Calculation from reduction potentials

Reaction 7.40 takes place when CU2SO4 (prepared by reacting CU2O and dimethyl sulfate) is added to water, while reaction 7.41 occurs when acid is added to a solution of K2Mn04. Equilibrium constants for such disproportionation reactions can be calculated from reduction potentials as in worked example 7.6. 

Because the dendrimer-encapsulated nanoparticles are so small, they do not have the properties of bulk metals. Therefore, it is not possible to calculate the reduction potential for the exchange reactions from tabulated literature data... 

Illustrative Example 14.1 Calculating Standard Reduction Potentials from Free Energies of Formation... 

We now need to set up and refine the corresponding files for the reduced forms. Save the refined coordinates (. out files) of each of the structures with a new name (e. g. co2 a6.hin). This can be done in Edit/View/HyperChem File with the usual Save as command. Open Tools/Set Metal Type for each of the new files and change the Oxidation state from III to II. Refine the structures, calculate the strain energy differences between the oxidized and the reduced forms for the most stable conformers, calculate the reduction potentials using Eq. 17.18.5 and compare the results with those in Table 17.18.1. 

The following principles allow calculation of cell potentials from reduction potentials ... 

Wang and Charles Han calculated the electron affinities of aldehydes and ketones by using the parameterized Huckel theory. Eight parameters were used to calculate the electron affinities of 16 compounds with a deviation of only 0.05 eV. However, some of the data were not published until the 1970s [35]. By measuring relative electron capture coefficients and scaling to the acetophenone data, more precise electron affinities could be obtained. This was further support for the validity of the ECD model. M. J. S. Dewar reproduced the experimental electron affinities of aromatic hydrocarbons using the MINDO/3 method and calculated Ea from reduction potentials [36]. 

Table 4.3 lists AAG values, the ECD Ea, and the Ea from 1/2, of several aromatic hydrocarbons obtained in this manner. The electron affinity for pentacene was determined by TCT, while that of coronene is the value obtained from reduction potentials [6]. The Ea are verified using CURES-EC. The calculated values are given in Table 4.3. Also listed are the weighted average of the values that cluster about the current evaluated values from a 1983 compilation [27]. The consistency of the Ea values in this table support the gas phase experiment and the assignments of lower values to excited states.

The electron affinities of the chlorobenzene isomers have been determined by scaling half-wave reduction potentials [22], With higher gas phase values higher values are obtained from reduction potentials. These are compared to the ECD and CURES-EC values in Table 11.9. The CURES-EC-calculated values for the above compounds support experimental quantities and suggest that the Ea of all halogenated benzenes can be calculated. The CURES-EC values are listed in Table 11.10. The Ea... 

The electron affinities of halogenated aromatic and aliphatic compounds and nitro compounds have been evaluated. Additional electron affinities for halogenated benzene, freons, heterocyclic compounds, dibenzofuran, and the chloro- and fluoroben-zenes are reported from ECD data. The first positive Ea for the fluorochloroethanes were obtained from published ECD data. The Ea of halogenated aromatic radicals have been estimated from NIMS data. The AEa of all the halobenzenes have been calculated using CURES-EC. The Ea of chlorinated biphenyls and chlorinated napthalenes obtained from reduction potentials have been revised based on variable solution energy differences. 

Similar PR experiments performed on P. denitrificans COX (50) have also revealed a rapid CuA-heme-a electron equilibration step with an observed rate constant of 30,430 2,300 s and with an equilibrium constant of 2.0 0.1 at 25°C, pH 7.0 (cf. Table VII) corresponding to a difference in reduction potentials between the heme-a [Fe /Fe )] and Cua [Cu VCu ] couples of + 18 + 1 mV. For Cua in this enzyme, a midpoint potential of 213 mV versus SHE was found under the aforementioned conditions (157), while the potential of heme-a was reported to be 428 mV versus SHE (158). The observed equilibrium constant thus disagrees considerably with an equilibrium constant calculated from these potential differences (K = 4300). This is not surprising. 

