Recent chemical patents

Microscopic dissociation constants have been used frequently (1,4) and complete sets of microscopic constants have been calculated (1) for substances with two (or more, in the case of extreme symmetry; see below) dissociating groups. Some microscopic constants have also been evaluated for more complicated cases (1), but apparently not the complete set for any particular compound. In this paper a simple mathematical procedure for accomplishing this will be presented and applied to glutamic acid. These constants for glutamic acid are to be used elsewhere (5) in a study of the electrostatic contribution to hindered rotation in microscopic ions of this substance.In order to extend the method in an approximate manner to compounds for which not all of the necessary experimental dissociation constants are available, electrostatic charge effects are considered.In connection with the development of the general procedure, certain analogies, which may be instructive, between the relative free energies of microscopic ions and spectroscopic energy levels, and between the microscopic dissociation constants and spectral lines, will be pointed out. IIIn the following discussion we shall speak only of the dissociation of protons, so that a single treatment will apply equally well to substances usually classified separately as acids, bases, and ampholytes.In considering a particular ampholyte (we shall use the term "ampholyte" to include the three classes mentioned above), let n + m be the maximum number of dissociable protons, where n is equal to the number of uncharged acid groups (e.g., -COOH) and m is equal to the number of cationic acid groups (e.g., -NHj). Then there are 2"~m microscopic ions and ( + microscopic dissociation constants to be taken into account (4). These ions and constants will all be different in unsymmetrical molecules such as those of most amino acids. But, at the other extreme, if all the acidic groups are identical (e.g., in ( )7 ( 6)), there will be only n + m + 1 different ions and n + m different dissociation constants (either n or m is equal to zero). For cases where there is some symmetry, but not of such a high order, the number of different ions and equilibrium constants will be intermediate (e.g., in dithionic (7) and pyrophosphoric (7) acids).Writing p = n + m, only 2P -1 of the p2p~1 microscopic dissociation constants mentioned above are independent (4). Hence, when there is no symmetry, 101

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confidence: 99%

Relative Free Energies and Dissociation Constants of Microscopic Ions

Hill¹

1944

“…As pointed out by Yosburgh and Cooper (12), a plot of the difference between observed optical density and the theoretical (calculated on the assumption of WAVE LENGTH -MILLIMICRONS the existence of a straight-line relation between the optical densities of the component solutions) against the solution composition (,r) should show a maximum (or minimum) at some solution composition related to the constitution of the complex ion. Furthermore, if but a single complex be formed, all maxima should fall at the same ,r value regardless of the wave length selected, providing the spectra of the mixture and the colored component differ at that wave length (5).…”

Section: Discussionmentioning

confidence: 99%

“…In view of the uncertainty existent relative to the compositions of these complex ions, it was felt that some further clarification, particularly in terms of the characteristic colors of the systems, was desirable. Recent successes in application of the absorption of monochromatic light to determination of the compositions of complex ions (5,6,12) through a modification of Job's method of continuous variations (7) suggested a suitable experimental approach. Although Job was apparently unsuccessful in applying his method to copper(II)chloride ion systems (8), the modified procedure has been found to be entirely applicable under the conditions here employed.…”

Section: Introductionmentioning

confidence: 99%

An Application of the Method of Continuous Variations to Complex-Ion Formation in Copper (II) Salt Solutions Containing Chloride Ion

Moeller¹

1944

“…The application of the boundary conditions for this case, the resolution of the resulting set of equations, and the use of eq 31 lead to the following expression for the reaction potential: = ( ) r"A"a"Ao) + r"m(t'ai,x,) x EnmPn"(il)eime (43) e"m(x.) j j ¿"+ with the definitions In an analogous way to the case of the prolate with one layer, we obtain for the Helmholtz free energy: The verification of eq 49 can be carried out in an analogous way to eq 32, i.e., by taking the limiting case when two neighborhood dielectrics become identical in their permittivity properties.…”

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confidence: 99%

“…surface tension measurements.40,41 On the other hand, continuum models are valid when only Columbic forces are present. If short-range interactions are important, a good selection is to use the continuum + supermolecule approach.Finally, the selection of the cavity's geometrical parameters may start by considering the barycenter of the nuclear charges and the molecular volume.19,42,43 (39) Pierotti, R. A.Chem. Rev.…”

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confidence: 99%

Free energy of a charge distribution in a spheroidal cavity surrounded by concentric dielectric continua

Gómez-Jeria¹,

Morales-Lagos²

1990

sumably, mercaptoethanol selectively blocks Pd surface sites for activating bicarbonate, thus favoring the transfer of conductionband electrons to H2-evolving sites.A comparison of the selectivity factor can be made between the Pd-Ti02 systems and the previously examined p h o t~s y s t e m~~ consisting of the photosensitizer deazariboflavin, dRFI, the electron mediator MV2+, the electron donor oxalate, and the catalyst Pd(@-CD,60 "C) colloids. The best selectivity factor of the PdTi02 systems (SF = 2.3; see Table I) is larger than that of dRFI/MV2+/oxalate/Pd(P-CD,60 "C) (SF = 0.013), indicating that the former exhibits lower selectivity for HC0,-reduction with respect to H 2 evolution than the latter. The basis for this difference in selectivity remains to be established, however.In conclusion, electron transfer from Ti02 to properly prepared catalytic Pd surface sites promotes the reduction of C02/HC0,-to formate. The selectivity exhibited by the Pd-Ti02 particle systems is quite noteworthy in relation to other semiconductorbased systems, which generate a broad distribution of products. Specific sites on the Pd surface favor C02/HCO< reduction over H2 evolution. The experimental results reported here as well as those of others2" suggest that other metals might exhibit selectivity in catalyzing the reduction of CO, to other desirable organic photoproducts.We present a theoretical treatment for the Helmholtz free energy of an arbitrary discrete charge distribution in a central prolate or oblate spheroidal cavity surrounded by two and three concentric dielectric continua of the same symmetry. The electrostatic interaction is accounted for by a multipolar expansion. This model permits us to consider in a simple way nonlinear dielectric effects and the nonsphericity of solute molecules. The results are presented in a suitable form to discuss them in terms of a virtual polarization charge distribution. Also, we give an explicit expression for the contributions coming from the zeroth-order multipole moments for any number of shells.