Electrostatic Considerations

In Chapter 8 we discussed the double-layer capacitance that is always present at the metal/solution interface. The value of a capacitance, per unit surface area is given by 

when a current step is applied, the potential will approach its final value following the equation 

It should be noted that the double layer capacitance is not a capacitor in the usual sense, because it has only one metal plate. The other side of this capacitor is somewhere in the solution, depending on the theory assumed and on the composition of the solution. Nevertheless, it behaves as a regular capacitor, except for the fact that its capacitance is often a function of potential 

Capacitors have been used in electronic devices for a century or longer. Their importance hinges on the simple equation 

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Chemical shifts can be observed for atoms in both organic and inorganic materials. Generally, E increases as the oxidation state of the atom increases. This dependence can be rationalized on the basis of simple electrostatic considerations in terms of an increased attraction for the electron by the atom making it that much harder to remove. These chemical shifts can range in magnitude from <1 eV to >10 eV. 

Turning next to the unitary part of AS0, this is given in Table 36 under the heading — N(dL/dT). It was pointed out in Secs. 90 and 106 that, to obtain the unitary part of AS0 in aqueous solution, one must subtract 16.0 e.u. for a uni-univalent solute, and 24.0 e.u. for a uni-divalent solute. In methanol solution the corresponding quantities are 14.0 and 21.0 e.u. In Table 36 it will be seen that, except for the first two solutes KBr and KC1, the values are all negative, in both solvents. It will be recalled that for KBr and KC1 the B-coefficients in viscosity are negative, and we associate the positive values for the unitary part of the entropy, shown in Table 29, with the creation of disorder in the ionic co-spheres. In every solvent the dielectric constant decreases with rise of temperature and this leads us to expect that L will increase. For KBr and KC1 in methanol solution, we see from Table 36 that dL/dT has indeed a large positive value. On the other hand, when these crystals dissolve in water, these electrostatic considerations appear to be completely overbalanced by other factors. 

In contrast, thermodynamic as well as spectroscopic properties of core water in AOT-reversed micelles are similar to those of pure water. Together with electrostatic considerations, this suggests that the penetration of counterions in the micellar core is negligible and that a relatively small number of water molecules are able to reconstruct the typical extended H-bonded structure of bulk water. 

In view of the similarities between the bonding models for carbene and carbyne complexes it is not surprising that similar patterns of reactivity should be observed for these compounds. Thus nucleophilic and electrophilic additions to the metal-carbon triple bond are anticipated under appropriate circumstances, and both orbital and electrostatic considerations will be expected to play a role. 

Heats of reaction and bond dissociation energies allow the estimation of the feasibility of homolytic processes, as these are largely — but not solely — governed by thermochemical effects. The quantitative treatment of heterolytic processes, however, presents a far more difficult problem. Basic electrostatic considerations indicate that the dissociation of a covalent bond into positive and negative ions is inherently a highly endothermic process. It will be facilitated by any mechanism that allows dissipation or stabilization of the incipient charges. Chemists have come to differentiate these... 

The obvious measures of lowering superficial gas velocity in the bed and the selection of wall and/or particulate materials certainly exist. But, in a given process, there is often no practical way to implement such solutions. Fluidization conditions are dictated by the application for which the bed is intended furthermore, the choice of particulate materials can seldom be made on the basis of electrostatic considerations. 

Amis proposed Equation (3)18 for the reaction rate constant involving a limiting case of head-on approach of an ion to a neutral dipolar molecule from electrostatic considerations, as would be the case for metal ion catalysts and neutral C = 0 or P = O substrates. This expression relates the natural log of the rate constant in a medium of dielectric constant (D) to the charge on the ion (Ze), the dipole moment... 

The interactions between the ions originally in solution and any added LiCl are best treated within the context of the Debye-Elttckel theory, which derives from a knowledge of electrostatic considerations. 

The stability constant for the outer sphere complex depends on the charge of the reacting species and the ionic strength of the medium, and can be readily calculated from electrostatic considerations. 

The approach that we will follow is known as the Debye-Hiickel theory. The activity laws discussed in the following are derived from a knowledge of electrostatic considerations, and apply to ions in solution that have an energy distribution that follows the well-known Maxwell-Boltzmann law. Strong electrostatic forces affect the behaviour and the mean positions of all ions in solution. 

Helmholtz Wied. Ann. vii, 337,1897) showed from electrostatic considerations that if M be the electric moment per sq. cm. of the. .interface expressed in electrostatic units then the difference of electric potential across the interface was related to the electric moment by the expression... 

The cloud point phenomena as a lower consolute solution temperature is becoming better understood in terms of critical solution theory and the fundamental forces involved for pure nonionic surfactant systems. However, the phenomena may still occur if some ionic surfactant is added to the nonionic surfactant system. A challenge to theoreticians will be to model these mixed ionic/nonionic systems. This will require inclusion of electrostatic considerations in the modeling. 

The regiochemistry of ketene iminium salt cycloadditions can also differ from ketene cycloadditions. Whereas reaction of styrene with a series of ketene iminium salts gave 3-phenyI-cyclobutanones7 (60-70% yield) similar to the regiochemistry of ketene cycloadditions, reaction with a series of acrylates and a,/J-unsaturated ketones gave cyclobutanones 5 with regiochemistry opposite to what would be expected from electrostatic considerations of ketene cycloadditions.s... 

From simple electrostatic considerations it is expected that the rate of condensation will depend strongly on the charge of the mononuclear species. This is qualitatively confirmed by the observation that condensation of the neutral species Co(NH3)2(N02)2(OH2)(OH) is much faster than condensation of +2 charged species such as Co(tach)(H20)2(OH)2+ or Co(tren)(H20)(OH)2+ (174). 

Exercise 18-5 Simple electrostatic considerations suggest that the acidities of... 

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