Proton equilibrium

Streitwieser pointed out that the eorrelation whieh exists between relative rates of reaetion in deuterodeprotonation, nitration, and ehlorination, and equilibrium eonstants for protonation in hydrofluorie aeid amongst polynuelear hydroearbons (ef. 6.2.3) constitutes a relationship of the Hammett type. The standard reaetion is here the protonation equilibrium (for whieh p is unity by definition). For eon-venience he seleeted the i-position of naphthalene, rather than a position in benzene as the referenee position (for whieh o is zero by definition), and by this means was able to evaluate /) -values for the substitutions mentioned, and cr -values for positions in a number of hydroearbons. The p -values (for protonation equilibria, i for deuterodeprotonation, 0-47 for nitration, 0-26 and for ehlorination, 0-64) are taken to indieate how elosely the transition states of these reaetions resemble a cr-eomplex. 

THE USE OF PROTONIC EQUILIBRIUM OF DIMERIC RHODAMINE 6G ON EXTRACTION OF IONIC ASSOCIATIONS... 

The neglect of higher-order terms in S2, etc. means that the changes in concentration or in instrument reading are small. In some cases, if a protonation equilibrium occurs, it has proved useful to add a pH indicator to provide a large absorbance change. 

A reactant may be present in two forms, or even three, that coexist. The components are related by one (or two) reactions that, we shall assume, equilibrate very rapidly compared to the rate of product buildup. The proportion in each form may be changed by some variable that the investigator keeps constant in a single experiment but later varies among a series of determinations. One instance in which this arises is that of a rapid protonation equilibrium. For example, suppose that the reactant A is partially protonated, and that it is the protonated form of the substrate, AH+, that is converted to product. This can be diagrammed in more than one way here we choose the form in which the protonation equilibrium is written as an acid ionization, which is the usual convention ... 

This situation is called a substrate titration. That is, the change in rate with [H+] is the sole consequence of an equilibrium incidental to the main event. It is customary to display pH-dependent rates by plots of (v/[A]t) versus pH that is, by log versus pH. Two common patterns are shown in Fig. 6-1, for cases in which there is a single protonation equilibrium. The case in Fig. 6-la corresponds to Eq. (6-81) we return later to Fig. 6-1 b. The line bends down, as do all instances of substrate titration. The apparent order of the reaction with respect to [H+] is +1 in the limit of low [H+] and 0 at high. 

The addition of alkanesulfonates to the reaction mixture shifts the protonation equilibrium in favor of more protonated micelles. Thus, a high yield of oxirane rather than of the glycol can be isolated (Table 33) [98]. 

We calculate the pH of solutions of weak bases in the same way as we calculate the pH of solutions of weak acids—by using an equilibrium table. The protonation equilibrium is given in Eq. 9. To calculate the pH of the solution, we first calculate the concentration of OH ions at equilibrium, express that concentration as pOH, and then calculate the pH at 25°C from the relation pH + pOH = 14.00. For very weak or very dilute bases, the autoprotolysis of water must be taken into consideration. 

The rate maximum at pH 4 is assigned to a specific reaction of the monoester anion 104 which exists exclusively under these conditions. Westheimer 57) first advanced a metaphosphate ion mechanism in which 102 is formed via a six-membered monoester-anion/water complex (103). An intramolecular proton transfer via a four-membered ring according to 105 m is also conceivable, as is the formation of a zwitterion 106 in a prior protonation equilibrium. 

If at the optimum distance R, the frequency flp is considerably smaller than at large distances (f fiClp R )/4 — 1), then along with the shift of the proton equilibrium position when the system goes to the transitional configuration, the contribution of transitions between the excited vibrational states of the proton increases and the proton transition may occur from the levels located near the top of the potential barrier. This case corresponds to the Kreevoy type of transition.49 In the limit /3fiflp(R )/4 1 we have the case of the overbarrier proton transition. However, the formulas of the nonadiabatic theory become inapplicable in this case and the reaction is an adiabatic one. 

