Acidity constant from titration curve

A difference plot, also called a Bjerrum plot, is an excellent means to extract metal-ligand formation constants or acid dissociation constants from titration data obtained with electrodes. We will apply the difference plot to an acid-base titration curve. 

Silicic Acid. Figure 6 (from Ref. 18) illustrates the effect of silicic acid on the titration curve of goethite ( -FeOOH). Dissolved silica is primarily present as H4Si04 below pH = 9. (The acidity constants of H4Si04 at Z = 0.5, 25°C, are pKa = 9.5, pKag = 12.6.) The shift in the titration curve caused by silica reflects a release of protons which can be explained with the reactions... 

The macroscopic dissociation constants are those determined directly from titration curves and can be used directly for calculation of the charge of the molecules at various pH values. They do not reveal which protons and acid groups are involved in the different ionization steps. For the simple monoamino monocarboxylic acids it is well known that the first pK value corresponds to that of the COOH group, the second to that of the NHJ group in agreement with the top part of the following scheme ... 

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. . ... 

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. 

Titrations curves for polyprotic acids have an inflection point for each hydrogen in the formula if the dissociation constant (Ka) for each hydrogen is very different from the others and if any dissociation constant is not too small. The titration curves of the polyprotic acids H2S04 and H3P04 are shown in Figures 5.6 and 5.7. Sulfuric acid has essentially one inflection point (like hydrochloric acid—compare with Figure 5.1(a)), while phosphoric acid has two apparent inflection points. Both hydrogens on the... 

Example 2.1 Evaluation of Surface Charge from Alkalimetric and Acidimetric Titration Curves and Determination of Surface Acidity Constants... 

The acidity constants calculated from every point in the titration curve (Figure 2.2a and b) are microscopic acidity constants (Eqs. 2.5, 2.6). Each loss of a proton reduces the charge on the surface and thus affects the acidity of the neighboring... 

From alkalimetric-acidimetric titration curves on hydrous ferric oxide the following intrinsic acidity constants have been obtained (I = 0.1 M, 25° C)... 

Whatever the aim of a particular titration, the computation of the position of a chemical equilibrium for a set of initial conditions (e.g. total concentrations) and equilibrium constants, is the crucial part. The complexity ranges from simple 1 1 interactions to the analysis of solution equilibria between several components (usually Lewis acids and bases) to form any number of species (complexes). A titration is nothing but a preparation of a series of solutions with different total concentrations. This chapter covers all the requirements for the modelling of titrations of any complexity. Model-based analysis of titration curves is discussed in the next chapter. The equilibrium computations introduced here are the innermost functions required by the fitting algorithms. 

The potentiometric titration curves of gels, which relate the pH of the exterior solution to the degree of ionization of the gel, resemble the titration curves of monofunctional acids or bases. However, the dissociation constants differ, often by two orders of magnitude, from the expected value for the functional group, and the slope of the curves is not the usual one. Addition of neutral salt changes the picture markedly and brings the curves closer to expectation. In the case of weak or medium... 

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. 

The possibility of determining the acids in wines from the titration curve using special equations has been extensively investigated in Portugal by Pato and coworkers (79). To keep the ionic force constant, appropriate dilution is needed. Tartaric, malic, lactic, and succinic acid were determined in musts and wines. 

TITRATION (Thermometric). This technique consists of the detection and measurement of the change in temperature of a solution as the titrant is added to it, under as near adiabatic conditions as possible. Experimentally, the titrant is added from a constant-delivery burette into die titrate (solution to be titrated) which is contained in an insulated container such as a Dewar flask. The resultant temperature-volume (or time) curve thus obtained is similar to odier titration curves, e.g., acid-base, in that the end point of the reaction can be readily ascertained. Since all reactions involve a detectable... 

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). 

The determination of partition caefcients by the potentiometric method is part of the function of the Sirus PCA101 (Avdeef, 1993). Typically, a preacidiLed solution of a weak acid is alkalimetrically titrated to some appropriately high pH the partition solvent such as octanol is then added, and the dual-solvent mixture is acidimetrically titrated back to the starting pH. Analysis of the two titration curves will yield two fKgS pl< and pol, where pdQ, is the apparent constant derived from... 

The procedure for potentiometric titration is presented in Chapter 1.6. In this titration, a standard acid titrant is added to a measured volume of sample aliquot in small increments of 0.5 mL or less, that would cause a change in pH of 0.2 unit or less per increment. The solution is stirred after each addition and the pH is recorded when a constant reading is obtained. A titration curve is constructed, plotting pH vs. cumulative volume titrant added. The volume of titrant required to produce the specific pH is read from the titration curve. 

For multistep complexation reactions and for ligands that are themselves weak acids, extremely involved calculations are necessary for the evaluation of the equilibrium expression from the individual species involved in the competing equilibria. These normally have to be solved by a graphical method or by computer techniques.26,27 Discussion of these calculations at this point is beyond the scope of this book. However, those who are interested will find adequate discussions in the many books on coordination chemistry, chelate chemistry, and the study and evaluation of the stability constants of complex ions.20,21,28-30 The general approach is the same as outlined here namely, that a titration curve is performed in which the concentration or activity of the substituent species is monitored by potentiometric measurement. 

Table 1 tabulates literature values for acidity constants of seven amine-Ptn complexes with notations on the temperature, ionic strength, total Ptn concentration, method employed, conditions and other remarks, and the reference number. At least six factors enter into comparing determinations of a single complex. First is the purity of the complex under investigation. Because they rely on chemical shifts of an individual species, NMR methods are less dependent on purity than potentiometric titrations, which are interpreted on the basis of equivalents of added base. Rarely is the raw titration data published, but in one case it is evident from a plot of the data that the titration curve reveals up to about 10% impurity [7], Without knowing whether the impurities are acidic, basic, inert, or even forming during... 

Fig. 2.14. (A) Potentiometric titration curves of a polymer imprinted with L-PA (PLPA), a polymer imprinted with benzylamine (PBA), a blank non-imprinted polymer (PBL) and acetic acid in MeCN/O.lM NaCl 70/30 (v/v). The NaOH equivalents (x-axis) are calculated based on the theoretical amount of carboxylic acid groups present in the polymer. In (B) is seen the calculated distribution as a function of the degree of ionization (a ). The polymer swelling (ml/ml) in this solvent system was constant in the pH interval 3-12 and was for PLPA 1.32 and for PBL 1.26. From Sellergren and Shea [67].

From a qualitative point of view, a minimum difference in ionization constants is to be expected, because even though a molecule contains two equivalent ionizable protons, once one proton has been lost, the second is retained more strongly by an energy amounting to e jOr (where e is the electronic charge, D is the dielectric constant, and r is the distance between the proton and the charge on the add anion). Thus, for oxalic acid, Ky is about 1000 21 for adipic add, Ky is only about SK2 (nearly the factor of 4). The titration curve of an add in which Ky = 415 2 can be shown to be-identical in every respect to the titration curve of a monobasic acid of one-half its molecular wdght and with dissodation constant Kyjl. 

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