Constant of Solutions

The electric field created between two plates of a parallel-plate condenser in a vacuum is greater than the field that exists between the same plates with the same 

The counter field and the resulting net field can be calculated in mathematical form, but historically a more empirical way has been used the field in the presence of a dielectric is simply expressed by dividing the field in its absence by an empirical dielectric constant. The greater the counter field set up by the medium between the plates (Fig. 2.26), the greater the dielectric constant and the less the net electric field. 

With this simple background model, then, it is easy to see that there will be a decrease of the dielectric constant of solutions (compared with that of the original 

Hydration Numbers from Dielectric Increment Measurements 

Source From J. B. Hasted, Aqueous Dielearics, Chapman and Hall, London, 1973. 

---

K Binding constant of solute based on concentration of micellized surfactant... 

Y Ishihama, H Katayama, N Asakawa. Novel sulfated polymer-coated capillary for the determination of hydrophobicity and the dissociation constants of solutes in acidic regions. Proceedings of 10th International Symposium on HPCE and Related Microscale Techniques, Kyoto, 1997, p 112. 

The effect of temperature is not so significant within the studied interval, probably due to the counter effect of a decrease in the adsorption constant of solute on the catalyst with increasing thermal levels. It is also to be noted that reactions carried out in heterogeneous photocatalysis display low activation energies. Moreover, most of the photocatalytic experiments are conducted at isothermal conditions (usually at room temperature), and therefore, temperature changes do not play a major role (Chen and Ray, 1999). 

Some of the facts that Hasted et al. established are shown in Table 2.11, They found that the lowering of the dieleetrie eonstant of 1 M solutions is in the range of 10-20%. This ean be nieely explained by taking the water in eontaet with the ion as dielectrically saturated (unable to orient on the demand of the external field), but still having a dieleetrie eonstant of only 6, eompared with the value of 80 for bulk water unaffected by ions. The table shows the number of water moleeules pa ion pair that one has to assume are saturated (i.e., irrotationally bound in the vicinity of each ion) to make the above model come out right (i.e., reproduce the measured dieleetrie constants of solutions). This model leads to a very simple equation for the dielectric constant of a solution ... 

Studies of the dielectric constant of solutions and the relaxation times of water in the presence of ions have been refined since the 1980 s and indeed difficulties do turn up if one looks at data from measurements over large frequency ranges. The variation of the dielectric constant with frequency has been studied particularly by Winsor and Cole, who used the Fourier transform of time domain reflectometry to obtain dielectric constants of aqueous solutions and the relaxation times in them. Their frequency ranges from over 50 MHz to 9 GHz. 

Measurements of dielectric constants of solutions allow the deduction of not only how many waters are taken up and held irrotationally by ions, but also how the ions affect the frequency of the movements of molecules near them. This will help a person interested in electrostatic effects calculate the local pressure near an ion (Section 2.22.1). 

In most of the modem versions of the Debye-Hiickel theory of 1923, it is still assumed that the dielectric constant to be used is that of water. The dielectric constant of solutions decreases linearly with an increase in the concentration of the electrolyte. Using data in the chapter, calculate the mean activity coefficient for NaCl from 0.1 M to 2 M solutions, using the full equation with correction for the space taken up by the ions and the water removed by hydration. Compare the new calculation with those of Stokes and Robinson. Discuss the change in a you had to assume. 

Concerning the 77 dependence of the rate constant of solution reactions, most often investigated experimentally is photoinduced EJZ (trans/cis) isomerization of stilbenes. The isomerization takes place by surmounting over a transition-state barrier on the excited-state potential surface. The reaction is very fast with a rate constant on the order of 10 s- due to a small height (of about 15 kj/mol) of the barrier. The rate constant observed in solvents decreases as 77 increases. To be more exact, however, k often decreases more slowly than 77 , describable by a fractional-power dependence on r/ as kgf, 77- with 0 < a < 1. Therefore, the 77 dependence of k ), deviates from that expected from the Kramers theory. 

Flux of component i, mol/m s Flux of solute, mol/m s Flux of solvent, mol/m s Kozeny-Carman constant Distribution constant of solute Membrane thickness, m Phenomenological coefficients... 

Dipole Moments and Dielectric Increments of Amino Acids, Peptides and Proteins. Dielectric constants of solutions of amino acids, peptides and proteins always are higher than those of the pure solvent, even when the solvent is a liquid as polar as -water In dilute solution the dielectric constant, s, is a linear function of the solute concentration, c... 

Wyman, J. jr. The Dielectric Constant of Solutions of Dipolar Ions. Chem. 

At the equivalence point [K+] = [NOT] and [NOT] — [K+] is a measure of the distance from that point. If n is the number of increments of potassium chloride solution added to V liters (assumed to be constant) of solution, and nQ is the value of n at the equivalence point, then... 

It is unfortunately true, however, that electric moments of substances determined from measurements on the dielectric constants of solutions are not independent of the solvent used, as has been shown by Muller20 and others. Some typical values of the apparent electric moment, ft, of nitrobenzene in a series of solvents are given in Table III, from the work of Jenkins.21 For this case, at least, there is a tendency... 

By measuring the static dielectric constant of solutions of polar polymers in nonpolar solvents, one may calculate a statistical mean dipole of the macromolecule. With polar solvents interesting information can be obtained concerning the interaction between polymer and solvent molecules. Finally the study of relaxation phenomena, including the accurate determination of the critical frequencies may lead us to a better knowledge of the statistical unit and of its interaction with its environment. 

---