This protonation equilibrium is characterized by the protonation constant of the complex ... 

In strong acids the convention is to write the protonation equilibrium of a weak base B as equation (5) the species H30+ in equation (1) (or such higher proton solvates as may be present) is just written as H+ for simplicity, without indicating its structural environment ... 

SAQ 6.10 The tetra-protic acid H4EDTA (V) has four possible proton equilibrium constants. Write an expression for each, for Ka(1) to Ka(4). 

A number of reductions of VOJ show acid catalysis with no rate saturation at high [H+]. This is consistent with a protonation equilibrium,... 

Spectral changes in the skeleton are observed when the base is changed into the conjugate acid, i.e., they are clearly observable at acidities of the medium which are some two logarithmic units of acidity greater than that required for half-protonation of the base (> 99% protonation). In the protonation equilibrium of a base B ... 

The light absorption act is fast compared with proton exchange rates and therefore the ultraviolet spectrum of a system in protonation equilibrium (1) is the superposition of the spectra of the base and the conjugate acid, each contributing according to its concentration. So the observed molar extinction coefficient is ven by (4), where a is the fraction of the base converted into the... 

In a protonation equilibrium such as (16), water molecules are involved in solvating all the dissolved species, but especially the... 

Sverjensky, D.A. Sahai, N. (1996) Theoretical prediction of single-site surface protonation equilibrium constants for oxides and silicates in water. Geochem. Cosmochim. Acta 60 3773-3797... 

According to Equation 6.6, the velocity of the EOF is directly proportional to the intensity of the applied electric held. However, in practice, nonlinear dependence of the EOF on the applied electric held is obtained as a result of Joule heat production, which causes the increase of the electrolyte temperature with consequent decrease of viscosity and variation of all other temperature-dependent parameters (protonic equilibrium, ion distribution in the double layer, etc.). The EOF can also be altered during a run by variations of the protonic concentration in the anodic and cathodic electrolyte solutions as a result of electrophoresis. This effect can be minimized by using electrolyte... 

The detailed investigation of the reduction mechanism by CV in thf-[NBu4][Pp6] showed that the first steps of the reduction of 32+ in the presence of acid occurred according to an ECrevE mechanism in which the intervening chemical reaction is a protonation equilibrium (Sch. 24, Path A). Therefore, in the presence of 1 equiv acid, the diffusion-controlled, one-electron... 

The DSP approach nicely answers the controversial question about which substituent parameters should be employed to correlate pKa data for 4-substituted pyridinium ions. Statistically, the best correlation is given by Eq. (9), which has values to measure the resonance contribution of a substituent, a result in keeping with chemical intuition. This correlation is statistically superior to a Hammett treatment, where both resonance and inductive effects of a group are combined into a single parameter, p or ap.53,54 Moreover, now it is possible to rationalize why a simple Hammett treatment using ap works so well. Equation (9) reveals that the protonation equilibrium is much more sensitive to an inductive effect (p, — 5.15) than to a resonance effect (p = 2.69). Hence, substituent parameters, such as erp, which are derived from a consideration of the dissociation constants for benzoic acids where resonance contributions are small serve as a useful approximation. The inductive effect is said to have a larger influence on pKa values for pyridinium ions than for benzoic acids because the distance between the substituent and the reactive site is shorter in the pyridine series.53... 

Although the quantitative theory of reactions in moderately concentrated solutions of strong acids is unsatisfactory, we do have a good qualitative idea of the processes involved in the acid-catalyzed hydrolysis and formation of esters. Under conditions where the degree of protonation of the substrate is small it is not possible to separate with confidence the factors which affect the solvolytic process and those which affect the preliminary protonation equilibrium. But there have been a number of recent studies of t ie behaviour of carboxylic acids and esters in very strongly acidic media, in. which they are essentially completely protonated. Under these conditions it is possible to observe the behaviour of the protonated species directly. It is appropriate to summarize the results of this research before discussing the reactions under more normal solvolytic conditions. 

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