Shape of the Titration Curve

Let s investigate the titration of 1 mol/L hydrochloric acid with 1 mol/L sodium hydroxide and two other titrations with concentrations of 10 and 10 mol/L. Table 9.1 lists the pH values for each volume V added these values are obtained fi om 

Added NaOH cm Concentrations of titrand and titrant solutions  

Some important points emerge from the study of the curve. They must be emphasized  

In another respect, experiments show that the curves obtained are identical regardless of the strong acids and bases that are facing each other provided they are in the same concentration and volume conditions. This has been proven theoretically (see Chap. 10). 

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The precision of the end point signal depends on the method used to locate the end point and the shape of the titration curve. With a visual indicator, the precision of the end point signal is usually between +0.03 mb and 0.10 mb. End points determined by direct monitoring often can be determined with a greater precision. 

This experiment shows how modifying the matrix of the solution containing the analyte can dramatically improve the shape of the titration curve. 

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. 

A biologically important point is revealed by the basic shape of the titration curves of weak electrolytes in the region of the pK, pH remains relatively unaffected as increments of OH (or H ) are added. The weak acid and its conjugate base are acting as a buffer. 

In the practice of potentiometric titration there are two aspects to be dealt with first the shape of the titration curve, i.e., its qualitative aspect, and second the titration end-point, i.e., its quantitative aspect. In relation to these aspects, an answer should also be given to the questions of analogy and/or mutual differences between the potentiometric curves of the acid-base, precipitation, complex-formation and redox reactions during titration. Excellent guidance is given by the Nernst equation, while the acid-base titration may serve as a basic model. Further, for convenience we start from the following fairly approximate assumptions (1) as titrations usually take place in dilute (0.1 M) solutions we use ion concentrations in the Nernst equation, etc., instead of ion activities and (2) during titration the volume of the reaction solution is considered to remain constant. 

This concept allows the shape of the titration curves to be explained by postulating that the chloroform droplet size decreases as the interfacial tension (ift) between the aqueous and chloroform phases is decreased by the presence of active surfactant. As the endpoint in a titration is approached the amount of active SDBS decreases as it complexes with the injected hyamine. The reduction in the amount of active surfactant material results in an increase... 

Titration curves of the weak bases with HCl in toluene (0.12 M) solvent are given in Fig. 36.1. The shapes of the titration curves indicate that toluene is an excellent solvent for these weak bases. 

The PLIMSTEX titration curve shows that CaM becomes more stable (more hydrogen-bonded) upon Ca-binding (Fig. 11.5A). The formation of CaM-4Ca species is the biggest contributor to the shape of the titration curve and accounts for the largest conformational change in the stepwise Ca binding. The earlier... 

The titration curves of acetic acid, H2PO4, and NH4 (Fig. 2-18) have nearly identical shapes, suggesting that these curves reflect a fundamental law or relationship. This is indeed the case. The shape of the titration curve of any weak acid is described by the Henderson-... 

Ribonuclease is an enzyme with 124 amino acids. Its function is to cleave ribonucleic acid (RNA) into small fragments. A solution containing pure protein, with no other ions present except H+ and OH- derived from the protein and water, is said to be isoionic. From this point near pH 9.6 in the graph, the protein can be titrated with acid or base. Of the 124 amino acids, 16 can be protonated by acid and 20 can lose protons to added base. From the shape of the titration curve, it is possible to deduce the approximate pATa for each titratable group.1-2 This information provides insight into the environment of that amino acid in the protein. In ribonuclease, three tyrosine residues have "normal values of pATa(=10) (Table 10-1) and three others have pA a >12. The interpretation is that three tyrosine groups are accessible to OH, and three are buried inside the protein where they cannot be easily titrated. The solid line in the illustration is calculated from pA"a values for all titratable groups. 

As can be seen in Figure 1, the shape of the titration curve of a solution of the acid H4L differs from that obtained in presence of an equal quantity of a metal ion, indicating that some reactions take place between edta and the cation. Let us consider the case of three different metal ions Li+, Mg2+ and Cu2+, for which the stability constant A, = [ML]/([M][L]) is equal to 1028, 108-7 and 10l8 > respectively (/ = 0.1 M (KC1) and 20 °C). 

Why study titration curves The shape of a pH titration curve makes it possible to identify the equivalence point in a titration, the point at which stoichiomet-rically equivalent quantities of acid and base have been mixed together. Knowing the shape of the titration curve is also useful in selecting a suitable indicator to signal the equivalence point. We ll explore both of these points later. 

In order to measure a wider range of compounds, the traditional pH titrimetic methods (Jander) are still of good use. In the pH metric method, the sample is titrated in a pH range of choice with acid or base. The titration is monitored with a pH electrode. The pKas can be calculated from the shape of the titration curve. In order to get good resolution small pH intervals are titrated thus limiting the throughput of the method and leading to an increase in sample consumption. For validation and reference measurement this methods is still the method of choice. 

The titration curve of conalbumin (Wishnia et al., 1961) is complicated by time-dependent reactions in the acid range. These reactions, however, appear to influence only the shape of the titration curve, and the count of... 

Back-titrations of the reaction solutions were also performed. The back titrant was O.OIN HCl solution. The shapes of the titration curves were similar for both the forward and back titrations. The number of milliequivalents added to reach the equivalence points was different for each titration pair. In the back titrations, the exchange capacities of the molecules were slightly smaller. The smaller exchange capacities can be explained by irreversible colloid formation. These colloids would remove some of the exchange sites from contact with the solution. A titration curve for K" " shows the two sites prevalent in the Na" series. The first site s pK differs from its Na" " analog by 0.7 units. The second site s pK is essentially the same as the Na" counterpart. This indicates that the lower pK... 

Wolfrom and coworkers have summated their analytical data on the barium acid salt of heparin, and have expressed the data in terms of a tetrasaccharide unit which comprises two molecular proportions each of 2-amino-2-deoxy-D-glucose residue and D-glucuronic acid residue, and 5 (rather than 6) ester sulfate groups, in an N S ratio of 2 5. The barium sulfur ratio was 1 2, which indicated that the sulfur is essentially present as ester sulfate, and hence the acidity must be due to the carboxyl group, in accordance with the shape of the titration curve. " ... 

Figure 4-4 illustrates comparative effects of the dissociation constants of the acid titrated and the salt produced on the shapes of the titration curves. 

If both the half-reactions involved in a redox titration can be made to behave reversibly at a suitable electrode, the shapes of the titration curves should conform closely to the calculated values, though as pointed out above, the electrode potential reaches its equilibrium value more and more slowly with increasing dilution. 

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). 

Chao and Cheng [76CHA/CHE] studied the determination of a number of anions, single or in mixtures, by a stepwise potentiometric titration with silver nitrate at pH = II. The silver ion activity was measured with a silver ion selective electrode based on silver sulphide. The data were also used to estimate the solubility products of the silver salts formed during a titration. The method is only sketched in the paper but appears to have proceeded along the following course. The potential of incipient precipitation ( prec) was estimated graphically from the shape of the titration curve. p,ec would thus be a measure of the silver ion activity at the nominal and known concentration of the anion in the presence of its silver salt. 

All of the foregoing wiU indicate to the reader that equations (27) and (28) demonstrate the origin of the S-shaped curves and reversed S-shaped curves typical of potentiometric titrations. The tables and figures to follow will illustrate the effects of various titration conditions on the shape of the titration curve. 

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