Analysis of Titration Data

The location of the end-point of a titration by using either the first or second derivative of the titration data was discussed in Chapter 9. These methods use only the data points near the end-point. Another approach. Gran s method, makes use of the complete data set. It is useful when either (i) the inflection at the end-point is poorly defined or (ii) data at the end-point is missing. 

Consider an acid-base titration. At any point before the end-point, the concentration of unreacted H is given by 10 P. Thus, to estimate the volume required to reach the end-point, it is merely necessary to plot 10 P versus titrant volume V and extrapolate to 10 P = 0. If dilution by the titrant is important, then the function 10 P should be multiplied by (Vq + / O/ where Vq is the initial volume. 

The chloride ion concentration at any point on the titration curve can be calculated from equation 20-5, which can be derived from the Nernst equation. 

Offset is used to scale the E values into a more convenient range and can be any potential value slope is the Nemst slope, theoretically 59.2 mV at 25 C. 

To obtain the end-point volume, the value of V where [Cl ] = 0, you need to calculate the x intercept. The x intercept = -intercept/slope = 32.83 mL, the endpoint volume for the titration. 

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Table 2 pA), values of various monobasic acids and aminium ions as determined by Hyperquad analysis of titration data at 1 x 10 3 M in anhydrous ethanol, T = 25.0 °C... 

Barnard T. E. and Bisogni J. J. (1985) Errors in Gran function analysis of titration data for dilute acidified waters. Water Res. 19, 393-399. 

The last of these (Zn3L/ ) is one of the most stable and is shown as (117f6). Information about the above series was derived from computer analysis of titration data, a procedure which gave the following series for cysteine (L ) (Perrin and Sayce, 1968) ... 

Analysis of Titration Data Generation of Binding Profiles... 

Liu, H. Fang, H.H.E (2002) Characterization of electrostatic binding sites of extracellular polymers by linear programming analysis of titration data. Biotechnology and Bioengineering, 80, 806-811. 

In this experiment students standardize a solution of HGl by titration using several different indicators to signal the titration s end point. A statistical analysis of the data using f-tests and F-tests allows students to compare results obtained using the same indicator, with results obtained using different indicators. The results of this experiment can be used later when discussing the selection of appropriate indicators. 

At pION s analytical services laboratory, the pKa of a molecule (whose structure may not be known beforehand) is first measured by the TFA method, because very little sample is consumed. (Sometimes there is not much more than 1 mg of sample with which to work.) Only when the analysis of the data proves problematic do we repeat the measurement, the second time using potentiometry, where more sample is required. If any indication of precipitation is evident, either DMSO or methanol is added to the titrated solution and the titration is repeated 3 times (using the same sample), with additional water added between the repeats, to obtain different Rw values of the mixed solvent solutions. It has been our experience that if the TFA method fails and more sample is available, the follow-up pH-metric method always works. 

An important question is whether we can use any indicator electrode. A redox electrode, i.e. inert in the range of potential where measurements are being done, is a possibility, especially for redox titrations. In other cases, the use of electrodes selective to the ion being titrated is better, such as pH electrodes in acid-base titrations. The method of analysis of the data obtained is, naturally, the same in all cases and independent of electrode material. 

To obtain accurate estimates of the number of binding sites (n), binding experiments (usually titrations) need to be performed under conditions where the total concentration of A is relatively high, specifically that cAit0, 1 / KAs these conditions define a stoichiometric titration where effectively all of the B added is bound until the sites on A are saturated. Titrations under these conditions are insensitive to the value of the association constant, so to obtain reliable estimates of KAss, data are needed from titrations at much lower concentrations, where cA, toi- V-Kaw It should be clear from this discussion that it is not easy to evaluate both n and accurately, and it is usually necessary to do a global analysis of several data sets, obtained under different concentration conditions. 

Equilibrium studies involving double-stranded trihelicates have demonstrated the co-operative nature of metal ion binding. A spectrophotometric titration investigation of the stepwise binding of copper(I) to a (substituted) tris-bipyridyl ligand system of the present type in dichloromethane-acetonitrile (1 1) indicated the formation of a single, well-defined product. From analysis of the data, the self-... 

Rather than resort to purely empirical selection of suitable values of ni and p(/Cint)< for equation 1 it is more usual to begin by fitting experimental data with values of m chosen to conform with the numbers of prototropic groups determined by several more direct and specific methods of examination of titration data. Even where the theoretical analysis of a titration curve is not attempted and exact values of p(Ki t), for each type of group are therefore lacking, the numbers of groups so determined may furnish valuable clues to the internal structure of the protein, especially when they are compared with the results of amino acid analyses. 

The results of uncontrolled trials should be discussed to the extent that they provide supportive evidence of effectiveness. This is followed by an analysis of dose-response or blood level-response information. This section should include (a) an integrated summary and analysis of all data, from animal, pharmacokinetic, pharmacodynamic, and other clinical pharmacol ogy trials, and from controlled and uncontrolled clinical trials that bear a dose-response or blood level-response relationship to effectiveness, (b) the method of dose selection, and (c) the choice of dose interval. Data that support the dosing recommendation proposed in labeling, including the recommended starting and maximal doses, the method of dose titration, and other methods regarding individualization of dosage also should be discussed. Any deviations from relatively simple dose-response or blood level-response relationships due to nonlinearity of pharmacokinetics, delayed effects, tolerance, etc., as well as limitations of the data, should be described. 

The variation of the photon correlation spectrum of a 0.25 mg/ml solution of PCS was studied during titration with aliquots of a. 05 mg/ml solution of rooster comb HA. Analysis of these data was performed using an iterative least-squares fit to a series of equally-spaced exponentials. Amplitudes, A, and time constants of each exponential are independently varied. We found that a single exponential fit sufficed initially 0.1)... 

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