Dissociation Curve titration

Typical values for pAlg are in the range of 9.0 to 9.8. At physiological pH, the a-carboxyl group of a simple amino acid (with no ionizable side chains) is completely dissociated, whereas the a-amino group has not really begun its dissociation. The titration curve for such an amino acid is shown in Figure 4.7. 

Similar possibilities might appear to exist for zein and pepsin, which also contain relatively large numbers of tyrosine residues. Because zein is insoluble in water, however, it has been titrated only in alcohol-water mixtures (Neuberger, 1934 Cohn, Edsall, and Blanchard, 1934), and pepsin is so unstable in neutral and alkaline solution that its dissociation curve above pH 6 (which must refer to the denatured protein) is known only approximately (Herriott and Northrop, 1934). 

Fig. 10. Dissociation curves of globin (solid line) and paraglobin (broken line) from interpolated graphical data of Roche (1930). Open circles are 3-seoond titration data and solid circles are back-titration for COHb (Steinhardt and Zaiser, 1951). Lower curve (inset) represents the difference between globin and paraglobin curvo.s, and the difference between 3-second and back-titration curves for COHb.

Here c = Cm + oic JKq and is equal to Ci when a = l. is calculated from surface titration experiments and Kq = Aocxpi-Uo/RT). Once nmax,Ko, n, and Uo are specified and the variation of tlto with pH known, then a plot of adsorption against pH can be constructed. Equation (80) reduces to Freundlich or Langmuir isotherms in given limiting cases, and when j/tq varies with pH in a manner parallel to the electrolyte dissociation curve the equation predicts adsorption curves that agree with the experimental observations of early workers. 

Fig. 12. Comparison of titration (full line) and polarographic (dotted line) dissociation curves. The shift is due to the recombination reaction.

It has been shown that for most acid-base titrations the inflection point, which corresponds to the greatest slope in the titration curve, very nearly coincides with the equivalence point. The inflection point actually precedes the equivalence point, with the error approaching 0.1% for weak acids or weak bases with dissociation constants smaller than 10 , or for very dilute solutions. Equivalence points determined in this fashion are indicated on the titration curves in figure 9.8. 

The principal limitation to using a titration curve to locate the equivalence point is that an inflection point must be present. Sometimes, however, an inflection point may be missing or difficult to detect, figure 9.9, for example, demonstrates the influence of the acid dissociation constant, iQ, on the titration curve for a weak acid with a strong base titrant. The inflection point is visible, even if barely so, for acid dissociation constants larger than 10 , but is missing when is 10 k... 

This method provides a reasonable estimate of the piQ, provided that the weak acid is neither too strong nor too weak. These limitations are easily appreciated by considering two limiting cases. For the first case let s assume that the acid is strong enough that it is more than 50% dissociated before the titration begins. As a result the concentration of HA before the equivalence point is always less than the concentration of A , and there is no point along the titration curve where [HA] = [A ]. At the other extreme, if the acid is too weak, the equilibrium constant for the titration reaction... 

Using its titration curve, determine the acid dissociation constant for the weak acid in problem 6. 

The titration curve of phosphoric acid in the presence of sodium hydroxide is shown in Figure 1. Three steps, corresponding to consecutive replacement of the three acidic hydrogens, and two inflection points, near pH = 4.5 and 9.0, are evident. Dissociation constants are = 7.1 x 10 = 6.3 x 10 ... 

In the discussion of the relative acidity of carboxylic acids in Chapter 1, the thermodynamic acidity, expressed as the acid dissociation constant, was taken as the measure of acidity. It is straightforward to determine dissociation constants of such adds in aqueous solution by measurement of the titration curve with a pH-sensitive electrode (pH meter). Determination of the acidity of carbon acids is more difficult. Because most are very weak acids, very strong bases are required to cause deprotonation. Water and alcohols are far more acidic than most hydrocarbons and are unsuitable solvents for generation of hydrocarbon anions. Any strong base will deprotonate the solvent rather than the hydrocarbon. For synthetic purposes, aprotic solvents such as ether, tetrahydrofuran (THF), and dimethoxyethane (DME) are used, but for equilibrium measurements solvents that promote dissociation of ion pairs and ion clusters are preferred. Weakly acidic solvents such as DMSO and cyclohexylamine are used in the preparation of strongly basic carbanions. The high polarity and cation-solvating ability of DMSO facilitate dissociation... 

