Disproportionation constant

Translational functions in eq. (100) cancel out because of the approximation adopted, the vibrational functions also cancel. The logarithm of the ratio of rotation functions possesses a constant value of —.246. The contribution of the exponential term is considerably higher and therefore determines the value of the disproportionation constant. Theoretical values of log K listed in Table X... 

In radical chemistry, one often needs to estimate a priori a value of the disproportionation constant. Before attempting to do this, let us start with the following consideration. In general, each closed-shell molecule can be converted to radical ions by a removal or an uptake of an odd number of electrons, and to polyions by a removal or an uptake of an even number of electrons. This statement can be expressed schematically as... 

Figure 15, Plot of the logarithms of disproportionation constants against the coulomb repulsion integrals for a series of 1,3,3-trimethylindolenin violenes (174).

A typical inorganic redox system of this type involves the equilibrium between metallic copper and copper(II) ions. In the absence of a complex-former the disproportionation constant is large and a solution of Cu+ ions is very unstable. However, in the presence of ammonia, copper(I) ions are bonded in a complex, constant K decreases and the -j8 curve exhibits three inflection points. 

Drastic changes in the disproportionation constants occur when alkaK cations are used instead of tetraalkylammonium ions. Typically, the potentials of the radical anion formation are less affected than that of the dianion formation. In the presence of alkali cations, AE shifts may reach values of more than 600 mV, which correspond to an increase in the K constant of more than 10 orders of magnitude [52, 53]. 

Fig. 1.15 Second-order superoxide disproportionation constant vs pH at 25 °C. Potassium superoxide ( 1 mM) in pH a 12 was mixed in a stopped-flow apparatus with buffers at various pH s and the change in absorbance at 250 nm monitored. The decays were second-order and data were treated in a similar manner to that described in Fig. 1.3. The full line fits Eqn. (1.231) using the parameters given in the text. Reprinted with permission from Z. Bradid and R. G. Wilkins, J. Am. Chem. Soc. 106, 2236 (1984). (1984) American Chemical Society.

It may not always be clear from the conditions for electrochemical generation which species is the effective EGB. In some cases a possible complication is fast disproportionation of radical-anion to dianion (Scheme 12). This can mean that for electrogeneration at, say, the first reduction potential E Jl) it is possible for either the radical-anion or the dianion to act as base, depending on the relative rates of protonation by acid HA (k and kp, the value of the disproportionation constant (Kj), and the rate at which equilibrium between radical-anion and dianion is attained. In principle, of course, it is also possible that electrogeneration at E p2) could lead to a situation where radical-anion was the effective base as a consequence of rapid reproportionation causing it to be present in high concentration, thus offsetting its probably much lower kinetic basicity. These points are discussed in more detail on p. 157. 

However, equilibria may be far from random when fluorine is involved. Table I shows the effects of the donor on disproportionation constants Kl and Kz (127) for redistribution of fluorine and chlorine ... 

The disproportionation constant K of the (S,S)-(S,S) combination [or (R,R)-(R,R) combination] is much larger than that of the (S,R)-(S,R) combination the ratio of the constant Ar[(S,S)-(S,S)]/Ar[(R,S)-(R,S)] = 4.0 for R = 1-naphthyl, 1.6 for R = 1-phenyl, and 1.8 for R = 1-cyclohexyl. Since the disproportionation is mainly controlled by the comproportionation rate constant, which is small for the strong interaction in a closed conformation [71], the reported results suggest that the homochiral pair adduct involves a stronger intermolecular interaction than the heterochiral pair adduct. 

Iodine monofluoride (IF) is unknown except in minute amounts observed spectroscopically. It is apparently too unstable with respect to disproportionation to IF5 and I2 to permit its isolation. The other isolable diatomic compounds have varying degrees of stability with respect to disproportionation and fall in the following stability order, where the numbers in parentheses represent the disproportionation constants for the gaseous compounds and the elements in their standard states at 25°C C1F (2.9 X KT") > IQ (1.8 X 10"3) > BrF (8 X KT3) > IBr (5 X 102) > BrCl (0.34). 

