PH titration curve

Periodic table a chart showing all the elements arranged in columns with similar chemical properties. (2.8) pH curve (titration curve) a plot showing the pH of a solution being analyzed as a function of the amount of titrant added. (8.5)... 

When a saturated solution of sulphur dioxide is titrated against approximately 2 M sodium hydroxide solution the following pH curve is obtained Figure 10.4) ... 

It was indicated that the original method can be extended on systems where two or three analytes can be determined from a single titration curve. The shifts DpH affected by j-th PT addition should be sufficiently high it depends on pH value, a kind and concentration of the buffer chosen and its properties. The criterion of choice of the related conditions of analysis has been proposed. A computer program (written in MATLAB and DELPHI languages), that enables the pH-static titration to be done automatically, has also been prepared. 

A plot of the pH of the analyte solution against the volume of titrant added during a titration is called a pH curve. The shape of the pH curve in Fig. 11.4 is typical of titrations in which a strong acid is added to a strong base. Initially, the pH falls slowly. Then, at the stoichiometric point, there is a sudden decrease in pH through 7. At this point, an indicator changes color or an automatic titrator responds electronically to the sudden change in pH. Titrations typically end at this point. However, if we were to continue the titration, we would find that the pH... 

Figure 11.5 shows a pH curve for a titration in which the analyte is a strong acid and the titrant is a strong base. This curve is the mirror image of the curve for the titration of a strong base with a strong acid. 

EXAMPLE 11.4 Sample exercise Calculating points on the pH curve for a strong add-strong base titration... 

This is point B in Fig. 11.4. Note that the pH has fallen, as expected, bur only by a very small amount. This small change is consistent with the shallow slope of the pH curve at the start of the titration. 

FIGURE 11.6 The pH curve for the titration of a weak acid with a strong base 25.00 mL of 0.100 m CH jCOOH(aq) with 0.150 m NaOHfaq . The stoichiometric point (S) occurs at pH > 7 because the anion CH jC02 is a base. The other points on the curve are explained in the text. 

Figures 11.6 and 11.7 show the different pH curves that arc found experimentally for these two types of titrations. Notice that the stoichiometric point does not occur at pH = 7. Moreover, although the pH changes reasonably sharply near the stoichiometric point, it does not change as abruptly as it does in a strong acid-strong base titration.

Now consider the overall shape of the pH curve. The slow change in pH about halfway to the stoichiometric point indicates that the solution acts as a buffer in that region (see Fig. 11.3). At the halfwayr point of the titration, [HA] = [A ] and pH = pfCa. In fact, one way to prepare a buffer is to neutralize half the amount of weak acid present with strong base. The flatness of the curve near pH = pKa illustrates very clearly the ability of a buffer solution to stabilize the pH of the solution. Moreover, we can now see how to determine pKa plot the pH curve during a titration, identify the pH halfway to the stoichiometric point, and set pKa equal to that pH (Fig. 11.8). To obtain the pfCh of a weak base, we find pK3 in the same way but go on to use pKa -1- pfq, = pKw. The values recorded in Tables 10.1 and 10.2 were obtained in this way. 

FIGURE 11.9 A commercially available automatic titrator. The stoichiometric point of the titration is detected by the sudden change in pH that occurs in its vicinity the pH is monitored electronically. The pH curve can be plotted as the reaction proceeds, as shown on the monitor screen. 

Because many biological systems use polyprotic acids and their anions to control pH, we need to be familiar with pH curves for polyprotic titrations and to be able to calculate the pH during such a titration. The titration of a polyprotic acid proceeds in the same way as that of a monoprotic acid, but there are as many stoichiometric points in the titration as there are acidic hydrogen atoms. We therefore have to keep track of the major species in solution at each stage, as described in Sections 10.16 and 10.17 and summarized in Figs. 10.20 and 10.21. 

