Bjerrum difference plots

Figure 3.1 Four-step construction of the Bjerrum difference plot for a three-pi molecule, whose constants are obscured in the simple titration curve (see text) (a) titration curves (b) isohydric volume differences (c) rotated difference plot (d) Bjerrum plot. [Avdeef, A., Curr. Topics Med. Chem., 1, 277-351 (2001). Reproduced with permission from Bentham Science Publishers, Ltd.]...

Figure 13-14 Bjerrum difference plot for the titration of glycine. Many experimental points are omitted from the figure for clarity. 

The spreadsheet in Figure 13-13 computes [H ] and [OH ] in columns C and D. beginning in row 16. The mean fraction of protonation, oH(measured) from Equation 13-59. is in column E. The Bjerrum difference plot in Figure 13-14 shows mh(measured) versus pH. Values of aHiA and aHA from Equations 13-61 are computed in columns F and G. and nH(theoretical) was computed with Equation 13-60 in column H. Column I contains the squares of the residuals, [wH(measured) — mh(theoretical)]2. The sum of the squares of the residuals is in cell B12. 

Avdeef (1998) has reported an automated potentiometric titration method for the determination of solubilities of drug substances containing ionizable groups, where a graphical procedure is used for the estimation of solubility constants based on Bjerrum difference plots. One useful relation derived in this work was ... 

Typically, 10 ml of 0.5 to 10 mM solutions of the samples were preacidified to pH 1.8-2.0 with 0.5 M HCl, and were ttien titrated alkalimetrically to some appropriate high pH (maximum 12.0). The titrations were carried out at 25.0 0.1 °C, at constant ionic strength using NaCl, and under an inert gas atmosphere. The initial estimates of pKg values were obtained from Bjerrum difference plots (nH vs. pH) and then were refined by a wei ted nonlinear least-squares procedure (Avdeef, 1992,1993). For each molecule a minimum of three and occasionally five or more separate titrations were performed and the average pXa values along with the standard deviations were calculated."... 

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. 

In acid-base titrations, a difference plot, or Bjerrum plot, is a graph of the mean fraction of protons bound to an acid versus pH. The mean fraction is nH calculated with Equation 13-59. For complex formation, the difference plot gives the mean number of ligands bound to a metal versus pL(= —log[ligand]). 

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 key element in the data analysis is the construction of the difference or Bjerrum plot. This plot shows the average number of bound protons versus pcH. The difference plot is obtained from the difference between two titration curves one is the titration of an ionizable substance and the other is a blank titration. Graphically, the pKa corresponds to the pH where the average number of bound proton equals 0.5 (or a multiple of 0.5 if multiple ionization takes place). Nowadays nonlinear regression calculations are used to derive pKa values form Bjerrum plots. 

Figure 6.8 shows the Bjerrum plots for an weak acid (benzoic acid, pKa 3.98, log So — 1.55, log mol/L [474]), a weak base (benzydamine, pKa 9.26, log So —3.83, log mol/L [472]), and an ampholyte (acyclovir, pKa 2.34 and 9.23, log So — 2.16, log mol/L I/40N ). These plots reveal the pKa and pA pp values as the pcH values at half-integral % positions. By simple inspection of the dashed curves in Fig. 6.8, the pKa values of the benzoic acid, benzydamine, and acyclovir are 4.0, 9.3, and (2.3, 9.2), respectively. The pA pp values depend on the concentrations used, as is evident in Fig. 6.8. It would not have been possible to deduce the constants by simple inspection of the titration curves (pH vs. volume of titrant, as in Fig. 6.7). The difference between pKa and pA pp can be used to determine log So, the intrinsic solubility, or log Ksp, the solubility product of the salt, as will be shown below.

Titration in a mixture with resolution of difference UV-visible spectra Data analysis for up to nine components with TITAN program Bjerrum plots for determinationn of systematic cone, errors Evaluation of digital potentiometric titns. by the Tubbs method... 

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