Molecular Imaging. Markus Rudin

rel="nofollow" href="#fb3_img_img_72666e19-075e-5053-a420-878b682e7148.png" alt="image"/> As in the preceding reaction series discussed in Ref. [2], the rate constant k for the forward reaction in Eq. (3.103) can be inferred from the overall bimolecular rate constant k₁ and the first ionization constant K₁ of QH₂ (k = k₁[H⁺]/K₁). The k’s and the values of calculated from them using Eq. (3.1) are given in Table II.

      It can be shown that the ΔF⁰ of reaction (3.103), needed for the estimation of is given by Eq. (3.104):

Table II. Kinetic and thermodynamic data for O₂ + QH⁻ reaction at 30^∘C^a

^aAll free energy units are in kcal mole⁻¹. ^bThere is an appreciable uncertainty in and therefore in ΔF⁰, of an amount α, where α may be about 0 to +5 kcalmole⁻¹, according to Latimer [73]. This uncertainty introduces a corresponding uncertainty in the which may be about 3 kcal mole⁻¹ less than those reported in this table. ^cx denotes the unsubstituted compound and y denotes the substituted compound.

      where is the standard oxidation potential of QH₂ (QH₂ = Q + 2H⁺ + 2e), is that of

      Note that M. is using here Latimer’s standard oxidation potentials whose values are opposite of IUPAC’s standard reduction potentials [73].

“F is the Faraday, and K_S is the equilibrium constant of reaction (3.100) for the formation of semiquinones or indophenols. The ΔF⁰’s of Table II were estimated using the known [74] the estimated [73] the value of −RT ln K_S discussed in the previous section (2.3kcal mole⁻¹) and the known [47] K₁.”

      Introducing into Eq. (3.4), these ΔF⁰’s and the effective radii later deduced, the values of Table II were computed.

       3.32.Excess Entropy of Activation

      In this section, M. shows how it is possible to estimate unknown entropy values.

      “All the entropy data needed for the estimation of and the experimental and the calculated excess entropy of activation of the electron transfer step, Eq. (3.103), are not available. However, some estimate of the undetermined entropy values may be made.

      For example, just as in the case of the ferric-hydroquinone reaction, ΔS^*_expt can be calculated from the frequency factor of the pseudo-rate constant and the entropy of ionization of QH₂, S₁.

      Assuming that S₁ equals the value for the hydroquinones and water (which are later shown to be equal) one finds in this way that cal mole⁻¹ deg⁻¹.

      The term is seen from the approximate equation, Eq. (3.10), to be about S⁰(1 + ΔF⁰/λ)/2 since e₁e₂ and are each equal to zero in reaction (3.103). In reaction (3.103), it is also expected that the translational, vibrational, and rotational entropies of the reactants are each about equal to those of the products.” Because of the very similar chemical structure of reagents and products.

      “Accordingly, if the entropy change S⁰ of reaction (3.103) were appreciable, the main contributions to it would arise from possible differences in the entropy of solvation of QH⁻ and O⁻₂. This would not be expected to be large so that S⁰/2 should be relatively small. Further, ΔF⁰/λ is calculated to be about 0.3, so we conclude that is small, in agreement with the estimated small value of

       3.33.Discussion

      “A comparison of Tables I and II shows that the rate constants of the redox step in the two series of reactions considered here differ from each other by a factor 10⁹ on the average. This difference stems from the considerable difference in the standard free energy change ΔF⁰ of the redox step in the two cases, one being about—13kcal mole⁻¹, the other perhaps lying between +17 and + 12kcal mole⁻¹, depending on the correct value of This difference in turn is related principally to the differences between standard oxidation potentials of the ferrous ion and of the oxygen molecule ion.

      According to the theory developed in Part I, the standard free energy change affects the reaction rate in the following way. During an ET step, there is first a reorganization of the solvent molecules about the reacting ions prior to the jump of an electron from one reactant to the other. Now, for a given