Exchange constants, derivation

J, exchange constant derived from the Korringa slope 5c, Overhauser relaxation rate (relaxation from electrons to ion)... 

Values of the phenomenological exchange constant derived from measurements on rare eartb-aluminum compounds are listed in table 18.15, those for the RX compounds (X = N, P, As, Sb, Bi) are listed in table 18.16, and those for other nuclei (B, Sn, Pt, Cu, etc.) are in tables 18.17 and 18.18. In cases where two or more inequivalent sites occur in the structure of the compound, the Knight shifts at the different sites are observed to be different, leading to different values of the constant st- Examples of this type are furnished by the RsAl, compounds, the RB4 compounds, and the RPts compounds. 

The value of ket > 6 x 108 cm8mol ls - - in the usual units for a bimolecular rate constant for homogeneous solution is > 6 x 105 M-ls l. The ferrocene self-exchange constant is 5 x 106 M-Ts-1 (29). Various cross reactions of substituted ferrocenes and ferricenium derivatives have bimolecular rate constants that exceed 10 M - -s l where the equilibrium constant exceeds unity (30). Further, in the cross reactions, the rate constants varied by almost two orders of magnitude for a change in driving force of -0.25 V (30). Thus, the data in Table II relating to the ferrocene-like molecules is reasonable. 

The exchange constants are also obtained from expressions like equation 94 that are derived with more sophisticated statistics (589). 

Figure 15.7a and b show the factor Fq for 1-2 and 2-4 exchangers, respectively, derived on the assumptions that the overall heat-transfer coefficient is constant and that all elements of a given fluid stream have the same thermal history in passing through the exchanger. As before, Fq is so defined that when... 

K represents the real equilibrium constant for an exchange between Z = 0 and Z = Zmax. The standard free energy of exchange is obtained as AG = — RT In K. The enthalpy of exchange is derived from the Vant Hoff equation, and the entropy change is calculated from the AG and AH values ... 

Nevertheless this paper is helpful to judge hydrolysis constants derived by cation exchange methods. The different pH-dependence of the sorption behaviour of Th(IV) onto different cation exchange materials shows that the evaluation of pH-dependent distribution (sorption) coefficients requires not only the fitting of the forma-tion constants logj (or log ) of the hydroxide complexes formed in solution but also of their equilibrium constants logio A ,m for the sorption onto the cation exchange material (CE) ... 

The silicate anions are dynamic structures and undergo very rapid intra- and inter-molecular exchange on a millisecond scale. However, first-order rate constants derived... 

The equations for any other exchange reaction, and indeed for any other mechanism, can be derived similarly. However, in most cases, the rate equations for isotope exchange are derived by the method of King and Altman and various extensions of the same also, the rate equations may be derived efficiently by the net rate constant method (Chapter 4). In most cases, the rate equations for isotope exchange are far too complicated to permit the determination of the usual kinetic constants. Nevertheless, ffiere are a number of simplifying assumptions which will permit the derivation of manageable rate equations in specific cases (Boyer, 1959 Fromm eta/., 1964 Darvey, 1973). 

Parameters derived by means of mean field analysis of experimental data 5 3j represents the 3d spin while the exchange constants J 2 Jj2 refer to the... 

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