Density pure-solvent

A film at low densities and pressures obeys the equations of state described in Section III-7. The available area per molecule is laige compared to the cross-sectional area. The film pressure can be described as the difference in osmotic pressure acting over a depth, r, between the interface containing the film and the pure solvent interface [188-190]. 

Let us now ask how this value could be used as a basis from which to measure the local disturbance of the water structure that will be caused by each ionic field. The electrostriction round each ion may lead to a local increase in the density of the solvent. As an example, let us first consider the following imaginary case let us suppose that in the neighborhood of each ion the density is such that 101 water molecules occupy the volume initially occupied by 100 molecules and that more distant molecules are not appreciably affected. In this case the local increase in density would exactly compensate for the 36.0 cm1 increment in volume per mole of KF. The volume of the solution would be the same as that of the initial pure solvent, and the partial molal volume of KF at infinite dilution would be zero. Moreover, if we had supposed that in the vicinity of each ion 101 molecules occupy rather less than the volume initially occupied by 100 molecules, the partial molal volume of the solute would in this case have a negative value. 

Exactly the same type of behavior is found for the freezing point of a solution except that the freezing point is lowei than that of the pure solvent. Thus we have two methods for molecular weight determination which are applicable to compounds with such low vapor pressure or which decompose so readily that the vapor density method cannot be used. 

In practice we do not measure viscosity directly. Instead, what is measured is time of flow for solutions and pure solvent in a capillary viscometer, the so-called efflux time. If the same average hydrostatic head is used in all cases, and since for very dilute solutions the density differences between the different concentrations are negligible, then the ratio of the efflux time of the solution, t, to that of the pure solvent, tg, may be taken as a measure of the ratio of the viscosities, i.e. 

However, if acetonitrile (density at 20.0°C = 0.786 g/mL) were the solvent, 1 liter of solution which would be essentially pure solvent would have a mass of only 786 g. We see that molarity of NaCl in acetonitrile would not be equivalent to the molality, but would be less. 

M (gmol-1) molar mass of the solute d (gem-3) density of the solution do (g cm-3) density of the pure solvent c (mol-1) concentration of the solute... 

Although we are not dealing with very dilute solutions, we may use the density term in equation 14.5 to estimate a correction to these values. However, we need to bear in mind that this estimate can be considered at several approximation levels. The most simple is to assume that In p is constant in the experimental temperature range, and thus only the reaction entropy is affected. Using the value for the pure solvent, p = 1.6227 kg dm-3 (at 20°C) [48], we obtain ArS 23 = -56.2 J K-1 mol-1. A more accurate calculation would include the variation of In p with the temperature, which, in the absence of experimental data, can be estimated from the coefficient of thermal expansion of the solvent, a ... 

Note that the first term is an average of the type (9.2.20) or (9.2.21), i.e., with a probability density of the pure solvent. The second quantity is a conditional average, i.e., we must use a conditional distribution instead of Since the... 

In a centrifugal field, dissolved molecules or suspended particles either sediment (if their density exceeds that of the pure solvent), or flotate for the opposite case (negative or inverse sedimentation). Under otherwise identical experimental conditions, the velocity of the molecules or particles depends on the viscosity of the solution or suspension and - very importantly - on the mass and shape of the dissolved species. Sedimentation and flotation are antagonized by the diffusion. Depending on the rotor speed and the molar mass of the dissolved/dis-... 

Solvents used here for a general liquid-liquid extraction method were selected from Snyders solvent selectivity triangle. As extraction liquids have to be composed of mixtures of three solvents which may enter into maximum interaction with the analyte, three solvents had to be selected that represent a wide variety of selective interactions. In addition, the solvents should be sufficiently polar to ensure quantitative extraction. Besides selectivity and polarity requirements, the solvents should also meet a few other criteria, mainly for practical reasons they should not be miscible with water, have low boiling points (for relatively fast evaporation procedures) and have densities sufficiently different from the density of water, for pure solvents as well as for selected binary or ternary mixtures of solvents. 

In solutions and in mixtures of liquids, additional light scattering arises from irregular changes in density and refractive index due to fluctuations in composition. If the solution is dilute, the density fluctuations are essentially identical to those existing in the pure solvent [9]... 

Here, the quantities jn ° and ji are, respectively, the chemical potentials of pure solvent and of the solvent at a certain biopolymer concentration V is the molar volume of the solvent and n is the biopolymer number density, defined as n C/M, where C is the biopolymer concentration (% wt/wt) and M is the number-averaged molar weight of the biopolymer. The second virial coefficient has (weight-scale) units of cm mol g. Hence, the more positive the second virial coefficient, the larger is the osmotic pressure in the bulk of the biopolymer solution. This has consequences for the fluctuations in the biopolymer concentration in solution, which affects the solubility of the biopolymer in the solvent, and also the stability of colloidal systems, as will be discussed later on in this chapter. 

The scattered light intensity from a polymer solution arises from the fluctuations in both the solvent density and the polymer concentration. These fluctuations are considered as stable during the timescale of the measurement in the static mode of light scattering (for more details, see Evans (1972)). The light scattered from just the polymer (in excess of the light scattered from the pure solvent) is given by (Burchard, 1994)... 

Steady-state and multifrequency phase and modulation fluorescence spectroscopy are used to study the photophysics of a polar, environmentally-sensitive fluorescent probe in near- and supercritical CF3H. The results show strong evidence for local density augmentation and for a distribution of cluster sizes. These results represent the first evidence for lifetime distributions in a "pure solvent system. 

Integration of Equation (8.114) after substitution of Equation (8.115) cannot be performed easily, because p is a function of the concentrations of the solutes and is generally different for each system. However, for dilute solutions lOOOp is large with respect to f=2 cMi and P approximates pu the density of the pure solvent. If these approximations are made, then... 

When a non-centrosymmetric solvent is used, there is still hyper-Rayleigh scattering at zero solute concentration. The intercept is then determined by the number density of the pure solvent and the hyperpolarizability of the solvent. This provides a means of internal calibration, without the need for local field correction factors at optical frequencies. No dc field correction factors are necessary, since in HRS, unlike in EFISHG, no dc field is applied. By comparing intercept and slope, a hyperpolarizability value can be deduced for the solute from the one for the solvent. This is referred to as the internal reference method. Alternatively, or when the solvent is centrosymmetric, slopes can be compared directly. One slope is then for a reference molecule with an accurately known hyperpolarizability the other slope is for the unknown, with the hyperpolarizability to be determined. This is referred to as the external reference method. If the same solvent is used, then no field correction factor is necessary. When another solvent needs to be used, the different refractive index calls for a local field correction factor at optical frequencies. The usual Lorentz correction factors can be used. 

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