Equilibrium constants deprotonation reaction

Four anthocyanin species exist in equilibrium under acidic conditions at 25°C/ according to the scheme in Figure 4.3.3. The equilibrium constant values determine the major species and therefore the color of the solution. If the deprotonation equilibrium constant, K, is higher than the hydration constant, Kj, the equilibrium is displaced toward the colored quinonoidal base (A), and if Kj, > the equilibrium shifts toward the hemiacetalic or pseudobase form (B) that is in equilibrium with the chalcone species (C), both colorless." - Therefore, the structure of an anthocyanin is strongly dependent on the solution pH, and as a consequence so is its color stability, which is highly related to the deprotonation and hydration equilibrium reaction constant values (K and Kj,). 

Fig. 5 Logarithmic plots of rate-equilibrium data for the formation and reaction of ring-substituted 1-phenylethyl carbocations X-[6+] in 50/50 (v/v) trifluoroethanol/water at 25°C (data from Table 2). Correlation of first-order rate constants hoh for the addition of water to X-[6+] (Y) and second-order rate constants ( h)so1v for the microscopic reverse specific-acid-catalyzed cleavage of X-[6]-OH to form X-[6+] ( ) with the equilibrium constants KR for nucleophilic addition of water to X-[6+]. Correlation of first-order rate constants kp for deprotonation of X-[6+] ( ) and second-order rate constants ( hW for the microscopic reverse protonation of X-[7] by hydronium ion ( ) with the equilibrium constants Xaik for deprotonation of X-[6+]. The points at which equal rate constants are observed for reaction in the forward and reverse directions (log ATeq = 0) are indicated by arrows.

Acetylene is sufficiently acidic to allow application of the gas-phase proton transfer equilibrium method described in equation l7. For ethylene, the equilibrium constant was determined from the kinetics of reaction in both directions with NH2-8. Since the acidity of ammonia is known accurately, that of ethylene can be determined. This method actually gives A f/ acid at the temperature of the measurement. Use of known entropies allows the calculation of A//ac d from AG = AH — TAS. The value of A//acij found for ethylene is 409.4 0.6 kcal mol 1. But hydrocarbons in general, and ethylene in particular, are so weakly acidic that such equilibria are generally not observable. From net proton transfers that are observed it is possible sometimes to put limits on the acidity range. Thus, ethylene is not deprotonated by hydroxide ion whereas allene and propene are9 consequently, ethylene is less acidic than water and allene and propene (undoubtedly the allylic proton) are more acidic. Unfortunately, the acidity of no other alkene is known as precisely as that of ethylene. 

The equilibrium constant for this reaction depends on the stability constants of the ionophore-M+ complexes and on the distribution of ions in aqueous test solution and organic membrane phases. For a membrane of fixed composition exposed to a test solution of a given pH, the optical absorption of the membrane depends on the ratio of the protonated and deprotonated indicator which is controlled by the activity of M+ in the test solution (H,tq, is fixed by buffer). By using a to represent the fraction of total indicator (Ct) in the deprotonated form ([C]), a can be related to the absorbance values at a given wavelength as... 

TLM Activity Coefficients. In the version of the TLM as discussed by Davis et al. (11), mass action equations representing surface complexation reactions were written to include "chemical" and "coulombic" contributions to the overall free energy of reaction, e.g., the equilibrium constant for the deprotonation reaction represented by Equation 2 has been given as... 

The SB-GA mechanism consists of a rapid equilibrium deprotonation of the ZH intermediate, followed by rate-limiting, general acid-catalysed leaving-group departure from the anionic cr-complex Z via the concerted transition state, 2. The derived expression for this mechanism is equation 4, where fctBH is the rate coefficient for acid-catalyzed expulsion of L from Z and K3 is the equilibrium constant for the reaction ZH Z- + BH. 

Irreversibility can be obtained if (1) the equilibrium constant for reaction (3), K = kf/kb, is large, that is, the EGB is a thermodynamically much stronger base than the deprotonated substrate, S . If that is the case, the substrate may be... 

A relatively stable aqua complex or protonated hypoastatous acid [H20At] has been assumed similarly, a protonated hypoiodous acid has been reported to exist in aqueous solutions (15). The equilibrium constant for the deprotonation reaction [Eq. (9)] has been estimated by extrapolation of data accrued from the lighter halogens to be < 10" (80), indicating that [H20At]" is a fairly weak acid. Another structure, the symmetric diaqua cationic complex [H20-At-0H2]", has also been proposed (79, 80). 

Redus, M., Baker, D.C., and Dougall, D.K., Rate and equilibrium constants for the dehydration and deprotonation reactions of some monoacylated and glycosylated cyanidin derivatives, J. Agric. Food Chem., 47, 3449, 1999. 

