Titration curves, theoretical

In Sections 10.11-10.16 it is shown how the change in pH during acid-base titrations may be calculated, and how the titration curves thus obtained can be used (a) to ascertain the most suitable indicator to be used in a given titration, and (b) to determine the titration error. Similar procedures may be carried out for oxidation-reduction titrations. Consider first a simple case which involves only change in ionic charge, and is theoretically independent of the hydrogen-ion concentration. A suitable example, for purposes of illustration, is the titration of 100 mL of 0.1M iron(II) with 0.1M cerium(IV) in the presence of dilute sulphuric acid ... 

Figure 10-3. Theoretical titration curves for the model compounds of Asp and His obtained from REX-CPHMD simulations [41]. Solid curves are the obtained by fitted the computed deprotonated fraction to the generalized Henderson-Hasselbach equation. The dashed lines indicate the computed pKa values...

First of all, the mesomerism of HBI is rendered complex by the presence of several protonable groups actually, HBI might exist, depending on pH, under cationic, neutral, zwitterionic, anionic, and possibly enolic forms (Fig. 3a). The experimental p/sTa s of model analogs of HBI in aqueous solutions have been studied. Titration curves follow two macroscopic transitions at pH 1.8 and pH 8.2, each corresponding to a single proton release [69]. Comparison of theoretical... 

Calcium is titrated with EGTA (l,2-bis-(2-amminoethoxyethane N,N,N, N -tetracetic acid) in the presence of the zinc complex of zincon as indirect indicator for calcium. Theoretical titration curves are calculated by means of the computer program HALTAFALL in order to assess accuracy and precision. The method gives a relative precision of 0.00028 when applied to estuarine water of 0.05-0.35% salinity. 

Figure 11A shows a theoretical example of a titration curve A + B = AB, where the signal is proportional to the amount of complex. The solid lines represent conditions where Bmax is equal to KD. Here for both presentations of signal vs either [Atotal] (total concentration of A added to the preparation) or [Afree] (concentration of non-complexed A in the solution, calculated as [Atotal] - ([AB]) the plot is curved and allows discrimination between free and complexed binding partners. If [Bmax] is substantially higher than KD the issue of active site... 

Theoretical (dotted line) and experimental (continuous line) titration curves for such a mixture are shown in Figure 6.8(b). The formation of mixed crystals and solid solutions limits the accuracy to 1-2% when the halides are present in similar concentrations. 

A theoretical treatment of combination titrations with an ideal indicator electrode was given by Meites et al. [89-91 ]. They have shown that the dilution effect causes a deviation of the titration curve inflection point from the equivalence point. However, this deviation is small compared with the error... 

When the second derivative of (5.32) is calculated and set equal to zero, the inflection point of the titration curve is obtained [23, 24, 133, 134). It has been found that the theoretical titration error generally increases with decreasing sample concentration, with increasing value of the solubility product or of the dissociation constant, with increasing value of the dilution factor and with increasing concentration of the interferents. Larger errors are obtained with unsymmetrical titration reactions. The overall error is a combination of these factors the greatest effect is exerted by the sample concentration, a smaller one by the equilibrium constant and the interferents, and the smallest by dilution. To obtain errors below 1%, it must approximately hold that eg, > 10 2 i,K< 10 , < 10 to 10" and r < 0.3. 

We now turn our attention to details of precipitation titrations as an illustration of principles that underlie all titrations. We first study how concentrations of analyte and titrant vary during a titration and then derive equations that can be used to predict titration curves. One reason to calculate titration curves is to understand the chemistry that occurs during titrations. A second reason is to learn how experimental control can be exerted to influence the quality of an analytical titration. For example, certain titrations conducted at the wrong pH could give no discernible end point. In precipitation titrations, the concentrations of analyte and titrant and the size of Ksp influence the sharpness of the end point. For acid-base titrations (Chapter 11) and oxidation-reduction titrations (Chapter 16). the theoretical titration curve enables us to choose an appropriate indicator. 

Theoretical titration curves for enzymes can be calculated from known crystal structures and first principles of electrostatics. Key amino acids at the active site have significantly perturbed pK values and unusual regions in which they are partially protonated over a wide pH region.3 In principle, such titration calculations can identify the active site of a protein whose structure is known, but whose function is not. 

Figure 12-11 Theoretical titration curves for the reaction of 50.0 mL of 0.040 0 M metal ion with 0.080 0 M EDTA at pH 10.00.

