Titration equation comparison

A comparison with the reversible interface can be made. The reversible solid electrolyte interface can be used in a similar way to explore the distribution of charge components at solid-water interfaces. As we have seen, the surface charge density, o, (Eqs. (3.1) and (iii) in Example 2.1) can be readily determined experimentally (e.g., from an alkalimetric titration curve). The Lippmann equations can be used as with the polarized electrodes to obtain the differential capacity from... 

A further improvement in the NMR titration comes from eliminating both pH and n entirely and expressing the comparison in terms of chemical shifts only.25,26 This is applicable to any pair of acids, AH+ and BH+, with a ratio of acidity constants K equal to /A 11. It is readily shown that the chemical shifts are related to each other by Equation (18), where 6a and Sb are the observed chemical shifts during the titration and SA, <5AH-, <5B, and <5BH- are limiting chemical shifts of unprotonated and protonated A and B. This is a nonlinear equation in the one parameter K, and it can be fit by nonlinear least squares. 

The typical plot of titration curves is presented in Fig. 6. By the comparison of H+ or OH- concentration changes, for defined volume of the acid or base, the surface charge can be calculated according to the equation ... 

If the observed titration curve is based on a false molecular weight, then the values of Z which one uses in Eq. (14) are equal to (Ma/MOZi. Thus the term wZ of the equation is equal to w Mi/Mi)Z, and, by comparison with Eq. (16), the apparent value of w becomes... 

At the equivalence-point, which represents the other extreme of the titration, a and h are equal, and cn may be neglected in comparison with CoH , since the solution is alkaline owing to hydrolysis of the salt of the weak acid and strong base. It is seen, from equation (42), therefore, that B is now equivalent to a — coh , and, neglecting the activity coefficients, equation (39) becomes... 

In a titration, then, the assignment is to determine the volume of the titrant necessary to reach the equivalence point, while one measures the pH (or a related quantity, such as the color of the added indicator) to monitor how close one is to that equivalence point. It is therefore logical to express the titration curve in terms of the titrant volume as a function of pH or [H+]. This approach, which will be followed here, leads to simple theoretical expressions for the course of the titration, expressions that can all be described in terms of a simple master equation, and that allow easy and direct comparison with experimental data. 

The curves from the direct and reverse potentiometric titration of metavanadate ions with the Lux bases NaOH and Na2C03 are presented in Fig. 1.2.14a. The neutralization process runs in two stages according to the equations (1.2.87) and (1.2.88), to which two small diffuse pO-drops (bends) in the potentiometric curves correspond. Nevertheless, these bends become apparent on the differential potentiometric titration curve, shown in Fig. 1.2.14b. The reverse titration results in two steps of neutralization, also, that confirms the reversibility of the process of the acid-base neutralization of vanadium(V) oxocompounds in molten Nal. Comparison with the corresponding dependencies for the molten equimolar KCl-NaCl... 

Tam KY andTakacs-Novac K, Multi-wavelengfii spectrophotometric determination of acid dissociation constants. Anal. Chim. Acta, 434, 157-167 (2001). NB A new spectrophotometric method was validated by comparison wifii file standard method of Albert and Serjeant, using 10 M solutions in 0.15M KCl. No details of pH meter calibration. In the novel method, operational pH values were converted to p[H] by a multi-parametric equation (ref. 12, Avdeef A). Sample concentrations of 10-100 uM were titrated in a Sirius GLpKa instrument and pH data were collected when drift was <0.02 pH/min. 15-25 wavelengfiis were used for each measurement. Note that errors are for reproducibility only, not accuracy. 

Comparison of the Henderson-Hasselbalcn Equation to Titration Curves of Polyelectrolytes and Model Proteins... 

The most efficient ojjerational design would be for the machine to operate over the range of the acid-base titration curve with the steepest An/Ap slope. Because the Hill coefficient, n, as defined in Equation (5.20) is a measure of the slope, it provides for ready comparison of efficiencies. The Hill coefficients for Model Proteins I through v are listed in Figure 5.34, and the slopes are plotted in the inset. Accordingly, the comparison of the efficiencies of Model Proteins i and v simply becomes iii/liy = 1.5/8.0 = 0.19. Thus, by increasing the hydropho-bicity by the replacement of five Val (V) residues by five Phe (F) residues, as indicated in Table 5.5, increases the efficiency of the protein-based machine by just over fivefold. 

Fig. 20.1. Comparison of the ionization constants of HjSO and H3PO4 (left scale), with those of several polymers measured in water at room temperature without added salt (right scale). For the polymers, the a dependence, when available, is determined by potentiometric titration using the p/f = pH + log a/1 — a empirical equation. For PEO, pK is not precisely known and a possible range of values deduced from those of ethers is indicated. The black circles are p/f values for PjVP and P4VP ( 5) according to M. Satoh ef uE Macromolecules 22 (1989) 1808-12 and for BPEI according to C. J. Bloys Van Treslong ef al., Reel. Trav. Chim. Pays-Bos 93 (1974) 171-8. The letters P, S and T refer to the pK values of the primary, secondary and tertiary amino groups in BPEI respectively, estimated by C. J. Bloys Van Treslong, Reel. Trav. Chim. Pays-Bas 97 (1978) 9-21.

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