The solvent affects the chemical equilibria of reactions. Second-order rate constants and equilibrium constants have been determined for the benzoate ion promoted deprotonation reactions of (m-nitrophenyl)nitromethane, (p-nitrophenyl)nitromethane, and (3,5-dinitrophenyl)nitromethane in methanol solution. The pKa values for the arylnitromethanes in methanol are the following pKa = 10.9, 10.5, and 9.86 for m-nitrophenyl)nitromethane, (p-nitrophenyl)nitromethane, and (3,5-dinitrophenyl)nitro-methane, respectively, relative to benzoic acid (pKa = 9.4). A Bronsted B value of... 

All of the above reactions and accompanying equilibrium constants may also be written for the complexes derived from trans-DDP. We shall be comparing the equilibrium-constant values for aquation and deprotonation of the cis- and /ran.v-complcxcs. 

To mimic c T-[(NH3)2Pt(H20)2]2+ with the more rapidly exchanging Pd11 and to prevent isomerization, it is necessary to employ the complex of ethylenediamine (en), [(en)Pd(H20)2]2+, that through chelation is necessarily cis. Upon titration with standard base an endpoint is reached after the addition of only one equivalent of base at pH 7.5, but the reversible titration curve is flattened on the pH axis and cannot be fitted with the equilibrium expression for a simple deprotonation. It was proposed that the mono-hydroxo complex dimerizes to abinuclear dihydroxo-bridged dimer [9], The two reactions and their equilibrium constant expressions follow. 

The measured equilibrium constants for this stepwise deprotonation scheme for Mo and W have been collected from the literature in [56]. They show that Mo is more hydrolyzed than W, and that the deprotonation sequence for Mo and W at pH = 1 reaches the neutral species M02(0H)2(H20)2. Assuming the deprotonation processes for the Sg compounds to be similar to those of Mo and W, Equations (6-9), V. Pershina and J.V. Kratz performed fully relativistic density-functional calculations of the electronic structure of the hydrated and hydrolyzed structures for Mo, W, and Sg [56]. By use of the electronic density distribution data, relative values of the free energy changes and by use of the hydrolysis model [29,30], constants of hydrolysis reactions (6-9) were defined [56]. These results show hydrolysis of the cationic species to the neutral species to decrease in the order Mo>W>Sg which is in agreement with the experimental data on hydrolysis of Mo and W, and on Sg [55] for which the deprotonation sequence may end earlier with a cationic species such as SgO(OH)3(H20)2+ that is sorbed on the cation-exchange resin. 

Using the p-KgS of NH3 (ca. 33) and ethyne (25) we would predict an equilibrium constant for this reaction of 108 (10 25/10 33)—well over to the right. Amide ions can be used to deprotonate alkynes. 

It is unfortunate that there has been so little work devoted to quantitative measurements of cation-pseudobase equilibria in methanol and ethanol since these media have several advantages over water for the determination of the relative susceptibilities of heterocyclic cations to pseudobase formation. The enhanced stability of the pseudobase relative to the cation in alcohols compared to water is discussed earlier this phenomenon will permit the quantitative measurement of pseudobase formation in methanol (and especially ethanol) for many heterocyclic cations for which the equilibrium lies too far in favor of the cation in aqueous solution to allow a direct measurement of the equilibrium constant. Furthermore, the deprotonation of hydroxide pseudobases (Section V,B) and the occurrence of subsequent irreversible reactions (Sections V,C and D), which complicate measurements for pKR+ > 14 in aqueous solutions, are not problems in alcohol solutions. Data are now available for the preparation of buffer solutions in methanol over a wide range of acidities.309-312 An appropriate basicity function scale will be required for more basic solutions. The series of -(substituted phenyl)pyridinium cations (163) studied by Kavalek et al.i2 should be suitable for use as indicators in at least some of the basic region. The Hm and Jm basicity functions313 should not be assumed90 to apply to methoxide ion addition to heterocyclic cations because of the differently charged species involved in the indicators used to construct these scales. 

The relative rates of reaction of the nucleic acid bases with heavy transition metal ions at neutral pH are in the same order as the relative nucleophilicites of the bases, that is G > A > C > U or T. This order parallels the relative rates of reactions for cA-[(NH3)2Pt(OH2)2] (see Figure 9), while the equilibrium constants for the same reactions are very close in magnitude. In contrast, HsCHgOH, which is more labile to substitution, nndergoes more favorable binding with deprotonation at N-3 of thymine residues in nucleic acids. Thus the relative facilities of individual reactions can lead to differences in initial product formation (kinetic control). Subsequent changes in the metal-nucleic acid complexes can be nnder kinetic or thermodynamic control. 

