Multiple inflection points

A potentiometric titration curve often has an inflection point at the PZC (Section 2.6.3). This property has been proposed as a method to determine the PZC [673]. The inflection point method gained some popularity after a publication by Zalac and Kallay [670]. Also, the differential potentiometric titration described in [674] is equivalent to the inflection point method. This method is not recommended by the present author as a standalone method to determine the PZC, but a few results obtained by the inflection point method, usually in combination with other methods, are reported in the tables in Chapter 3 (as Inflection in the Methods columns). In [675], the potentiometric titration curve of one sample had two inflections, and the inflection at the lower pH was assumed to be the PZC. The potentiometric titration curves of other samples had one inflection each. Reference [676] reports an inflection point in the titration curve of niobia at pH 8, which is far from the pHg reported in the literature. A few examples of charging curves without an inflection point or with multiple inflection points are discussed in Section 2.6.3. 

Caplan and Essig (1989) provided a simple model of active ion transport, having properties consistent with a multidimensional inflection point when one of the variables was the electrical potential difference across the membrane. A multiple inflection point may not be unique other conditions may exist where flows Ji and J2 simultaneously pass through an inflection point of on variation of Xi at constant X2, and vice versa. It is frequently not possible to vary both forces independently in biological systems. However, if Xi can be controlled experimentally along a proper pathway, while X2 is kept constant, the response of the flows to change in Xi will permit a thermodynamic characterization of the system. 

Mg in fertilizers is based on such proceedings thereof has been applied on multiple occasions. In milk fermentation, where the samples were dried, calcined in a furnace at 600 °C, the ash was dissolved in 0.03 M HCl, the solution was centrifuged and the supernatant was thus analyzed . The complexometric method for determination of Ca(II) and Mg(II) can be carried out in a single titration with EDTA in alkaline solution, using a Ca-ISE for potentiometric determination of two endpoints. This is accomplished on digitally plotting pCa values measured by the ISE as a function of the volume V of titrant added to the aliquot of analyte the first and second inflection points of the curve mark the Ca(II) and Mg(n) equivalences, respectively. ... 

Note that because this compound does have multiple basic functionalities, two ionization equilibria could be written for this amphoteric species. At mobile pH values between 3 and 5 the existence of multiple species is expected. Since the two pK values are close to one another 2pKa units apart), the inflection points overlap, making titration and/or chromatographic... 

A simple preliminary test of the JMAYK applicability to each studied case is worth of mentioning. The simple multiple of temperature, T, and the maximum reaction rate, da/dt, which should be confined to the value of 0.63 0.02, can be used to check its appropriateness. Another handy test is the value of shape index, i.e., the ratio of intersections, b and bz, of the in inflection slopes of the observed peak with the linearly interpolated peak baseline, which should show a linear relationship of the kind = 0.52 + 0.916 Tu/Ts - , where Ti s are the respective inflection-point temperatures [397,530]. 

To illustrate the complexity, we will take a simple case in which the enzymes typically follow the Michaelis-Menten kinetic mechanism. We will also make the following assumptions (a) only one ionic form of the enzyme is active (mono-protic), (b) no change occurs in RDS due to ionization, and (c) the enzyme maintains active conformation within the experimental pH range. For this type of enzyme, an observable quantity, e.g., rate constant (k), depends on the pH of the system as follows (i) the plot of k against pH resembles a titration curve, yielding at the inflection point the pK of the acid involved, (ii) the follows the ionization of the enzyme—substrate complex, (iii) the fC follows the ionizations of both the free enzyme and the enzyme—substrate complex, and (iv) the follows the ionization of the free enzyme only, even when there are multiple intermediates on the reaction pathway. 

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