Dielectric constant of the solvent

At large distances, 0 and w.j r) qfljzry ssxt z is the macroscopic dielectric constant of the solvent. 

Flere u. j(r,T,P) is the short-range potential for ions, and e is the dielectric constant of the solvent. The solvent averaged potentials are thus actually free energies that are fimctions of temperature and pressure. The... 

If this electrostatic treatment of the substituent effect of poles is sound, the effect of a pole upon the Gibbs function of activation at a particular position should be inversely proportional to the effective dielectric constant, and the longer the methylene chain the more closely should the effective dielectric constant approach the dielectric constant of the medium. Surprisingly, competitive nitrations of phenpropyl trimethyl ammonium perchlorate and benzene in acetic anhydride and tri-fluoroacetic acid showed the relative rate not to decrease markedly with the dielectric constant of the solvent. It was suggested that the expected decrease in reactivity of the cation was obscured by the faster nitration of ion pairs. 

The dyes prepared in this way show a positive solvatochromism as the dielectric constant of the solvent increases, indicating that they possess a predominantly nonpolar structure. Substituents on the phenyl group in the 4-position of the selenazole ring have little influence on the absorption spectra. 

EIectrosta.tlcs. Electrostatic interactions, such as salt bridges, result from the electrostatic attraction that occurs between oppositely charged molecules. These usually involve a single cation, eg, the side chain of Lys or Arg, or the amino terminus, etc, interacting with a single anion, eg, the side chain of Glu or Asp, or the carboxyl terminus, etc. This attractive force is iaversely proportional to the distance between the charges and the dielectric constant of the solvent, as described by Coulomb s law. 

Remember that e is the dielectric constant of the solvent. The examples show the value for cyclohexane (2.0). 

Mercaptoquinolines of this type exist in the zwitterion or the zwitterion-extended quinone form to a greater extent than do the analogous hydroxy compounds ° (see Table V and Section II,R), and the color of 8-mercaptoquinoline has been attributed to the zwitterion structure.The concentration of the zwitterion decreases as the dielectric constant of the solvent decreases in the order H2O > MeOH > EtOH > Bu OH as indicated by the change in the molecular extinction coefficient. ... 

J mol ). This is additional evidence in favor of rate limitation by inner diffusion. However, the same reaction in the presence of Dowex-50, which has a more open three-dimensional network, gave an activation energy of 44800 J mol , and closely similar values were obtained for the hydrolysis of ethyl acetate [29] and dimethyl seb-acate [30]. The activation energy for the hydrolysis of ethyl acetate on a macroreticular sulphonated cationic exchanger [93] is 3566 J mol . For the hydrolysis of ethyl formate in a binary system, the isocomposition activation energy (Ec) [28,92] tends to decrease as the solvent content increases, while for solutions of the same dielectric constant, the iso-dielectric activation energy (Ed) increases as the dielectric constant of the solvent increases (Table 6). 

At large distances the curve of Fig. 8b is a plot of — (c2/ r)> where t is the macroscopic dielectric constant of the solvent at the temperature considered. For small values of r the curve deviates from this value but at every point the slope of the curve must represent the mean intensity of the mutual attraction or repulsion at the particular temperature considered. If the curve of Fig. 86 for dissociation in solution is to be useful, every point on this curve must belong to the same temperature T. That is to say, when we consider any change in the distance r between the ions, we are interested in an isothermal change in r. 

Let us now consider a pair of ions in aqueous solution from such a crystal. In the Debye-Hilckel theory it is assumed that in pure solvent, the mutual potential energy is — e2/ r, where e is the macroscopic dielectric constant of the solvent,2 until the ions come into contact with each... 

C is the alcohol concentration. The AAG°(C) plots against the inverse dielectric constant of the solvent showed that at low alcohol concentration all points measured are on a single straight line for all the alcohols used. At higher alcohol concentrations, however, the AAG° values are situated on different curves I45 One can conclude that... 

It should be noted that the properties of a CTC depend to a considerable degree on the conditions of their preparation. Temperature increase, in particular, favors the accumulation of complete charge transfer states in a CTC. In the case of a CTC obtained in solution, the increase of dielectric constant of the solvent has the same effect. The method of preparation of a CTC also affects the kinetic curves of the accumulation and depletion of complete transfer states arising at protoirradiation. 