Details of the electrochemical reduction of 36 and the possible existence of the monoanionic intermediate (36) (R = Ph) are not yet settled. The neutral dimer is reported to undergo a single, chemically reversible, two-electron reduction at a mercury electrode (E = -1.26 V in CH3CN) (79), although the process was less reversible (R = Ph or Me) in propylene carbonate (81) and totally irreversible at platinum (79). The peak separation of 45 mV (at mercury), which contrasts with the expected value of 30 mV for a reversible two-electron reduction, is reported to be essentially independent of the cyclic voltammetric scan rate (79). Although this seems to imply that the overall process may consist of two closely spaced one-electron waves, mixing solutions of [36] (R = Ph) and 36 (R = Ph) did not produce a sufficient concentration for [36] (R = Ph) to be detected by ESR spectroscopy. Thus, the high disproportionation constant for the reaction ... 

The most widely studied examples are cyclooctatetraene (COT,I) and its derivatives. In such conventional aprotic solvents as DMF, dimethyl sulfoxide (DMSO), or acetonitrile containing tetraalkylammonium salts, two distinct one-electron reduction waves are observed at approximately —1.64 V and —1.80 V versus SCE, with AE separations varying from —130 V to —240 mV [43,53-56]. In THF and NH3, this separation reduces further [57-59], and in the presence of all alkali salts [60,61] even two-electron reduction waves with positive AE differences were obtained, indicating large disproportionation constants. The unusually small separation of the two redox steps in comparison to the... 

Ga and Ga n.m.r. spectra of acetonitrile solutions of mixtures of gallium halides have been analysed to determine the disproportionation constants of GaX3Y , GaX2YI, and GaXjY" (X, Y = C1, Br, I). °... 

Figure 6. Device for determining the disproportionation constants of aromatic hydrocarbons as a function of temperature. (Reproduced from reference 8. Copyright 1977 American Chemical Society.)...

The apparent disproportionation constant corresponding to reaction 25 is the following ... 

Disproportionation constants, Aidisp, have been measured from oxidation potentials in acetonitrile and other solvents for the thianthrene, 4,4,-dimethoxybiphenyl, and 9,10-di-p-anisylanthracene cation radicals (Hammerich and Parker, 1973). In acetonitrile they are, respectively, 2 3 x 10-9, 2-7 x 10-5 and 1-9 x 10-4, indicating that these cation radicals, like the violenes have a very small tendency toward disproportionation. 7sfdiSp f°r thianthrene cation radical (l.xl0-9) and the tetrathioethylene cation radical (5xl0-8) have been measured in molten aluminum chloride-sodium chloride at 140° (Fung et al., 1973). 

The fact that the disproportionation constant used here described the spin concentration profile well, suggests that the polaron oxidation potential to the bipolaron state is slightly more positive than the oxidation... 

Thus, as we have already found out, the data of chronopotentiometric experiments cannot be presented in simple form such as Eq. (2.9) or (2.10) to calculate the equilibrium stability constants of LVIs by a standard routine. In our opinion, this method is more appropriate for the studies of intervalence reaction kinetics (see the next chapter) rather than equilibrium. However, some information on the intervalence equilibria also can be obtained in certain cases. For example, equilibrium disproportionation constant may be estimated from the shape of the wave, as was pointed out above, ii K > A and the plot in semi-logarithmic coordinates is typically S-shaped as in Fig. 2.10. 

At the concentrations of Ge(lV) equal to or less than 0.75 x 10" mol cm , the formation of Ge(II) intermediate brings about no separate transition time provided the restriction (3.8) holds true. However, the chronopotentiometric curves of the second stage of the process are typically S-shaped when being plotted as functions of the time variable ln(y — v/F )/ /( where the current time is substituted by = y/i— (see Sect. 2.4.3). This implies the formation of Ge(ll) intermediate with a disproportionation constant larger than 4. The kinetics of the Ge(ll) decomposition reaction manifests itself at higher concentrations (plot 2b in Fig. 3.2). 

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