Solvent coefficient

Solubility in water, selected solvents Coefficient of thermal expansion Hardness/flexibility... 

Fig. 242. Loss of weight of nitrocellulose powder at a temperature of 60°C I—evolution of moisture ( elimination ), II—evolution of solvent ( coefficient of emission ) [24].

Use the moisture content in step 2 to choose the appropriate extraction procedure, solvent, coefficients, and equations. 

Acid Solvent Coefficients of equation [9.106] Components of energy of ion association process, kJ mol ... 

They introduced a solvent coefficient (Henry s law constant) for each Eu species to account for the energy difference between the ideal gas and the particular liquid in question. They found, for a particular choice of major cation (i.e., Ca or Mg) in the solvent, 2EuO to be more soluble than EU2O3 in going from the ortho-or metasilicate end member of the mixture to the aluminosilicate end member. This result was not expected because the aluminosilicate end member has a higher fraction of its oxygen bound into polymer chains. This would be expected to decrease the activity of free oxide ion in the aluminosilicate melts, which according to eq. (21.4) would favor formation of Eu(III) at the expense of Eu(II), just opposite to what was observed. 

In a binary liquid solution containing one noncondensable and one condensable component, it is customary to refer to the first as the solute and to the second as the solvent. Equation (13) is used for the normalization of the solvent s activity coefficient but Equation (14) is used for the solute. Since the normalizations for the two components are not the same, they are said to follow the unsymmetric convention. The standard-state fugacity of the solvent is the fugacity of the pure liquid. The standard-state fugacity of the solute is Henry s constant. 

When a condensable solute is present, the activity coefficient of a solvent is given by Equation (15) provided that all composition variables (x, 9, and ) are taicen on an (all) solute-free basis. Composition variables 9 and 4 are automatically on a solute-free basis by setting q = q = r = 0 for every solute. 

Note that in liquid phase chromatography there are no detectors that are both sensitive and universal, that is, which respond linearly to solute concentration regardless of its chemical nature. In fact, the refractometer detects all solutes but it is not very sensitive its response depends evidently on the difference in refractive indices between solvent and solute whereas absorption and UV fluorescence methods respond only to aromatics, an advantage in numerous applications. Unfortunately, their coefficient of response (in ultraviolet, absorptivity is the term used) is highly variable among individual components. 

The value of coefficient depends on the composition. As the mole fraction of component A approaches 0, approaches ZJ g the diffusion coefficient of component A in the solvent B at infinite dilution. The coefficient Z g can be estimated by the Wilke and Chang (1955) method ... 

Umesi, N.O. (1980), Diffusion coefficients of dissoived gases in iiquids -Radius of gyration of solvent and solute . M.S. Thesis, The Pennsylvania State University, PA. 

As pointed out earlier, the contributions of the hard cores to the thennodynamic properties of the solution at high concentrations are not negligible. Using the CS equation of state, the osmotic coefficient of an uncharged hard sphere solute (in a continuum solvent) is given by... 

There are many other applications. They include detemiination of the ratios of the partition coefficients P IPq) of solutes B and C in two different solvents by using the themiodynamic cycle ... 

In principle, simulation teclmiques can be used, and Monte Carlo simulations of the primitive model of electrolyte solutions have appeared since the 1960s. Results for the osmotic coefficients are given for comparison in table A2.4.4 together with results from the MSA, PY and HNC approaches. The primitive model is clearly deficient for values of r. close to the closest distance of approach of the ions. Many years ago, Gurney [H] noted that when two ions are close enough together for their solvation sheaths to overlap, some solvent molecules become freed from ionic attraction and are effectively returned to the bulk [12]. 

A quite different approach was adopted by Robinson and Stokes [8], who emphasized, as above, that if the solute dissociated into ions, and a total of h molecules of water are required to solvate these ions, then the real concentration of the ions should be corrected to reflect only the bulk solvent. Robinson and Stokes derive, with these ideas, the following expression for the activity coefficient ... 

The introductory remarks about unimolecular reactions apply equivalently to bunolecular reactions in condensed phase. An essential additional phenomenon is the effect the solvent has on the rate of approach of reactants and the lifetime of the collision complex. In a dense fluid the rate of approach evidently is detennined by the mutual difhision coefficient of reactants under the given physical conditions. Once reactants have met, they are temporarily trapped in a solvent cage until they either difhisively separate again or react. It is conmron to refer to the pair of reactants trapped in the solvent cage as an encounter complex. If the unimolecular reaction of this encounter complex is much faster than diffiisive separation i.e., if the effective reaction barrier is sufficiently small or negligible, tlie rate of the overall bimolecular reaction is difhision controlled. 

As it has appeared in recent years that many hmdamental aspects of elementary chemical reactions in solution can be understood on the basis of the dependence of reaction rate coefficients on solvent density [2, 3, 4 and 5], increasing attention is paid to reaction kinetics in the gas-to-liquid transition range and supercritical fluids under varying pressure. In this way, the essential differences between the regime of binary collisions in the low-pressure gas phase and tliat of a dense enviromnent with typical many-body interactions become apparent. An extremely useful approach in this respect is the investigation of rate coefficients, reaction yields and concentration-time profiles of some typical model reactions over as wide a pressure range as possible, which pemiits the continuous and well controlled variation of the physical properties of the solvent. Among these the most important are density, polarity and viscosity in a contimiiim description or collision frequency. 

In the sections below a brief overview of static solvent influences is given in A3.6.2, while in A3.6.3 the focus is on the effect of transport phenomena on reaction rates, i.e. diflfiision control and the influence of friction on intramolecular motion. In A3.6.4 some special topics are addressed that involve the superposition of static and transport contributions as well as some aspects of dynamic solvent effects that seem relevant to understanding the solvent influence on reaction rate coefficients observed in homologous solvent series and compressed solution. More comprehensive accounts of dynamics of condensed-phase reactions can be found in chapter A3.8. chapter A3.13. chapter B3.3. chapter C3.1. chapter C3.2 and chapter C3.5. 

For analysing equilibrium solvent effects on reaction rates it is connnon to use the thennodynamic fomuilation of TST and to relate observed solvent-mduced changes in the rate coefficient to variations in Gibbs free-energy differences between solvated reactant and transition states with respect to some reference state. Starting from the simple one-dimensional expression for the TST rate coefficient of a unimolecular reaction a— r... 

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