Suppose we are titrating the triprotic acid H P04 with a solution of NaOH. The experimentally determined pH curve is shown in Fig. 11.13. Notice that there are three stoichiometric points (B, D, and F) and three buffer regions (A, C, and E). In pH calculations for these systems, we assume that, as we add the hydroxide solution, initially NaOH reacts completely with the acid to form the diprotic conjugate base... 

U 4 Interpret the features of the pH curve for the titration of a strong or weak acid with a strong base and a strong or weak base with a strong acid (Sections 11.4 and 11.5). 

When plotted on a graph of pH vs. volume of NaOH solution, these six points reveal the gross features of the titration curve. Adding additional calculated points helps define the pH curve. On the curve shown here, the red points A-D were calculated using the buffer equation with base/acid ratios of 1/3 and 3/1. Point E was generated from excess hydroxide ion concentration, 2.00 mL beyond the second stoichiometric point. You should verify these additional five calculations. 

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 ... 

In connection with the above, we shall still consider the pH curves of the displacement titrations, because in fact they represent a back-titration of an alkaline reacting salt (e.g., NaA) with a strong acid or of an acidic reacting salt (e.g., MX) with a strong base, so that in Fig. 2.19 the foregoing data of equivalence point and initial point are of direct application. 

The titration is represented in Fig. 2.22 by plotting the Pt electrode potential versus the titration parameter k. BB is the voltage curve for titration of Fe2+ with Ce4+ and B B that for titration of Ce4+ with Fe2+ they correspond exactly to the pH curves BB and B B in Fig. 2.18, with the exception that the initial point in Fig. 2.22 would theoretically have an infinitely negative and an infinitely positive potential, respectively. In practice this is impossible, because even in the absence of any other type of redox potential there will be always a trace of Fe3+ in addition to Fe2+ and of Ce3+ in addition to Ce4+ present. Further, half way through the oxidation or reduction the voltage corresponds to the standard reduction potentials of the respective redox couples it also follows that the equivalence point is represented by the mean value of both standard potentials ... 

Figure 6.3 A schematic pH curve for the titration of a strong acid with a strong base. At the equivalence point, the amount of alkali added is the same as the amount of acid in solution initially, allowing for an accurate calculation of the acid s concentration. Note how the end point is determined by extrapolating the linear regions, and drawing a third parallel line between them...

Figure 6.5 A typical pH curve for the titration of carbonic acid (a weak acid) with a strong base. The concentration of H2CO3 and HCOj are the same after adding half the neutralization volume of alkali. At this point, pH = p...

Figure I-I. Weak acids act as buffers in a pH range near their pK s. According to the Henderson-Hasselbalch equation, when the ratio of conjugate base to conjugate acid, [A ]/[HA] is plotted versus pH, a titration curve is generated that indicates a region of good buffering at pH = pK I pH unit.

Figure 9.30 The behavior of oleate surfactants as a function of pH equilibrium titration curve of sodium oleate at 25 °C. Note the micelles at higher pH, and the vesicles at lower pH. The chemical name of oleic acid is ctT-9-octadecenoic acid, with 18 carbon atoms. (Modified from Cistola et al, 1988.)...

A zinc(II) complex 22a with an alcohol-pendent polyamine has been synthesized (23). The alcoholic OH deprotonates with pifa of 8.6 (determined by pH-metric titration), yielding 22b. Reaction of 22 (2 mM) with a phosphotriester diethyl(4-nitrophenyl) phosphate (0.1 mM) in 10 mM TAPS buffer (pH 8.6) at 25°C seemed to promote phosphoryl-transfer reactions to 23, just like acyltransferred intermediates 10 and 16a in the reactions between Znn-macrocyclic complexes with an alcohol pendent and NA (see Scheme 4). The pH dependence of the first-order rate constants gave a sigmoidal curve with an inflection point around the pKa value of 8.6. The hydrolysis of the substrate phosphotriester to the phosphodiester product diethyl phosphate thus seemed to... 

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