To extract acid dissociation constants from an acid-base titration curve, we can construct a difference plot, or Bjerrum plot, which is a graph of the mean fraction of bound protons, H, versus pH. This mean fraction can be measured from the quantities of reagents that were mixed and the measured pH. The theoretical shape of the difference plot is an expression in terms of fractional compositions. Use Excel SOLVER to vary equilibrium constants to obtain the best fit of the theoretical curve to the measured points. This process minimizes the sum of squares [nH(measured) -nH( theoretical) 2. 

Calculate some points on the theoretical titration curve before performing the experiment. Then compare the theoretical and experimental results. Also note the coincidence of the potentiometric and visual end points. 

Using the pKa values from problem 3, construct the theoretical titration curve showing the equivalents of H+ or OH reacting with 1 mol of glycine as a function of pH. Note that the shape of this curve is independent of the pfCa. Sketch similar curves for glutamic acid (pK./s equal 2.19,4.25, and 9.67), histidine (pfCa s equal 1.82,6.00, and 9.17) and lysine (pfCa s equal 2.18,8.95, and 10.53). 

Ruzic, I. and Nikolic, S., 1982. The influence of kinetics on the direct titration curves of natural water systems - theoretical considerations. Anal. Chim. Acta, 140 331-334. 

The identicalness of the ionization sites in a linear polyelectrolyte (Tanford, 1961) stimulated the interest of Walter and Jacon (1994) in a possible relationship between Kz and M of ionic polysaccharides displaying the characteristic titration curve of a weak, monobasic acid. Without any theoretical assumption, Eq. (S.4) was derived from simple algebra by combining elementary principles of the dissociation theory of weak acids with polymer segment theory ... 

Before the equivalence point the couple OjRi is in excess and determines the potential, and after the equivalence point the couple in excess is 02/R2 and this determines the potential. Therefore, by use of expressions (13.1) and (13.2) it is possible to construct the theoretical titration curve if the values of and Ef are known (Fig. 13.1). 

The correction factor, c, for hydrochloric acid interference is calculated with reference to the titration curve obtained in the blank run described above. The titer corresponding to the second inflection point, near —320 mV, is subtracted from that corresponding to the first inflection point (near +130 mV) to obtain the titer for the carboxyl group in p-hydroxybenzoic acid. Subtraction of the theoretical titer for p-hydroxybenzoic acid, a, from this value affords the HC1 interference correction factor, c ... 

Bowden, J. W., A. M. Posner, and J. P. Quirk. 1977. Ionic adsorption on variable charge mineral surfaces Theoretical charge development and titration curves. Aust. J. Soil. Res. 15 121-136. 

A stepwise change in pH can be applied outside a protein-containing membrane applied on top of an ISFET, at the interface between the membrane and the electrolyte, using a flow-through system [ 10]. This pH step will lead to simultaneous diffusion and chemical reaction of protons and hydroxyl ions in the membrane. A theoretical description of these phenomena, elaborated in the next subsection, leads to the conclusion that the diffusion of protons in the membrane is delayed by a factor that depends linearly on the protein concentration. Consequently, the time needed to reach the end point in the obtained titration curve also depends linearly on the protein concentration. The effect of both the incubation time and the protein concentration will be simulated and experimentally verified. 

The existence of these earlier reviews makes it possible for the present treatment to be limited in scope. It will be sufficient to touch only superficially on experimental techniques and on the theoretical derivation of equations The major objective will be, as the title of the paper implies, to show what one can learn from titration curves that is of general interest to protein chemistry. 

The relation between structure and acidity of organic compounds has been the subject of much study. Those aspects which are of interest in connection with protein titration curves have been reviewed in definitive manner by Edsall and Wyman (1958) and by Edsall (1943), and the reader is referred to these reviews for a discussion of the theoretical and empirical principles which are involved. For the present purpose it is sufficient to extract the data which will lead to the expected pK values of the titratable groups of proteins, and this has been done in Table I. 

The preceding equations have not yet been used as basis for the analysis of any actual titration curve of a protein. It should be feasible soon to apply the theory to the titration curve of myoglobin, the complete three-dimensional structure of which should be available soon (Kendrew et al., 1961). This will permit exact localization of all titratable groups on the protein molecule and, hence, the theoretical evaluation of the from assumed intrinsic pK s. It is not to be expected that these values will accurately reproduce the titration curve, but it is to be expected that the cause of observed deviations will be relatively easy to determine. Essentially three possibilities would be looked for in such a first application of the theory. 

Titration curves cannot measure these variations in charge. Only Zh is determinable. However, theoretical equations relate charge fluctuations to the titration curve, so that they can be calculated. One obvious result of charge fluctuations is that (Zh) is not the same as, and this is in fact the parameter by which the spread of molecules among different values of Zh is usually characterized. 

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