Protonations at Equilibrium

Often protonations are coupled to electron transfers. It is expected that in this case the electrochemical mechanism will be sensitive to the availability of protons (pH and nature of solvent). 

It has been known for a long time that pH affects the kinetics of the reduction of the benzoquinones. The reduction generally becomes more irreversible at higher pH values. On this basis it has been proposed that the reduction pathway of BQ is HeHe (proton-electron-proton-electron) at low pH and eHeH at higher pH. The pK, the and the rates of the individual steps in the square scheme will determine the preferred pathway for reduction. 

Laviron has further developed the theory for quinone-like systems. Assuming that the protonations were at equiUbrium (fast with respect to the electron transfers), and that the transfer coefficients for the electrode reactions were all 0.5, he was able to show that such systems behaved exactly like two sequential one-electron transfers, with apparent heterogeneous rate constants  

This approach has been utilized by Deakin and Wightman in analyzing the pathway for the oxidation of catechol to o-quinones.  

The quinone electrochemistry story becomes even more complex, and the role of adsorption and solution chemical reactions are still being actively investigated this topic has been reviewed by Chambers.  

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Laviron, E. 1984. Electrochemical reactions with protonations at equilibrium Part X. The kinetics of the /)-benzoquinone/hydroquinone couple on a platinum electrode. Journal of Electroanalytical Chemistry 164, 213-227. 

Since the protons are in different environments they are expected to produce two distinct lines in the NMR spectrum. The intensities of these lines reflect the relative concentrations of the protons at equilibrium. On the basis of the theory of chemical relaxation (section 7.6), the relaxation time associated with proton... 

CVSIM SIMULATING CYCLIC VOLTAMMETRY EXPERIMENTS EXAMPLE 6 Protonations at equilibrium. 

Weak bases do not have a large attraction for the protons of an acid. A small fraction of the molecules of a weak base are protonated at equilibrium. For example, methylamine is a weak base. When it dissolves in water, a low concentration of methylammonium ions forms. 

Figure Al.4.1. A PH molecule at equilibrium. The protons are labelled 1, 2 aud 3, respectively, aud the phosphorus uucleus is labelled 4.

For large molecules, such as proteins, the main method in use is a 2D technique, called NOESY (nuclear Overhauser effect spectroscopy). The basic experiment [33, 34] consists of tluee 90° pulses. The first pulse converts die longitudinal magnetizations for all protons, present at equilibrium, into transverse magnetizations which evolve diirhig the subsequent evolution time In this way, the transverse magnetization components for different protons become labelled by their resonance frequencies. The second 90° pulse rotates the magnetizations to the -z-direction. 

Scheme VIII has the form of Scheme II, so the relaxation time is given by Eq. (4-15)—appjirently. However, there is a difference between these two schemes in that L in Scheme VIII is also a participant in an acid-base equilibrium. The proton transfer is much more rapid than is the complex formation, so the acid-base system is considered to be at equilibrium throughout the complex formation. The experiment can be carried out by setting the total ligand concentration comparable to the total metal ion concentration, so that the solution is not buffered. As the base form L of the ligand undergoes coordination, the acid-base equilibrium shifts, thus changing the pH. This pH shift is detected by incorporating an acid-base indicator in the solution.

Three kinds of equilibrium potentials are distinguishable. A metal-ion potential exists if a metal and its ions are present in balanced phases, e.g., zinc and zinc ions at the anode of the Daniell element. A redox potential can be found if both phases exchange electrons and the electron exchange is in equilibrium for example, the normal hydrogen half-cell with an electron transfer between hydrogen and protons at the platinum electrode. In the case where a couple of different ions are present, of which only one can cross the phase boundary — a situation which may exist at a semiperme-able membrane — one obtains a so called membrane potential. Well-known examples are the sodium/potassium ion pumps in human cells. 

R represents the thiazole ring and the thiazole ring protonated at the heterocyclic nitrogen atom. The subscripts and 0 refer to equilibrium and initial concentrations, respectively. 

Also considered as possibilities have been transition states involving IV, below, the conjugate base of II, and either RjNHJ or BH+ 29,30. This mechanism, with II and IV maintained at equilibrium by rapid, reversible proton transfers and BH + or R2NH2 assisting separation of the leaving group from intermediate IV in the rate-limiting step, may be formulated as... 