An indicator of soil corrosivity is the value of soil oxidation-reduction (ORP) or redox potential. It is calculated from the potential difference measured with a probe that contains an inert platinirm (Pt) electrode and a saturated calomel electrode (Hg/HgjClj/KCl, +0.241 V versus SHE) as a reference electrode. The value of this soil redox piotential depends on the dissolved oxygen content in the piore water and provides some information on the conditions under which sulfate-reducing bacteria could grow. The use of redox potentials to predict soil corrosivity is presented in Table 4. 

Rate constants in the cross-reactions between [Felphenls] and 1,2-, 1,3-, and 1,4-benzenediols have been used to calculate the reduction potentials of the corresponding H2At radicals. The values correlate with HOMO energies derived from molecular orbital calculations. ... 

The UV-visible absorption spectrum of Ru(2,2 -bipyridine)3 maximum at about 450 nm, from which the energy in volts for process XI-39 may be estimated. The standard reduction potential for the R" /R couple is about 1.26 V at 25°C. Estimate from this information (and standard reduction potentials) the potential in volts for processes XI-40 and XI-41. Repeat the calculation for alkaline solutions. 

Other Coordination Complexes. Because carbonate and bicarbonate are commonly found under environmental conditions in water, and because carbonate complexes Pu readily in most oxidation states, Pu carbonato complexes have been studied extensively. The reduction potentials vs the standard hydrogen electrode of Pu(VI)/(V) shifts from 0.916 to 0.33 V and the Pu(IV)/(III) potential shifts from 1.48 to -0.50 V in 1 Tf carbonate. These shifts indicate strong carbonate complexation. Electrochemistry, reaction kinetics, and spectroscopy of plutonium carbonates in solution have been reviewed (113). The solubiUty of Pu(IV) in aqueous carbonate solutions has been measured, and the stabiUty constants of hydroxycarbonato complexes have been calculated (Fig. 6b) (90). 

Equations and provide a method for calculating equilibrium constants from tables of standard reduction potentials. Example illustrates the technique. 

This is a quantitative calculation, so it is appropriate to use the seven-step problem-solving strategy. We are asked to determine an equilibrium constant from standard reduction potentials. Visualizing the problem involves breaking the redox reaction into its two half-reactions ... 

C19-0134. Use standard reduction potentials from Table 19-1 and Appendix F to determine. sp for as many metal hydroxides as the table allows. Compare your values with those in Appendix E. If there are. sp values for hydroxides in Appendix E that cannot be calculated from standard reduction potentials in Appendix F, use the. STjp values to calculate the appropriate standard reduction potentials. 

The cyclic voltammograms of ferrlcyanlde (1.0 mM In 1.0 M KCl) In Fig. 2 are Illustrative of the results obtained for scan rates below 100 mV/s. The peak separation is 60 mV and the peak potentials are Independent of scan rate. A plot of peak current versus the square-root of the scan rate yields a straight line with a slope consistent with a seml-lnflnlte linear diffusion controlled electrode reaction. The heterogeneous rate constant for the reduction of ferrlcyanlde was calculated from CV data (scan rate of 20 Vs using the method described by Nicholson (19) with the following parameter values D 7.63 X 10 cm s , D, = 6.32 X 10 cm s, a 0.5, and n =1. The rate constants were found to be... 

An increase in reducible surface-bound material during ennoblement was demonstrated using galvanostatic reduction" techniques to monitor potential as a stainless steel coupon was cathodically polarized. Coulombs of reducible material were calculated from the duration of regions of polarization rate lag that indicated reduction of surface-bound material. Longer exposure times and thicker biofouling were not sufficient to increase the abundance of reducible surface-bound material. The increase seemed to be associated with increased... 

Related Polymer Systems and Synthetic Methods. Figure 12A shows a hypothetical synthesis of poly (p-phenylene methide) (PPM) from polybenzyl by redox-induced elimination. In principle, it should be possible to accomplish this experimentally under similar chemical and electrochemical redox conditions as those used here for the related polythiophenes. The electronic properties of PPM have recently been theoretically calculated by Boudreaux et al (16), including bandgap (1.17 eV) bandwidth (0.44 eV) ionization potential (4.2 eV) electron affinity (3.03 eV) oxidation potential (-0.20 vs SCE) reduction potential (-1.37 eV vs SCE). PPM has recently been synthesized and doped to a semiconductor (24). 

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