effect is zero because of the high solubility of this sugar in water. Viscosity and density have also been evaluated at different temperatmes in methyl sulfoxide, and were fitted to appropriate equations by use of least-squares methods. The apparent molal volume calculated in this way is in perfect agreement with the theoretical data, whereas the differences for D-glucose and sucrose are 8 and 4%, respectively. 

Several studies of the physical properties of sulphates have been carried out these will not be treated in detail but are listed as follows a determination of the dissociation constants of some univalent sulphate ion-pairs,the electrostriction of ammonium sulphate, dielectric and n.m.r. investigations of phase transitions in lithium ammonium sulphate, the surface structure of barium sulphate crystals in aqueous solution, optical activity and the electro-optical effect in crystals of Cd2(NH4)2(S04)3, apparent molal volumes and heat capacities of Na2S04, K2SO4, and MgS04 in water, and densities, heats of fusion, and refractive indices of double sulphates of univalent metals. ... 

The apparent molal volumes and compressibilities of galactose, glucose, maltose, sucrose, and dextran have been calculated fiom measurements of the density and ultrasound velocity of their aqueous solutions at 25 C. C- and H-n.m.r. lattice relaxation times T, have been used to provide information on the temperature dependence of the rotational mobility of both the sugar and the water molecules in concentrated aqueous solutions of sucrose and trehalose. ... 

On the other hand t and A r contain the rate constants of the equilibrium under study and, for bimolecular reactions, the concentrations of the species involved in the reaction [4b, 8]. Had counter-ion site binding been a one step process the determination of t would have provided a direct estimation of the lifetime of the bound counter-ions and, therefore, of the exchange rate between bound and free counterions. On the other hand the study of as a function of concentration would have permitted to obtain informations on the distribution of bound counterions between those bound with and without dehydration. Unfortunately, as will be shown in Section 4, site binding is a multistep process involving at least two equilibria. All of the unknown quantities involved in such a process (four rate constants, two volume changes and the concentrations of the species) cannot be obtained from ultrasonic absorption data alone. Independent measurements become necessary. For this purpose we have measured the density d of the polyelectrolyte solutions from which can be obtained the apparent molal volume FcP of the polyelectrolyte CP (C counterion, P polyion) according to ... 

Measurements of apparent molal volumes have also been performed on poly-methacrylic acid, polystyrenesulfonic acid and carboxymethylcellulose. The results are reported elsewhere [19] together with a method for the evaluation of the contribution of electrostriction to the apparent molal volumes of polyions. Nuclear magnetic resonance measurements together with density measurements have permitted us to show [20] that for CoPP the electrostriction per site of polyion is equal to that of a equivalent and is about 20 cm equiv." ... 

Rather precise apparent molal data are required to see the cosolvent dependence of the transfer functions. With volumes, a precision in densities of... 

Molar volumes of solute and solvent, Vy and Vs, are determined from apparent molar volumes Oy (Section II.F) by density measurements. In terms of the measured densities of the solution and the pure solvent, d and d, the apparent molar volume is given by (molarity and molality scale, respectively)... 

The main problem in calculating molar volumes from density measurements is the difficulty of measuring reliable densities at low electrolyte molalities. An estimation of the error of apparent molar volumes... 

Partial molal volumes are d( t( rminable from experiment by a variety of methods, the most commonly used one involving the computation of the apparent molal olume, pure solvent. The quantity

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A single homogeneous phase such as an aqueous salt (say NaCl) solution has a large number of properties, such as temperature, density, NaCl molality, refractive index, heat capacity, absorption spectra, vapor pressure, conductivity, partial molar entropy of water, partial molar enthalpy of NaCl, ionization constant, osmotic coefficient, ionic strength, and so on. We know however that these properties are not all independent of one another. Most chemists know instinctively that a solution of NaCl in water will have all its properties fixed if temperature, pressure, and salt concentration are fixed. In other words, there are apparently three independent variables for this two-component system, or three variables which must be fixed before all variables are fixed. Furthermore, there seems to be no fundamental reason for singling out temperature, pressure, and salt concentration from the dozens of properties available, it s just more convenient any three would do. In saying this we have made the usual assumption that properties means intensive variables, or that the size of the system is irrelevant. If extensive variables are included, one extra variable is needed to fix all variables. This could be the system volume, or any other extensive parameter. 

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