As the titration begins, mostly HAc is present, plus some H and Ac in amounts that can be calculated (see the Example on page 45). Addition of a solution of NaOH allows hydroxide ions to neutralize any H present. Note that reaction (2) as written is strongly favored its apparent equilibrium constant is greater than lO As H is neutralized, more HAc dissociates to H and Ac. As further NaOH is added, the pH gradually increases as Ac accumulates at the expense of diminishing HAc and the neutralization of H. At the point where half of the HAc has been neutralized, that is, where 0.5 equivalent of OH has been added, the concentrations of HAc and Ac are equal and pH = pV, for HAc. Thus, we have an experimental method for determining the pV, values of weak electrolytes. These p V, values lie at the midpoint of their respective titration curves. After all of the acid has been neutralized (that is, when one equivalent of base has been added), the pH rises exponentially. 

The shapes of the titration curves of weak electrolytes are identical, as Figure 2.13 reveals. Note, however, that the midpoints of the different curves vary in a way that characterizes the particular electrolytes. The pV, for acetic acid is 4.76, the pV, for imidazole is 6.99, and that for ammonium is 9.25. These pV, values are directly related to the dissociation constants of these substances, or, viewed the other way, to the relative affinities of the conjugate bases for protons. NH3 has a high affinity for protons compared to Ac NH4 is a poor acid compared to HAc. 

Potentiometric titration curves The procedure involves the addition of a salt of a weak acid to the resin and the determination of the pH of the equilibrated solution. Table 9 shows the pK values of the OH groups and dissociation constants of the studied resin. The first ionization occurs at a pH slightly higher than that of sul-... 

Each leg of the titration curve is calculated separately. The first leg, from pH 1 to 6, corresponds to the dissociation of protonated alanine, H2A+. The second leg, from pH 6 to 11, corresponds to the dissociation of zwitterionic alanine, HA. It s as if we started with H2A+ at low pH and then titrated with NaOH. When 0.5 equivalent of NaOH is added, the deprotonation of H2A+ is 50% done when 1.0 equivalent of NaOH is added, the deprotonation of H2A+ is complete and HA predominates when 1.5 equivalent of NaOH is added, the deprotonation of H A is 50% done and when 2.0 equivalents of NaOH is added, the deprotonation of HA is complete. 

With a knowledge of the pH at the stoichiometric point and also of the course of the neutralisation curve, it should be an easy matter to select the appropriate indicator for the titration of any diprotic acid for which K1/K2 is at least 104. For many diprotic acids, however, the two dissociation constants are too close together and it is not possible to differentiate between the two stages. If K 2 is not less than about 10 7, all the replaceable hydrogen may be titrated, e.g. sulphuric acid (primary stage — a strong acid), oxalic acid, malonic, succinic, and tartaric acids. 

Weak acid with a strong base. In the titration of a weak acid with a strong base, the shape of the curve will depend upon the concentration and the dissociation constant Ka of the acid. Thus in the neutralisation of acetic acid (Ka— 1.8 x 10-5) with sodium hydroxide solution, the salt (sodium acetate) which is formed during the first part of the titration tends to repress the ionisation of the acetic acid still present so that its conductance decreases. The rising salt concentration will, however, tend to produce an increase in conductance. In consequence of these opposing influences the titration curves may have minima, the position of which will depend upon the concentration and upon the strength of the weak acid. As the titration proceeds, a somewhat indefinite break will occur at the end point, and the graph will become linear after all the acid has been neutralised. Some curves for acetic acid-sodium hydroxide titrations are shown in Fig. 13.2(h) clearly it is not possible to fix an accurate end point. 

