Proton condition

The point of zero charge pHpzc corresponds to the zero proton condition at the surface ... 

The pHpZc (zero proton condition, point of zero charge) is not affected by the concentration of the inert electrolyte. As Fig. 2.3 shows, there is a common intersection point of the titration curves obtained with different concentrations of inert electrolyte. 

To facilitate understanding, Eq. (v) was derived on the basis of charge balance it can be derived directly on the basis of the proton condition (using H20, and =AIOH as a reference). 

As we have seen, the net surface charge of a hydrous oxide surface is established by proton transfer reactions and the surface complexation (specific sorption) of metal ions and ligands. As Fig. 3.5 illustrates, the titration curve for a hydrous oxide dispersion in the presence of a coordinatable cation is shifted towards lower pH values (because protons are released as consequence of metal ion binding, S-OH + Me2+ SOMe+ + H+) in such a way as to lower the pH of zero proton condition at the surface. 

The net charge at the hydrous oxide surface is established by the proton balance (adsorption of H or OH" and their complexes at the interface and specifically bound cations or anions. This charge can be determined from an alkalimetric-acidimetric titration curve and from a measurement of the extent of adsorption of specifically adsorbed ions. Specifically adsorbed cations (anions) increase (decrease) the pH of the point of zero charge (pzc) or the isoelectric point but lower (raise) the pH of the zero net proton condition (pznpc). 

Thus, according to this interpretation the zero proton condition is at pH = 8.6. Furthermore, an ion exchange reaction... 

V Specifically adsorbed species are those that are bound by interactions other than electrostatic ones. To what extent SO and Ca2+ can form inner-sphere complexes is not yet well established. SO2 is able to shift the point of zero proton condition of many oxides. 

Specific adsorption of ions other than protons causes the pzc and the iep to shift along the pH scale (Stumm, 1992). Specifically adsorbed cations (anions) shift the titration curve and the point of zero proton condition at the surface (pznpc) to lower (higher) pH values, whereas the iep is moved to higher (lower) pH values. The shift of the iep of hematite to a lower pH by adsorbed EDTA and Cl" is shown in Figure 10.8. 

Attempted y-deprotonation of the y,y-disubstituted Z-a,/ -unsaturated complex carbonyl(>)5-cyclopentadienyl)(4-methyl-l-oxo-2-pentenyl)(triphenylphosphane)iron, followed by exposure to protonating conditions, leads to a mixture of uncharacterized products no regenerated starting complex was detected37. 

A 13C NMR study on (104) under strongly protonating conditions (86AQ(C)6l) has determined the equilibrium between the protonated azide (105) and the protonated tetrazolopyridinium salt (106). Comparison of the 13C NMR values of (104) in tiifluoroacetic acid (i.e., those of (105) or (106)) with those of 2-azido-l-ethylpyridinium salt (107) and l-methyltetrazolo[l,5-a]pyridinium salt (108) revealed unambiguously that the bicyclic cation (106) is present under these conditions. 

Gas-phase protonation of spiropentane 19 using 3HeT+ or D3+ as protonating agents provided initially the comer protonated spiropentane, which rearranged into 1 -methylcy-clobutyl cation (i.e. bicyclobutonium ion 9)45. Under mild protonating conditions, cis- and trows-2-methylcyclopropylcarbinyl cations 17 and 18 were observed. These cations were presumably formed through the isomerization of the 1-methylcyclobutyl cation 9 into the... 

Proton condition—A condition of balance between species that contain the proton and counteracting species that do not contain the proton at a particular end point such as the dead end. 

The numerical values for the correction term (i.e., the second term in equation 37) are given in Table 3.5. Since we are frequently interested in the equilibrium concentrations of the various species in a solution of a given pH ( = p H), it is convenient to convert K Vo K. With the operational K, calculations can be carried out for all species in terms of concentrations, with the exception of H". In equilibrium calculations, concentration conditions and charge balance or proton conditions must be formulated in terms of concentrations. 