Because at equilibrium virtually all the HCl molecules have donated their protons to water, HCl is classified as a strong acid. The proton transfer reaction essentially goes to completion. The H30+ ion is called the hydronium ion. It is strongly hydrated in solution, and there is some evidence that a better representation of the species is H904+ (or even larger clusters of water molecules attached to a proton). A hydrogen ion in water is sometimes represented as H + (aq), but we must remember that H+ does not exist by itself in water and that H CC is a better representation. 

FIGURE 10.4 In this molecular portrayal of the structure of a solution of ammonia in water at equilibrium, we see that NH, molecules are still present because only a small percentage of them have been protonated by transfer of hydrogen ions from water. In a typical solution, only about 1 in 100 NH, molecules is protonated. The overlay shows only the solute species. 

The reaction is very fast in both directions, and so is always at equilibrium in water and in aqueous solutions. In every glass of water, protons from the hydrogen atoms are ceaselessly migrating between the molecules. This type of reaction, in which one molecule transfers a proton to another molecule of the same kind, is called autoprotolysis (Fig. 10.9). 

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. 

We can predict the pH at any point in the titration of a polyprotic acid with a strong base by using the reaction stoichiometry to recognize what stage we have reached in the titration. We then identify the principal solute species at that point and the principal proton transfer equilibrium that determines the pH. 

The results for [16] annulene are similar. The compound was synthesized in two different ways, both of which gave 103, which in solution is in equilibrium with 104. Above -50°C there is conformational mobility, resulting in the magnetic equivalence of all protons, but at — 130°C the compound is clearly paratropic there are 4 protons at 10.565 and 12 at 5.35 5. In the solid state, where the compound exists entirely as 103, X-ray crystallography shows that the molecules are nonplanar with almost complete bond alternation The single bonds are 1.44-1.47 A and the double bonds are 1.31-1.35 A. A number of dehydro and bridged... 

Most acids and bases are weak. A solution of a weak acid contains the acid and water as major species, and a solution of a weak base contains the base and water as major species. Proton-transfer equilibria determine the concentrations of hydronium ions and hydroxide ions in these solutions. To determine the concentrations at equilibrium, we must apply the general equilibrium strategy to these types of solutions. 

All carboxylic acids are weak. In an aqueous solution at equilibrium, a small fraction of the carboxylic acid molecules have undergone proton transfer to water molecules, generating hydronium ions and anions that contain the—CO2 carboyylate CH3 CO2 H((317)-FH2 0(/) CH3 CO2 (atj) + H3 0 (aq)... 

In a solution of hydrofluoric acid, HF molecules donate protons to water molecules, generating H3 O and F" ions. As discussed in Chapter 16, the forward reaction and the reverse reaction must occur at equal rates in a solution that is at equilibrium. In an aqueous solution of HF that is at equilibrium, hydronium ions donate protons to fluoride ions to generate molecules of H2 O and HF ... 

The rates of protonation and deprotonation reactions are sufficiently large in comparison with corresponding diffusion rates, so that it can be assumed that these reactions are at equilibrium even when current is flowing, that is, the following equations are valid everywhere at t > 0, t being the time ... 

Thus, at equilibrium, the transbilayer concentration gradient of the weak acid reflects the inverse of the transbilayer concentration gradient of protons (Fig. 14). For example, a pH difference of 2 units (e.g., internal pH = 9 and external pH = 7) shoud lead to 100-fold higher concentration of weak acid within the vesicle as compared to the external concentration. 

Figure 10-4. The double- and single-site titration models for His and Asp groups [42]. (A) In the double site model, only one X is used for describing the equilibrium between the protonated and deprotonated forms, while the tautomer interversion process is represented by the variable x. (B) In the single-site model, protonation at different sites is represented by different X variables. HSP refers to the doubly protonated form of histidine. HSD and HSE refer to the singly protonated histidine with a proton on the h and e nitrogens, respectively. ASP1 and ASP2 refer to the protonated carboxylic acid with a proton on either of the carboxlate oxygens...

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