Weak acids with weak bases. The titration of a weak acid and a weak base can be readily carried out, and frequently it is preferable to employ this procedure rather than use a strong base. Curve (c) in Fig. 13.2 is the titration curve of 0.003 M acetic acid with 0.0973 M aqueous ammonia solution. The neutralisation curve up to the equivalence point is similar to that obtained with sodium hydroxide solution, since both sodium and ammonium acetates are strong electrolytes after the equivalence point an excess of aqueous ammonia solution has little effect upon the conductance, as its dissociation is depressed by the ammonium salt present in the solution. The advantages over the use of strong alkali are that the end point is easier to detect, and in dilute solution the influence of carbon dioxide may be neglected. 

This potential reflects itself in the titration curves of weak polyacids such as poly(acrylic acid) and poly(methacrylic acid) [32]. Apparent dissociation constants of such polyacids change with the dissociation degree of the polyacid because the work to remove a proton from the acid site into the bulk water phase depends on the surface potential of the polyelectrolyte. 

It is worth mentioning that an attempt was made by Tsao and Willmarth to determine the acid dissociation constant of HO2. The reaction between hydrogen peroxide and peroxydisulphate was used for the generation of the HO2 radical. However, these experiments, like others where the HO2 radical is studied under steady-state conditions, could yield only a value of acidity constant multiplied by a coefficient consisting of a ratio of kinetic parameters. Unfortunately, in this case there are no independent data for the kinetic coefficient, and the value of cannot be evaluated. Considering the kinetic analogue of the titration curve it can be stated only that ionization of HO2 becomes important in the pH range from 4.5-6.5. The value of acidity constant of HO2 obtained by Czapski and Dorfman is (3.5 + 2.0)x 10 mole.l. . ... 

Attention is secondly focused on Figure 6.5 (B) which represents the titration curve of a weak acid against a strong base. The poor dissociation of the weak acid is reflected in the initial conductivity being low. The addition of alkali results in the formation of highly ionized sodium acetate and the conductance of the solution begins to increase. 

Case A is depicted in Fig. 2.17. The pH curves were obtained by assuming full dissociation of the acid and the base and by calculating the pH at each X from the H+ concentration remaining, i.e., on the basis of the part (1 - X) not yet titrated. Considering the shape and vertical position of the curves and the pH value of the equivalence point, we can list the following characteristics ... 

In titrations we normally have to deal mainly with weak to fairly strong acids (or bases), so that for acids we can use the equation Ka = [H+ ] [A- ]/[HA] hence [H+] = KB [HA]/[A ]. When only a part X of the acids has been titrated, we find [H+ ] = Ka (1 - A)// this equation is approximately valid, because the salt formed is fully dissociated, whereas the dissociation of the remaining acid has been almost completely driven back. Hence for the pH curve we obtain the Henderson equation for acid titration ... 

The titration course can be illustrated (see Fig. 2.20) by a pAg curve whose values are obtained from the silver potential EAg = E g + RT/Fln aAg+ or at 25° C EAg = EAg - 0.05916 pAg. As AgN03 as a salt is fully dissociated into ions, the initial point of the curve is determined by the original concentration the later part of the curve up to the titration end-point can be obtained in the same way because the Ag+ concentration undergoes a simple reduction as a consequence of the withdrawal of Ag+ into the AgCl precipitate. At the... 

Subsequently, Bos and Dahmen used in m-cresol65 (e = 12.29 at 25° C) a potentiometric titration method combined with conductometry. Essential precautions were the preparation of water-free m-cresol (<0.01% of water), the use of a genuine Bronsted base B, e.g., tetramethylguanidine (TMG), and the application of a glass electrode combined with an Ag-AgCl reference electrode filled with a saturated solution of Me4NCl in m-cresol. The ion product of the self-dissociation of m-cresol, Ks, was determined from the part beyond the equivalence point of the potentiometric titration curve of HBr with TMG comparison with titration curves calculated with various Ka values showed the best fit for Ks = 2 10 19... 

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