Experimental Titration Data

The procedure described in the preceding paragraph will of course measure the number of hydrogen ions bound to or dissociated from all substances which are present in the solution under study. The accuracy of an experimental electrometric titration curve depends to a considerable degree on the absence of buffers, carbon dioxide, and any other substance, other than the protein of interest, which is capable of acting as an acid or base. 

Titration studies are nearly always carried out so as to maintain the same ionic strength and protein concentration throughout the curve, but this is not essential for all applications. Titration curves are always dependent on ionic strength, and a curve which is not obtained at constant ionic strength can be duplicated only if the ionic strength changes are duplicated. Titration curves are often independent of protein concentration, but will depend on the concentration whenever the possibility of association between protein molecules exists. 

Titration curves may sometimes depend on the time which has elapsed, between addition of acid or base and the measurement of pH. (This is true, for instance, of the alkaline part of the curve shown in I dg. 2.) By the same token, the titration curve obtained by addition of successive increments of acid or base to the same protein solution will sometimes differ from the curve obtained by addition of successively larger increments of acid or base, each to a fresh aliquot of the initial protein solution. 

Some titration curves or parts of titration cruves are independent of the initial pH, i.e., the number of H+ ions which are bound in going from, say, a reference point at pH 5 to pH 4, is the same as the number bound in 

We have described titration curves as records of the number of hydrogen ions attached to a protein molecule at any pH, relative to the number attached at an arbitrary reference pH. It is advantageous however to choose as reference point a position on the titration curve which has physical significance. There are three such positions  

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Fitting of experimental titration data to determine the rate constants for a reversible reaction ethanol + acetic Acid <-> ethyl acetate +water ... 

Figure 4.2 Potentiometric titration curves (a) experimental titration data (b) first derivative of curve a (c) second derivative of curve a.

Studies of metal speciation in oceanic water show that experimental titration data fit models which consider one class of ligands (33-36, 57, 108) or two classes of ligands (32, 37, 69, 109). Attempts to fit experimental data to models which consider more than two classes of ligands did not improve goodness of fitting. 

Fitting of experimental titration data to determine the rate... 

Figure A-19 Modelled titration curves against experimental titration data (curve (e) in Fig. 2 of [69FAU/DER]) for the system 20 mL KHCO3/KOH 1 M + 10 mL KOH 1 M + 2 mL ZrOCb IM (diluted with pure water to 100 mL), assuming formation of different Zr-carhonate complexes. The assumed formation constants (logn, ) are given in parentheses in the legend.

Modelled titration curves against experimental titration data (curve (e) in Fig. 2 of [69FAU/DER]) for the system 20 mL KHCO3/KOH 1 M + 10... 

The experimental titration data for the series of Model Proteins I, i, ii, iii, iv, and v are listed in Table 5.5 and shown in Figure 5.34, where the differential effects of charge-charge and apolar-polar repulsion become apparent. For Model Proteins i, ii, iii, iv, and v, for each systematic shift in pKa there occurs a corresponding increase in Hill coefficient. Model Protein I, however, does not fall within the series, because it exhibits a pKa shift without an increase in magnitude of the Hill coefficient. Model Protein I and iv exhibit essentially the same Hill coefficient of 2.7, whereas the pKa values differ by 0.3 pH units. 

Experiment 10 at the Book Companion Website www.whfreeman.com/ exploringchem5e teaches you how to fit the theoretical expressions 10-14 or 10-15 to experimental titration data. Excel Solver is used to find the best values of analyte concentration and p to fit the measured data. 

The acidic groups have different pK values depending on their location on the carbon surface relative to the location of nonacidic groups that can exert an inductive effect on them [46], Then, by a potentiometric titration method it is assumed that the system under study consists of acidic sites characterized by their acidity constants K. The site population can thus be described by a continuous pK, distribution function f(pKJ [54-57]. The experimental titration data are thus transformed into a proton-binding curve from which the distribution of acidity constants is obtained by using, for example, the splines-based numerical procedure SAIEUS suggested by Jagiello [58]. 

Values of p/Tapp and n obtained by fitting experimental titration data can reasonably correlate such data accurately over a range of a near 0.5, but the... 

In Fig. C microscopic acidity constants of the reaction AlOHg =AIOH + H+ for y-AI203 are plotted as a function of AIOH. The data are for 0.1 M NaCICV This figure illustrates (within experimental precision) the conformity of the proton titration data to the constant capacitance model. Calculate the capacitance. 

Macroscopic experiments allow determination of the capacitances, potentials, and binding constants by fitting titration data to a particular model of the surface complexation reaction [105,106,110-121] however, this approach does not allow direct microscopic determination of the inter-layer spacing or the dielectric constant in the inter-layer region. While discrimination between inner-sphere and outer-sphere sorption complexes may be presumed from macroscopic experiments [122,123], direct determination of the structure and nature of surface complexes and the structure of the diffuse layer is not possible by these methods alone [40,124]. Nor is it clear that ideas from the chemistry of isolated species in solution (e.g., outer-vs. inner-sphere complexes) are directly transferable to the surface layer or if additional short- to mid-range structural ordering is important. Instead, in situ (in the presence of bulk water) molecular-scale probes such as X-ray absorption fine structure spectroscopy (XAFS) and X-ray standing wave (XSW) methods are needed to provide this information (see Section 3.4). To date, however, there have been very few molecular-scale experimental studies of the EDL at the metal oxide-aqueous solution interface (see, e.g., [125,126]). 

Figures 13 to 17 show some experimental plots of titration data according to Eq. (14). For some of the examples chosen, ion binding data were available, so that the left-hand side of Eq. (14) could be plotted against Z.

Fig. 5.35. (A) Degree of ionisation (a as a function of mobile phase pHapp for the solutes BA and D,L-PA and for PBA. a was calculated from the corresponding potentiometric titration data (see Fig. 2.14, in Chapter 2). (B) Product of the degree of ionisation of the solute (a B) and the polymer PBA (b a) (x 100) versus mobile phase pHapp (solid line). Overlayed are the experimental data from Fig. 5.34 (dashed line). From Sellergren and Shea [129].

Accurate measurement of surface acidity constants for reactions 11 and 12 can be difficult (Davis and Kent, 1990 Dzombak and Morel, 1990), especially for natural systems (Stollenwerk, 1995). Acidity constants are often derived from acid-base titration data (Parks and de Bruyn, 1962), and constants for several metal oxides have been published. These published values have been used as initial estimates for modeling adsorption in natural systems with complex mineralogy. The acidity constants have then been optimized simultaneously with equilibrium constants for other solutes to give the best fit to experimental data (Goldberg and Glaubig, 1988b Kent et al, 1995 Kent et al., 2001). 

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