Refractive index molar refraction

Theoretical and structural studies have been briefly reviewed as late as 1979 (79AHC(25)147) (discussed were the aromaticity, basicity, thermodynamic properties, molecular dimensions and tautomeric properties ) and also in the early 1960s (63ahC(2)365, 62hC(17)1, p. 117). Significant new data have not been added but refinements in the data have been recorded. Tables on electron density, density, refractive indexes, molar refractivity, surface data and dissociation constants of isoxazole and its derivatives have been compiled (62HC(17)l,p. 177). Short reviews on all aspects of the physical properties as applied to isoxazoles have appeared in the series Physical Methods in Heterocyclic Chemistry (1963-1976, vols. 1-6). 

Other techniques previously described for general investigation of tautomeric equilibria (76AHC(S1)1> involve heats of combustion, relaxation times, polarography, refractive index, molar refractivity, optical rotation, X-ray diffraction, electron diffraction, neutron diffraction, Raman, fluorescence, phosphorescence and photoelectron spectroscopy, and mass spectrometry. The application of several of these techniques to tautomeric studies has been discussed in previous sections. Other results from the more important of these will be referred to later in this section. 

Molar Refraction-Refractive Index. Molar refraction [i2] is related to molar volume (T ) and refractive index (n) by the equation ... 

Melting Point. Boiling Point. Density. Refractive index. Molar Refraction. 

Intensive Variables Temperature, Pressure, Dielectric constant, Density, Boiling point. Viscosity, Concentration, Refractive index. Molar enthalpy. Chemical potential. Molality, Specific heat. Free energy per mole. 

Fundamental Limitations to Beers Law Beer s law is a limiting law that is valid only for low concentrations of analyte. There are two contributions to this fundamental limitation to Beer s law. At higher concentrations the individual particles of analyte no longer behave independently of one another. The resulting interaction between particles of analyte may change the value of 8. A second contribution is that the absorptivity, a, and molar absorptivity, 8, depend on the sample s refractive index. Since the refractive index varies with the analyte s concentration, the values of a and 8 will change. For sufficiently low concentrations of analyte, the refractive index remains essentially constant, and the calibration curve is linear. 

Thus, if (ni) is the refractive index of the mixture and (V[) is the equivalent molar volume of the mixture,... 

Taking known values for the molar refractivities of water and methanol, and again assuming a range of values for the equilibrium constant (k) and the refractive index (ni) of the methanol/water associate, the actual values that fit the equation for these... 

Data Source Equilibrium Constant (k) Mol.Vol. of Associate Density of Associate Molar Refractivity of Associate Refractive Index of Associate... 

Using the average value for the equilibrium constant, the distribution concentration of the different components of a methanol water mixture were calculated for initial methanol concentrations ranging from zero to 100%v/v. The curves they obtained are shown in Figure 28. The molar refractivities of 11.88 is also in accordance with that expected since the molar refractivity s of water and methanol are 3.72 and 8.28 respectively. The refractive index of the associate of 1.3502 is, as would be expected, higher than that of either water or methanol. 

The molar refraction, / m, is a measure of the size of a molecule. It is calculated with Eq. (8.5), the Lorenz-Lorentz equation, where , d, and M are the refractive index, the density, and the molecular weight, respectively. 

The subscripts 1,2,3 refer to the main solvent, the polymer, and the solvent added, respectively. The meanings of the other symbols are n refractive index m molarity of respective component in solvent 1 C the concentration in g cm"3 of the solution V the partial specific volume p the chemical potential M molecular weight (for the polymer per residue). The surscript ° indicates infinite dilution of the polymer. 

The polarisability, a, of the molecule is proportional to the refractive index increment dn/dc, and to the relative molar mass of the molecule in question. The full relationship is ... 

The apparent molar volume of interfacial water in AOT-reversed micelles is lower and its refractive index is greater than that of pure water. These findings, together with other experimental evidence, emphasize that these water molecnles are destructured, immobilized, and polarized by the ionic head of AOT [2,84,89]. In particular, it has been reported that the... 

The behavior of the different amines depends on at least four factors basicity, nucleophilicity, steric hindrance and solvation. In the literature (16), 126 aliphatic and aromatic amines have been classified by a statistical analysis of the data for the following parameters molar mass (mm), refractive index (nD), density (d), boiling point (bp), molar volume, and pKa. On such a premise, a Cartesian co-ordinate graph places the amines in four quadrants (16). In our preliminary tests, amines representative of each quadrant have been investigated, and chosen by consideration of their toxicity, commercial availability and price (Table 1). 

Special care has to be taken if the polymer is only soluble in a solvent mixture or if a certain property, e.g., a definite value of the second virial coefficient, needs to be adjusted by adding another solvent. In this case the analysis is complicated due to the different refractive indices of the solvent components [32]. In case of a binary solvent mixture we find, that formally Equation (42) is still valid. The refractive index increment needs to be replaced by an increment accounting for a complex formation of the polymer and the solvent mixture, when one of the solvents adsorbs preferentially on the polymer. Instead of measuring the true molar mass Mw the apparent molar mass Mapp is measured. How large the difference is depends on the difference between the refractive index increments ([dn/dc) — (dn/dc)A>0. (dn/dc)fl is the increment determined in the mixed solvents in osmotic equilibrium, while (dn/dc)A0 is determined for infinite dilution of the polymer in solvent A. For clarity we omitted the fixed parameters such as temperature, T, and pressure, p. 

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