Sulfur species, equilibrium constants

That the photoreactive species is the carbonium ion and not the corresponding alcohol is clearly indicated by the relative concentrations of the two species present. The calculated equilibrium constant for 5% aqueous sulfuric acid implies an alcohol content of 2 7 x 10 %, much too low to account for any detectable photoreaction from this covalent species. In addition, when the tropylium salt is irradiated in the absence of acid, neither 3 nor 4 is detected as a product, but rather ditropyl (5) and its photoisomer (6) are observed. 

Involvement of AModo species in electrophilic C-iodinations needs to be considered since a number of imidazoles are known to form such compounds in basic medium. Charge-transfer complexes, too, are quite well known. They seem to be of the n -type through the unshared electron pair at N-3. Equilibrium constants for their formation are known to increase regularly in line with electron-donating powers of substituents (or vice versa). Some KCT values at 20°C (L M are imidazole (200), 1-methylimidazole (333), 1,2-dimethylimidazole (1165), 4-phenylimidazole (152), and 4,5-diphenylimidazole (141) (83BSB923). The charge-transfer complexes formed between iodine and imidazole-2-thiones appear to involve the sulfur atoms (88JA2586). 

Table I. Equilibrium Constants for Hg(II) and Reduced Sulfur Species...

Possible methods of determining the extent of protonation include absorption spectroscopy at a wavelength for which species with n and fir-1 protons have different extinction coefficients, freezing point depression, and electrical conductivity (15). Of these, we have utilized only spectroscopy, which has the disadvantage that only the equilibrium constants for the most highly protonated states are accessible if, as is usual, the species with low protonation are insoluble. In this method, the extinction coefficient c of the compound is determined as a function of the H2SO4 content in the sulfuric acid solvent and correlated with the Hammet acidity function H0 (18) to give the pKB value of the protonated species,... 

Figure 8.13. Equilibrium concentrations of biochemically important redox components as a function of pe at a pH of 7.0 (a) nitrogen (b) nitrogen, with elemental nitrogen N2 ignored (c) iron and manganese (d) sulfur (e) carbon. These equilibrium diagrams have been constructed from equilibrium constants listed in Tables 8.6a and 8.6b for the following concentrations Cr (total carbonate carbon) = 10 M [HjSCaq)) + [HS ] -I- [SOri = 10 M [NOj-] + [NOj"] + [NH ] = 10 M = 0.78 atm and thus [NjCaq)] = 0.5 x 10 M. For the construction of (b) the species NH4 , NOj, and NO are treated as metastable with regard to Nj.

The application of standard electrode potential data to many systems of interest in analytical chemistry is further complicated by association, dissociation, complex formation, and solvolysis equilibria involving the species that appear in the Nemst equation. These phenomena can be taken into account only if their existence is known and appropriate equilibrium constants are available. More often than not, neither of these requirements is met and significant discrepancies arise as a consequence. For example, the presence of 1 M hydrochloric acid in the iron(Il)/iron(llI) mixture we have just discussed leads to a measured potential of + 0.70 V in 1 M sulfuric acid, a potential of -I- 0.68 V is observed and in 2 M phosphoric acid, the potential is + 0.46 V. In each of these cases, the iron(II)/iron(III) activity ratio is larger because the complexes of iron(III) with chloride, sulfate, and phosphate ions are more stable than those of iron(II) thus, the ratio of the species concentrations, [Fe ]/[Fe ], in the Nemst equation is greater than unity and the measured potential is less than the standard potential. If fomnation constants for these complexes were available, it would be possible to make appropriate corrections. Unfortunately, such data are often not available, or, if they are, they are not very reliable. 

Sulfur is weakly soluble in H2O (10 M at 298 K) [33, 34], but Na2S is very soluble [35]. In deaerated aqueous solutions, the alkali-metal polysulfide system contains, in addition to H2O and alkali-metal cations, OH , H+, H2S, HS , S-, 82 , 83 , 84 , and 85 . It is usually considered that 85 is the least reduced polysulfide in water. However, it has been reported, in several papers [26, 36], that in basic aqueous solutions, at high temperatures, a blue color is observed, suggesting the stability of 83 . The polysulfide equilibrium constants, interrelating polysulfide speciation, A a, K i, and Kq, have been well established [36, 37]. The species in solution are related by the equilibria ... 

We make a start by considering a solution with a total sulfur concentration of 1.0 m. Where ions or other dissolved species are present, we also assume that the solutions are ideal that is, activity is equal to the concentration in molarity units. As a first step, consider the reduction of S(s) to the —2 oxidation state represented by S , HS , and H2S. The prevalent dissolved species will depend on the pH and the acid-base equilibrium constants. 

Using this equation and mass action law for Eqs. (1.62), (1.63), (1.64), and (1.65), stability fields of aqueous sulfur species can be shown on logfo -pH diagram at constant temperature, pressure and ionic strength. The boundary lines for dissolved sulfur species on Fig. 1.28 correspond to the concentration of each aqueous sulfur species which is equal to that of the other one. For example, at the boundary line between H2S and HS, mnjS is equal to mns- pH at this boundary can be obtained from equilibrium constant for (1.52) which is given by... 

For species 11 we will use the intrinsic barrier for hydroxide addition to trimethyl phosphate, G = 19 (calculated using rate and equilibrium data from reference 100) and assume the same value for the attack of hydroxide at sulfur on dimethyl sulfate. This (nonobservable) rate will be estimated using a Brpnsted type plot from the rate constants for diaryl sulfates (diphenyl sulfate,and bis p-nitrophenyl sulfate), estimated from the rate for phenyl dinitrophenyl sulfate,assuming equal contributions for the two nitro groups. This gives ftg = 0.95, and thus for dimethyl sulfate log k = 11.3... 

For this equilibrium, the ion product constant has a value of approximately 2.7 X 1CP4. However, the discussion is complex and other species are present in sulfuric acid as a result of equilibria that can be written as... 

The "equilibrium boxes" for the solvents (Fig. 10-1) indicate the range over which differentiation occurs outside the range of a particular solvent, all species are leveled. For example, water can differentiate species (i.e., they are weak adds and bases) with pKa s from about 0 to 14 (such as acetic acid). Ammonia, on the other hand, behaves the same toward acetic acid and sulfuric acid because both lie below the differentiating limit of —12. The extent of these ranges is determined by the autoionization constant of the solvent (e.g, —14 units for water). The acid-base behavior of several species discussed previously may be seen to correlate with Fig. 10.1.11... 

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