Equilibrium constants for electron

The redox potential of CuIIL/CuIL couple is related to the equilibrium constant for electron transfer (KET) according to the equation ... 

The most important thing about Equations 17-6 and 17-7 is that the equilibrium constant for electron-transfer reactions can be calculated from standard electrode potentials without ever having to make experimental measurements. 

Equilibrium Constants for Electron Transfer from Contact Ion Pairs P+ TpM(CO)j- in Dichloromethane Solutions... 

In the late 1960s several major advances were made in the study of thermal electron reactions. These were based on the ECD, the extension of the magnetron method of studying electron molecule reactions to determine equilibrium constants for electron molecule reactions, and the invention of high-pressure thermal electron negative-ion sources for mass spectrometry [5-7], Electron swarms were also used to determine rate constants for thermal electron reactions [8, 9]. The electron affinities of molecules were measured using electron and alkali metal beams [10, 11]. Relative electron affinities were obtained from the direction of the reaction of a negative ion with a molecule [12, 13], Other major advances were photodetachment and photoelectron spectroscopy [14—17],... 

Figure 6.11 Ion intensities in an ICR cell containing benzoquinone and naphthoquinone at the indicated pressures, from [56]. The equilibrium constant for electron transfer gives relative electron affinities.

There are many other types of solution data that support the half-wave reduction potential and charge transfer complex data. These include the measurement of cell potentials or equilibrium constants for electron transfer reactions. Another important condensed phase measurement involving a negative ion is the determination of electron spin resonance spectra. In these studies the existence of a stable molecular anion is established and the spin densities can be measured [79]. The condensed phase measurements support the electron affinities in the gas phase and extend the measurements to lower valence-state electron affinities. 

Rate Constants and Equilibrium Constants for Electron Transfer Reactions of Aromatic Molecules in Solution... 

The separation of the redox potentials has enabled the three-electron reduced state with Fe heme b of PdNOR to be characterized spectroscopically. It was proposed that the thermodynamic barrier presented by the lower potential of heme b prevents the two-electron reduction of the binuclear center to avoid the formation of a stable inactive Fe -heme bj, NO adduct. However, a much smaller difference between E- of heme c and heme bj, was deduced from the equilibrium constant for electron transfer between the two hemes in the electron backflow experiments indicating that, as with CcO, the redox centers exhibit negative cooperativity. Thus reduction of the redox center with the lowest E- is more difficult when the other centers are already reduced resulting in an apparent decrease of E- of the center. 

The negative charge is shared equally by all three oxygens Stabilization of nitrate ion by electron delocalization increases the equilibrium constant for its formation... 

Table 17 3 compares the equilibrium constants for hydration of some simple aldehydes and ketones The position of equilibrium depends on what groups are attached to C=0 and how they affect its steric and electronic environment Both effects con tribute but the electronic effect controls A hydr more than the steric effect... 

A striking example of an electronic effect on carbonyl group stability and its rela tion to the equilibrium constant for hydration is seen m the case of hexafluoroacetone In contrast to the almost negligible hydration of acetone hexafluoroacetone is completely hydrated... 

Instead of stabilizing the carbonyl group by electron donation as alkyl substituents do trifluoromethyl groups destabilize it by withdrawing electrons A less stabilized carbonyl group IS associated with a greater equilibrium constant for addition... 

Phenols that bear strongly electron withdrawing substituents usually give low yields of carboxylated products their derived phenoxide anions are less basic and the equilibrium constants for their carboxylation are smaller... 

In the previous section we saw how voltammetry can be used to determine the concentration of an analyte. Voltammetry also can be used to obtain additional information, including verifying electrochemical reversibility, determining the number of electrons transferred in a redox reaction, and determining equilibrium constants for coupled chemical reactions. Our discussion of these applications is limited to the use of voltammetric techniques that give limiting currents, although other voltammetric techniques also can be used to obtain the same information. 

Determining Equilibrium Constants for Coupled Chemical Reactions Another important application of voltammetry is the determination of equilibrium constants for solution reactions that are coupled to a redox reaction occurring at the electrode. The presence of the solution reaction affects the ease of electron transfer, shifting the potential to more negative or more positive potentials. Consider, for example, the reduction of O to R... 

The acidity of a lydrocarbon can be determined in an analogous way. If the electronic spectra of the neutral and anionic forms are sufficiently different, the concentrations of each can be determined directly, and the equilibrium constant for... 

The other C=N systems included in Scheme 8.2 are more stable to aqueous hydrolysis than are the imines. For many of these compounds, the equilibrium constants for formation are high, even in aqueous solution. The additional stability can be attributed to the participation of the atom adjacent to the nitrogen in delocalized bonding. This resonance interaction tends to increase electron density at the sp carbon and reduces its reactivity toward nucleophiles. 

The rates of both formation and hydrolysis of dimethyl acetals of -substituted benzaldehydes are substituent-dependent. Do you expect to increase or decrease with increasing electron-attracting capacity of the pam substituent Do you expect the Ahydroi to increase or decrease with the electron-attracting power of the substituent How do you expect K, the equilibrium constant for acetal formation, to vary with the nature of the substituent ... 

Electronic and steric effects operate in the sane duection. Both cause the equilibrium constants for hydration of aldehydes to be greater than those of ketones. 

These equations do not necessarily show the actual charges the important point is that all three are single-electron events. The asterisks can be thought of as an isotopic label, but need not be anything that concrete, since certain line-broadening techniques (Section 11.5) provide EE rate constants without them. The Marcus cross relation is an expression for kA% as a function of kAA, bb> and A, the equilibrium constant for Eq. (10-67). It reads,... 

What this implies is that given one equilibrium constant for addition of a nucleophile of known 7 to a carbonyl compound, one could estimate the equilibrium constant for addition of another nucleophile to the same carbonyl compound. This requires knowing the slope of the plot of log K versus y this slope is not very sensitive to the nature of the carbonyl compound, but it is at least known that A H2o/ MeOH depends on the electron-withdrawing power of the groups bonded to the carbonyl, and thus more information is needed to estimate an equilibrium constant for strongly electron-withdrawing substituents. From Ritchie s studies of nucleophile addition to trifluoroacetophenone," we can derive a slope for log K versus 7 of 0.42, distinctly less than the value of 1 for formaldehyde or simple benzaldehydes. 

Comproportionation equilibrium constants for Equation 9.3 between dications and neutral molecules of carotenoids were determined from the SEEPR measurements. It was confirmed that the oxidation of the carotenoids produced n-radical cations (Equations 9.1 and 9.3), dications (Equation 9.2), cations (Equation 9.4), and neutral ir-radicals (Equations 9.5 and 9.6) upon reduction of the cations. It was found that carotenoids with strong electron acceptor substituents like canthaxanthin exhibit large values of Kcom, on the order of 103, while carotenoids with electron donor substituents like (J-carotene exhibit Kcom, on the order of 1. Thus, upon oxidation 96% radical cations are formed for canthaxanthin, while 99.7% dications are formed for P-carotene. This is the reason that strong EPR signals in solution are observed during the electrochemical oxidation of canthaxanthin. 

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