When HX is a carbon acid the value of the rate coefficient, ) for a thermodynamically favourable proton transfer rarely approaches the diffusion limit. Table 1 shows the results obtained for a few selected carbon acids which are fairly representative of the different classes of carbon acids which will be discussed in detail in Sect. 4. For compounds 1—10, the value of k i is calculated from the measured value of k, and the measured acid dissociation constant and, for 13, k, is the measured rate coefficient and k1 is calculated from the dissociation constant. For 11 and 12, both rate coefficients contribute to the observed rate of reaction since an approach to equilibrium is observed. Individual values are obtained using the measured equilibrium constant. In Table 1, for compounds 1—10 the reverse reaction is between hydronium ion and a carbanion whereas for 11, 12 and 13 protonation of unsaturated carbon to give a carbonium ion is involved. For compounds 1—12 the reverse reaction is thermodynamically favourable and for 13 the forward reaction is the favourable direction. The rate coefficients for these thermodynamically favourable proton transfers vary over a wide range for the different acids. In the ionization of ketones and esters, for which a large number of measurements have been made [38], the observed values of fe, fall mostly within the range 10s—101 0 1 mole-1 sec-1. The rate coefficients observed for recombination of the anions derived from nitroparaffins with hydronium ion are several orders of magnitude below the diffusion limit [38], as are the rates of protonation and deprotonation of substituted azulenes [14]. For disulphones [65], however, the recombination rates of the carbanions with hydronium ion are close to 1010 1 mole-1 sec-1. Thermodynamically favourable deprotonation by water of substituted benzenonium ions with pK values in the range —5 to —9 are slow reactions [27(c)], with rate coefficients between 15 and 150 1 mole-1 sec-1 (see Sect. 4.7). 

An external aldimine forms with 1-serine, which is deprotonated to form the quinonoid intermediate. This intermediate is reprotonated on its opposite face to form an aldimine with d-serine. This compound is cleaved to release d-serine. The equilibrium constant for a racemization reaction is 1 because the reactant and product are exact mirror images of each other. 

The radiation chemistry of 2-propanol is analogous to that of methanol, that is, the main reactive species are Cs and (CH3)2 COH. In alkaline solution, (CH3)2 COH deprotonates to (CH3)2CO . In the presence of N2O or acetone, es is converted to (CH3)2 C0H/(CH3)2C0 by the reactions in Eqs. 30 and 18, or the reaction of Eq. 20, respectively. The solvated electron in 2-propanol has been utilized to study electron-transfer reactions between aromatic radical anions (donor) and aromatic molecules (acceptor) [16]. The donor-acceptor pairs studied were pyrene-anthracene, pyrene-9,10-dimethylanthracene and w-terphenyl-/ -terphenyl. In the first two cases an equilibrium was established and the parameters forward and kback were measured this was the first example of the measurement of an equilibrium constant by use of pulse radiolysis. The rate constants for the electron-transfer reactions were examined in terms of the Marcus theory [17]. 

In natural waters, other surface reactions will be occurring simultaneously. These include protonation and deprotonation of the >FeOH site at the inner o-plane and complexation of other cations and anions to either the inner (o) or outer (IS) surface planes. Expressions similar to Equation (5) above can be written for each of these reactions. In most studies, the activity coefficients of surface species are assumed to be equal to unity thus, the activities of the surface sites and surface species are equal to their concentrations. Different standard states for the activities of surface sites and species have been defined either explicitly or implicitly in different studies (Sverjensky, 2003). Sveijensky (2003) notes that the use of a hypothetical 1.0 M standard state or similar convention for the activities of surface sites and surface species leads to surface-complexation constants that are directly dependent on the site density and surface area of the sorbent. He defines a standard state for surfaces sites and species that is based on site occupancy and produces equilibrium constants independent of these properties of the solids. For more details about the properties of the electrical double layer, methods to calculate surface specia-tion and alternative models for activity coefficients for surface sites, the reader should refer to the reference cited above and other works cited therein. 

In this case the equilibrium constant (ATi = kx/k x) for reaction (1) is large and the EGB is thermodynamically a much stronger base than the conjugate base of the substrate, S . Consequently, all of the substrate may be deprotonated by an EGB formed either in situ or ex situ and converted into product by addition of another reactant in a subsequent step. This situation is rarely met in reactions where EGBs have advantages over conventional, chemically formed, bases. 

The second group of values came from studies where it was assumed that polymerization reactions occurred, such as the formation of H5As206 (aq>, in addition to the deprotonation reaction. For chemical and mathematical reasons, the dissociation constant calculated from a set of measurements becomes smaller as one introduces polymeric anions into the model. The differences of the models chosen, at first appearance, could serve to explain the differences of the equilibrium constants given in the previous table. Unfortunately, the situation, from the perspective of data evaluation, is more complex. In principle, there should be a sufficient dilution of arsenious acid for which one would not expect the formation of a significant proportion of species like HsAsaOe caq) upon addition of base. For such a condition, the equilibrium constant determined assuming that only the monomer exists, should approach that determined for the multi-species model. Britton and Jackson (1934) performed potentiometric titration at two concentrations of arsenious acid (0.0170 and 0.0914 molar) and obtained essentially the same... 

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