Apparent molal volume

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]. 

The apparent molal volumes and heat capacities were calculated from the relations... 

In connection with Vaslow s measurements (150) of the apparent molal volumes of the alkali metal chlorides in solutions, we call attention to the earlier measurements by Halasey on the temperature dependence of the partial molal volumes. These measurements suggest (31) that the... 

Pierrot D, Millero FJ (2000) The apparent molal volume and compressibility of seawater fit to the Pitzer equations. J Soln Chem 29 719-742... 

Desnoyers, J.E. and Arel, M. Apparent molal volumes of n-alkylamine hydrobromides in water at 25°C hydrophobic hydration and volume changes. Can. J. Chem. 1967, 45, 359-366. 

An alternative procedure draws on the definition of an apparent molal volume in a binary mixture, based on the relation... 

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. 

Calculated from apparent molal volume of anion at infinite dilution (f) and Avogadro s number (6.023X10 molecules/mole). 

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 next step is to perform a simultaneous regression of NaCl(aq) apparent molal volumes from 25-350 C. Over this wide range of temperature, however, and particularly above 300 C, standard-state properties based on the infinitely dilute reference state exhibit a very complex behavior (7,8), which is related to various peculiarities of the solvent. Thus in their representation of NaCl(aq) volumetric properties, Rogers and Pitzer (7) adopted a reference composition of a hydrated fused salt, NaCl IOH2O, to minimize the P and T dependence of the reference state volume and to adequately fit volumetric ta to 300°C and 1 kb. In this study the (supercooled) fused salt is used as the reference state. The equation for the apparent molal volume on this basis can be easily derived from that for the excess Gibbs energy of Pitzer and Simonson (, and is given by ... 

Apparent molal volumes of NaCl solutions from 25-350 C were used to fit Equation 17 and the following P and T function for V2, Wj and... 

Figure 3. Apparent molal volumes of NaCl(aq) solutions at 350 C and pressures to 1 kb. The curves are calculated from Equation 16 and the parameters given in Table I.

Table I. Parameters for Equation 16 Evaluated from Isothermal-isobaric Apparent Molal Volumes of NaCl Solutions at 350 C and Various Pressures...

Table II. Parameters for Equations 17 and 19 Evaluated from Apparent Molal Volumes of NaCl Solutions up to 350 C and 1 kb...

Fig. 3. Variation of the apparent molal volumes and the ionic viscosity coefficient B across the lanthanide series.

Schmidt and co-workers ° have also measured apparent molal volumes and viscosities of several electrolytes in anhydrous ethylenediamine at 25°C and extrapolated the data to obtain F . They observed that Masson s equation (eqn 2.3.66) was valid over the concentration range studied and their data indicate that S is negative in this solvent. A theoretical value for the limiting slope, is not available. The viscosity data are in agreement with the Jones-Dole equation over the concentration range studied, but the coefficients of this equation were not reported. 

The excess volume may be related to values of the apparent molal volume which is much more frequently tabulated, by the equation... 

DDC AFOSR-68-1887 3 285-6 1968 CA 69 27987 50215 RELATIVE VISCOSITY AND APPARENT MOLAL VOLUME OF N-METHYLPROPIONAMIDE SOLUTIONS AT VARIOUS TEMPERATURES. 

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