Molecular Imaging. Markus Rudin

for the cited polyatomic ions would be approximately the actual crystallographic radii. This is also consistent with the assumption that only the first layer of the water molecules about a monoatomic ion is saturated, since a hydrated monoatomic ion has about the same radius as these polyatomic ions.

      With a slightly different for an ion when it is a reactant and when it is a product it was suggested that a mean value for a be adopted.” “The crystallographic radii of Fe⁺², Fe⁺³, and H₂O are [2] 0.75, 0.60, and 0.72. The mean of the first two is 0.68Å.”

      The refinements of the theory will take into account the effect of the radii variations on the reaction rate.

      When organic ions are considered one has to consider two new features. “First, the ion is far from being spherical and, second, it is possible that that the effective radius a could be quite different when this particle is a charged reactant and when it is an uncharged product. This is discussed later, where it is inferred from entropy data that the effective polarizing radius of a hydroquinone-like ion such as HOC₆H₄O⁻ is about the same as that of the hydroxyl ion. It is further suggested that the dielectric saturation around this group when it is a charged particle be neglected as a first approximation, and that a equals the crystallographic radius of the oxygen group 1.4Å. This approximation can be removed by a refinement of the theory.”

       3.29.Excess Free Energy of Activation

      “Experimental values of ΔF^* were calculated from the rate constant k given in Table 1, using Eq. (3.1) and setting Z equal to 10¹³ liter mole⁻¹ sec⁻¹ in that equation. These values are reported in Table I.

      Using the effective radii and the ΔF⁰’s deduced in the preceding section and setting D_op = 1.8 and D_s = 78.5 at 25^∘C, values of were obtained with the aid of Eqs. (3.2)–(3.4), and are given in Table I. These results will be discussed in detail later.”

An important note: M. later [71] used for Z the value 10¹¹ liter mole⁻¹ sec⁻¹ instead of 10¹³ liter mole⁻¹ sec⁻¹ of Ref. [72].

       3.30.Excess Entropy of Activation

      “Experimental values for the excess entropy of activation of reaction (3.99), were calculated from the data.”

      It may be instructive to report, from note 26 in Ref. [2], how this calculation was done.

      The pseudo-rate constant k₁ of Eq. (3.97) has an activation energy E₁, say, and a frequency factor A₁ so that k₁ = A₁ exp(−E₁/RT). Values of A₁ were determined experimentally. The rate constant k, Eq. (3.99), has a frequency factor A, say, which can be calculated from the known A₁ [51] and the known [70] entropy of ionization of QH₂, ΔS₁ say. It is found that A = A₁[H⁺] exp(− S₁/R). According to Eq. (3.7), is then found by setting A = Z exp(ΔS^*/R), Z being in Ref. [2] equal to 10¹³ liter mole⁻¹ sec⁻¹ [72]. But see the previous note on the correct value of Z.

      “The values of were computed from Eq. (3.9) using the previously determined radii and ΔF⁰ and using the calculated ΔS⁰.” From note 27 in Ref. [2]: “ΔS⁰ = −∂ ΔF⁰/∂T and therefore according to Eq. (3.101), where ΔS and ΔS_S are the standard entropy changes in reactions (3.97) and (3.100), respectively [51, 70]. Since the sum of the translational, rotational, and vibrational entropies of the reactants and of the products of reaction should be about the same, it may be assumed that S_S is essentially zero.”

      “In this way was found to be 46, 57, 47, and 44cal mole⁻¹ deg⁻¹, and to be 36, 38, 36, and 31 entropy units, for the 2,6-dichloro, benzo, tolu, and duro hydroquinones, respectively. The average of the former group of values is 49 and that of the latter is 35. Values of were also computed from the approximate equation, Eq. (3.10). They agreed well with the exact calculated values, within about one and a half entropy units.”

       (b)AEROBIC OXIDATION OF THE LEUCOINDOPHENOLS

       3.31.Excess Free Energy of Activation

      “The overall reaction of the leucoindophenols with dissolved oxygen is represented by Eq. (3.102), where QH₂ denotes a leucoindophenol such as HOC₆H₆NHC₆H₆OH, and Q denotes the corresponding indophenol HOC₆H₄NC₆H₄O.

      A mechanism consistent with the data [51] involved the ionization of QH₂ to QH⁻, which then transferred an electron to O₂:

      This