Equations will be presented for three cases—the second-order reactions of two polar molecules, two ions, and one of each. The result in each case suggests a linear relation between the logarithm of the rate constant and the inverse of the dielectric constant of the solvent. 

Solvents have also been shown to play a role in the reaction mechanism in acidic solution, although there is no marked effect related to the dielectric constant of the solvent. 

Here, d is the radius of the cavity around the solute (given in A), the dipole fi is given in A and au, and d is the macroscopic dielectric constant of the solvent. The crucial problem, however, is that the cavity radius is an arbitrary parameter which is not given by the macroscopic model, making the results of eq. (2.18) rather meaningless from a quantitative point of view. A much more quantitative model is provided by the semimicroscopic model described below. 

However, a number of examples have been found where addition of bromine is not stereospecifically anti. For example, the addition of Bf2 to cis- and trans-l-phenylpropenes in CCI4 was nonstereospecific." Furthermore, the stereospecificity of bromine addition to stilbene depends on the dielectric constant of the solvent. In solvents of low dielectric constant, the addition was 90-100% anti, but with an increase in dielectric constant, the reaction became less stereospecific, until, at a dielectric constant of 35, the addition was completely nonstereospecific.Likewise in the case of triple bonds, stereoselective anti addition was found in bromination of 3-hexyne, but both cis and trans products were obtained in bromination of phenylacetylene. These results indicate that a bromonium ion is not formed where the open cation can be stabilized in other ways (e.g., addition of Br+ to 1 -phenylpropene gives the ion PhC HCHBrCH3, which is a relatively stable benzylic cation) and that there is probably a spectrum of mechanisms between complete bromonium ion (2, no rotation) formation and completely open-cation (1, free rotation) formation, with partially bridged bromonium ions (3, restricted rotation) in between. We have previously seen cases (e.g., p. 415) where cations require more stabilization from outside sources as they become intrinsically less stable themselves. Further evidence for the open cation mechanism where aryl stabilization is present was reported in an isotope effect study of addition of Br2 to ArCH=CHCHAr (Ar = p-nitrophenyl, Ar = p-tolyl). The C isotope effect for one of the double bond carbons (the one closer to the NO2 group) was considerably larger than for the other one. ... 

Solvent effects on the rate of the decarbonylation of MeCOMn(CO)5 were examined by Calderazzo and Cotton (50) and are presented in part in Table IV. In general they are very small, and no regular trends can be discerned. This virtual lack of dependence of the rate on the nature of the solvent and very little correlation between the rate and the dielectric constant of the solvent are typical of substitution reactions of metal carbonyls (J). In the light of the foregoing, a qualitative observation that CpFe(CO)2-COMe decarbonylates much more readily on treatment at reflux in nonpolar heptane or cyclohexane than in polar dioxane is somewhat intriguing 219). 

A detailed kinetic study of the reaction of trialkyl phosphites (44) with benzil has been carried out (see Chapter 2 for the reactions of a-diketones with trialkyl phosphites). The reaction is first-order in both phosphite and benzil and the rate constant increases with the dielectric constant of the solvent. The authors propose initial attack of phosphite at carbonyl carbon (45), in opposition to the original suggestion by Ramirez, who proposed initial attack at carbonyl oxygen. 

K = is the reciprocal Debye length and e, is the dielectric constant of the solvent. Through most of what follows we use the ideal conductor approximation, Eq. (66). Ionic effects will be considered in Section IV.D. 

In the relationship shown above, A and B are constants depending on temperature, viscosity of the solvent, and dielectric constant of the solvent, C is the concentration expressed in gram equivalents per liter, and Ac represents the equivalent conductance of the solution. A0 is the equivalent conductance at infinite dilution - that is, at C = 0, when the ions are infinitely apart from one another and there exists no interionic attraction, a represents the degree of dissociation of the electrolyte. For example, with the compound MN... 

The dielectric constant of the solvent in the microenvironment of the polymer chain has been shown to be different from that in the bulk solvent (19). This change in dielectric constant might enhance the nucleophilicity of the pyridine ring and therefore increase the rate of quaternization. The kinetic results are consistent with the observations of Overberger et al., (20), who showed that increased hydrophobic nature of the substrate led to faster reaction rates in nucleophilic catalysis. In the present case one would expect the butadiene copolymer to be more hydrophobic than the methylvinylether copolymer. An alternative synthesis of supernucleophilic polymers has been achieved using the following reaction sequence. 

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