Any acid-base equilibrium can be described by a system of fundamental equations. The appropriate set of equations comprises the equilibrium constant (or mass law) relationships (which define the acidity constants and the ion product of water) and any two equations describing the constitution of the solution, for example, equations describing a concentration and an electroneutrality or proton condition. Table 3.6 gives the set of equations and their mathematical combination for pure solutions of acids, bases, or ampholytes in mono-protic or diprotic systems. 

Instead of the proton condition, the electroneutrality equation can be used. Independent of chaise type, a combination of electroneutrality and concentration condition gives the proton condition. Na in NaHX or Na2X is used as a symbol of a nonprotolyzable cation (Li, K, . . . ). 

There are alternative algebraic functions. Instead of writing the electro-neutrality equation, we can derive a relation called the proton condition. If we made our solution from pure H2O and HB, after equilibrium has been reached the number of excess protons must be equal to the numtier of proton deficiencies. Excess of deficiency of protons is counted with respect to a zero level reference condition representing the species that were added, that is, H2O and HB. The number of excess protons is equal to [H ] the number of proton deficiencies must equal [B ] -I-[OH ]. This proton condition gives, as in equation iva, [H" ] = [B ] -f lOH-]. 

We note that equation 40b is identical to the proton condition (iva) of Example 3.3a that is, the choice of HB as a component is equivalent to our earli( r notion of HB and H2O as reference level. In examining equations 39 and 40, we see that there are effectively four unknown species activities (B, HB, OH, and H ), the activity of H2O being constant for the dilute solution. As n Example 3.3a, there are four independent relationships 39a, 39d, 40a, and 40b, the remaining expressions being irrelevant for our conditions. Although water is always a component in our tableaux, we will omit it from subsequent tableaux for simplicity, the concentration of H2O being effectively constant for dilute solutions. 

Approximations in the proton condition similar to those used in the previous examples are not permissible in this case. However, an approximation might be possible in the concentration condition. Because Ac is a weak base, [Ac ] > [HAc] and [Ac ] = C. If we combine this approximation with the proton condition and the two equilibrium constants, we obtain... 

As shows by Example 3.4, the acidity equilibrium for HCl can be ignored because [HCl] < [Cl"]. Similarly, HCl can be neglected in the subsequent concentration and proton conditions. 

Computing the equilibrium composition of a 10" M HA solution, we simply have to find where on the graph Ae appropriate proton condition is fulfilled. The condition to be satisfied is... 

The same graph can be used to compute the equilibrium concentrations of a 10" M solution of NaA, In this case the proton condition is... 

The proton conditions of equations 48 and 49 correspond to the two equivalence points in acid-base titration systems. The half-titration point is usually (not always) given by pH = pAT. Thus the qualitative shape of the titration curve can be sketched readily along these three points (Figure 3,3a). 

It is obvious from the graph that no approximation in the proton condition is possible. In order to find the point where the proton condition is fulfilled, we move slightly to the right of the intersection of log[HAc] with log[OH"] and find by trial and error where the proton condition is fiilfilled, that is, at... 

Figure 3.6. Equilibrium composition of diprotic acid (Example 3.12). A 5 x 10 M sodium phthalate solution (Na2P) has a pH of 8.6. Proton condition 2 [H2PI + [HP ] + [H ] = [OH ] [HP ] = [OH ].

Because proton conditions corresponding to equivalent points / = 0 and / = 1 can readily be identified, titration curves can be sketched expediently with the help of the log concentration diagram. 

The reference level is defined by the composition of a pure solution of HA in H2O (/ = 0 [ANC] = 0), which is defined by the proton condition, [H l = [A-] -i- [OH ]. (In this and subsequent equations, the charge type of the eicid is unimportant the equation defining the net proton excess or deficiency can always be derived from a combination of the concentration condition and the condition of electroneutrality.) Thus in a solution containing a mixture of HA and NaA, [ANC] is a conservative capacity parameter. It must be expressed in concentrations (and not activities). Addition of HA (a species defining the reference level) does not change the proton deficiency and thus does not affect [ANC]. 

In the same monoprotic acid-base system, the base-neutralizing capacity with respect to the reference level (/ = 1) of a NaA solution (proton condition [HA] -I- [H ] = [OH ]) is defined by... 

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