Molar volume and molecular

The Einstein theory shows that volume fraction is the theoretically favored concentration unit in the expansion for viscosity, even though it is not a practical unit for unknown solutes. As was the case in the Flory-Huggins theory in Chapter 3, Section 3.4b, it is convenient to convert volume fractions into mass/volume concentration units for the colloidal solute. According to Equation (3.78), 0 = c(V2/M2), where c has units mass/volume and V2 and M2 are the partial molar volume and molecular weight, respectively, of the solute. In viscosity work, volumes are often expressed in deciliters —a testimonial to the convenience of the 100-ml volumetric flask In this case, V2 must be expressed in these units also. The reader is advised to be particularly attentive to the units of concentration in an actual problem since the units of intrinsic viscosity are concentration when the reduced viscosity is written as an expansion of powers of concentration c. (The intrinsic viscosity is dimensionless when the reduced viscosity is written as an expansion of powers of volume fraction 0.) With the substitution of Equation (3.78), Equation (42) becomes... 

Molar compressibility (6) = Mlp)P where /and M are the molar volume and molecular weight, respectively. 

Aqueous solubility data for the 12 aromatic hydrocarbons studied in this investigation are reported in this section. The solubilities determined spanned a range of 106. The solubilities measured at 25°C are compared with values reported by other investigators and are correlated with molecular parameters such as carbon number, molar volume, and molecular length. 

Correlations of Solubility with Molecular Parameters. The aqueous solubility of aromatic hydrocarbons has been shown by Klevens (25) to be related to carbon number, molar volume, and molecular length. These parameters along with the molar solubilities (expressed as — In S) of the compounds studied are presented in Table XIII. Figures 5 through 7 demonstrate the relationship between each of these parameters and solubility. These figures show that there are several compounds whose anomalous behavior makes accurate extrapolations of solubility from these relationships impossible. For example, anthracene and phenanthrene are structural isomers. They, therefore, have identical carbon numbers and very similar molar volumes. However, their aqueous solubilities differ by more than a factor of 20. Phenanthrene, fluoranthene, pyrene, and triphenylene all have very similar molecular lengths but their respective aqueous molar solubilities at 25°C are 5.6 X 10 6, 1.0 X 10"6, 6.8 X 10"7, and 2.8 X 10 8. 

Figure 1. Graph of the Reciprocal of the Diffusivity against the Product of the Cube Root of the Molar volume and the Square Root of the Molecular Weight...

The solvent triangle classification method of Snyder Is the most cosDBon approach to solvent characterization used by chromatographers (510,517). The solvent polarity index, P, and solvent selectivity factors, X), which characterize the relative importemce of orientation and proton donor/acceptor interactions to the total polarity, were based on Rohrscbneider s compilation of experimental gas-liquid distribution constants for a number of test solutes in 75 common, volatile solvents. Snyder chose the solutes nitromethane, ethanol and dloxane as probes for a solvent s capacity for orientation, proton acceptor and proton donor capacity, respectively. The influence of solute molecular size, solute/solvent dispersion interactions, and solute/solvent induction interactions as a result of solvent polarizability were subtracted from the experimental distribution constants first multiplying the experimental distribution constant by the solvent molar volume and thm referencing this quantity to the value calculated for a hypothetical n-alkane with a molar volume identical to the test solute. Each value was then corrected empirically to give a value of zero for the polar distribution constant of the test solutes for saturated hydrocarbon solvents. These residual, values were supposed to arise from inductive and... 

First-order estimates of entropy are often based on the observation that heat capacities and thereby entropies of complex compounds often are well represented by summing in stoichiometric proportions the heat capacities or entropies of simpler chemical entities. Latimer [12] used entropies of elements and molecular groups to estimate the entropy of more complex compounds see Spencer for revised tabulated values [13]. Fyfe et al. [14] pointed out a correlation between entropy and molar volume and introduced a simple volume correction factor in their scheme for estimation of the entropy of complex oxides based on the entropy of binary oxides. The latter approach was further developed by Holland [15], who looked into the effect of volume on the vibrational entropy derived from the Einstein and Debye models. 

Table 20.4 Density, molecular weight, heat of fusion, molar volume and degree of polymerization of PET, P(HB60-ET40)/PET and P(HB80-ET20)/PET blends...

An alternative explanation for the lower sampling rates of very hydrophobic compounds is that the membrane may become rate limiting again for compounds with large molar volumes and low conformational freedom, dne to the fact that molecular size may be too large to fit into the transient cavities in the LDPE. Combining Eqs. 3.36 and 3.38 gives the condition for membrane controlled uptake... 

To model the solubility of a solute in an SCF using an EOS, it is necessary to have critical properties and acentric factors of all components as well as molar volumes and sublimation pressures in the case of solid components. When some of these values are not available, as is often the case, estimation techniques must be employed. When neither critical properties nor acentric factors are available, it is desirable to have the normal boiling point of the compound, since some estimation techniques only require the boiling point together with the molecular structure. A customary approach to describing high-pressure phenomena like the solubility in SCFs is based on the Peng-Robinson EOS [48,49], but there are also several other EOS s [50]. 

A final quasi-thermodynamic approach to molecular structure effects has been proposed by Good et al. (17-18) which relates molar volumes and the Girifalco-Good interaction parameter, as... 

Using PCA, Cramer found that more than 95% of the variances in six physical properties (activity coefficient, partition coefficient, boiling point, molar refractivity, molar volume, and molar vaporization enthalpy) of 114 pure liquids can be explained in terms of only two parameters which are characteristic of the solvent molecule (Cramer 111, 1980). These two factors are correlated to the molecular bulk and cohesiveness of the individual solvent molecules, the interaction of which depends mainly upon nonspecific, weak intermolecular forces. 

The correlation between aqueous solubility and molar volume discussed by McAuliffe [5] for hydrocarbons, and the importance of the cavity term in the solvatochromic approach, indicates a significant solubility dependence on the molecular size and shape of solutes. Molecular size and shape parameters frequently used in quantitative structure-water solubility relationships (QSWSRs) are molecular volume and molecular connectivity indices. Moriguchi et al. [33] evaluated the following relationship to estimate Cw of apolar compounds and a variety of derivatives with hydrophilic groups ... 

Equation (14.26) gives the dependence of the pressure in the phase as a function of r, the variable that determines the position in the field, in terms of the molar volume and the average molecular mass. Both of these latter quantities are themselves dependent on the position of the field. 

The determination of molar volumes of molecular species in the liquid phase can be performed with the Rackett equation [58], requiring critical temperature, pressure and volume as well as a further fitting parameter. It is possible to calculate the molar volumes of electrolyte species using the two-parameter equation of Clarke (see Ref. [52]). 

The second class comprises conventional solids, defined by a chemical formula, but whose property requirements are very minimal. In this class we included lignin, cellulose, mannan, galactan, xylan, arabinan and the biomass. The properties specified in the database include molecular weight, heat of formation, solid molar volume, and solid heat capacity. 

Very accurate quadratic fits may be obtained from Equation 11, although Equation 12 is not so accurate and is not so well justified theoretically however, it is the simplest available description. Note that the volume fraction, cf>, must be used and that this implies the use of partial molar volume and knowledge of molecular weight. Equation 11 works remarkably well and applies equally well to bovine serum albumin and casein. 

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