Titration curves experimental

In the overview to this chapter we noted that the experimentally determined end point should coincide with the titration s equivalence point. For an acid-base titration, the equivalence point is characterized by a pH level that is a function of the acid-base strengths and concentrations of the analyte and titrant. The pH at the end point, however, may or may not correspond to the pH at the equivalence point. To understand the relationship between end points and equivalence points we must know how the pH changes during a titration. In this section we will learn how to construct titration curves for several important types of acid-base titrations. Our... 

Finding the End Point Potentiometrically Another method for locating the end point of a redox titration is to use an appropriate electrode to monitor the change in electrochemical potential as titrant is added to a solution of analyte. The end point can then be found from a visual inspection of the titration curve. The simplest experimental design (Figure 9.38) consists of a Pt indicator electrode whose potential is governed by the analyte s or titrant s redox half-reaction, and a reference electrode that has a fixed potential. A further discussion of potentiometry is found in Chapter 11. 

Experimental arrangement for recording a potentiometric redox titration curve. 

In a titrimetric method of analysis the volume of titrant reacting stoichiometrically with the analyte provides quantitative information about the amount of analyte in a sample. The volume of titrant required to achieve this stoichiometric reaction is called the equivalence point. Experimentally we determine the titration s end point using a visual indicator that changes color near the equivalence point. Alternatively, we can locate the end point by recording a titration curve showing the titration reaction s progress as a function of the titrant s volume. In either case, the end point must closely match the equivalence point if a titration is to be accurate. Knowing the shape of a titration... 

As the titration begins, mostly HAc is present, plus some H and Ac in amounts that can be calculated (see the Example on page 45). Addition of a solution of NaOH allows hydroxide ions to neutralize any H present. Note that reaction (2) as written is strongly favored its apparent equilibrium constant is greater than lO As H is neutralized, more HAc dissociates to H and Ac. As further NaOH is added, the pH gradually increases as Ac accumulates at the expense of diminishing HAc and the neutralization of H. At the point where half of the HAc has been neutralized, that is, where 0.5 equivalent of OH has been added, the concentrations of HAc and Ac are equal and pH = pV, for HAc. Thus, we have an experimental method for determining the pV, values of weak electrolytes. These p V, values lie at the midpoint of their respective titration curves. After all of the acid has been neutralized (that is, when one equivalent of base has been added), the pH rises exponentially. 

The pH at the equivalence point is thus approximately 3.7 the secondary ionisation and the loss of carbonic acid, due to any escape of carbon dioxide, have been neglected. Suitable indicators are therefore methyl yellow, methyl orange, Congo red, and bromophenol blue. The experimental titration curve, determined with the hydrogen electrode, for 100 mL of 0.1 M sodium carbonate and 0.1M hydrochloric acid is shown in Fig. 10.7. 

In Fig. 15.7 are presented (a) the part of the experimental titration curve in the vicinity of the equivalence point (b) the first derivative curve, i.e. the slope of the titration curve as a function of V (the equivalence point is indicated by the maximum, which corresponds to the inflexion in the titration curve) and (c) the second derivative curve, i.e. the slope of curve (b) as a function of V (the second derivative becomes zero at the inflexion point and provides a more exact measurement of the equivalence point). 

For further discussion of experimental methods for determination of electrophoretic titration curves of proteins, see the recent study by Gianazza et al. [129], For discussion of the free solution mobility of DNA see Stellwagen et al. [368],... 

After the usual corrections for analyte impurity, potential drop in the solution and volume increase during titration, the experimental results were in perfect agreement with the theoretical hyperbolic curve. 

At first we determined, by means of the DVP method, ifTMAX of 2,4-dinitro-phenolate, 2,5-dinitrophenol picrate, acetate and benzoate, which lay between 10 3 and 10 5. Next, separate potentiometric titrations of 2,5-dinitrophenol and picric acid were carried out on the basis of the previously known (see above) ptfax = 6.5 and P hx2- = 100 for 2,5-dinitrophenol and p.fiTHX = 3.0 for picric acid, we calculated titration curves for estimated values of 0 and obtained, for the best fit between the experimental and calculated curves, K o = 10 21 for both 2,5-dinitrophenol and picric acid. In both instances changing fTMA0H for 1 to 10 6 did not alter the calculated titration curve. Finally, for potentiometric titrations of other acids with TMAOH while using / TMAX values from DVP results, in addition to Kn 0 = 10 21, we obtained the best fit between the experimental and calculated curves again when pifbenzoic acid = 1 (see Fig. 4.12)... 

Thus the best approach for HTS purposes is to experimentally determine the effect of enzyme titration on the observed reaction velocity, and to then choose to run the assay at an enzyme concentration well within the linear portion of the curve (as in Figure 4.6). Again, the other details of the assay conditions can affect the enzyme titration curve, so this experiment must be performed under the exact assay conditions that are to be used for library screening. 

First of all, the mesomerism of HBI is rendered complex by the presence of several protonable groups actually, HBI might exist, depending on pH, under cationic, neutral, zwitterionic, anionic, and possibly enolic forms (Fig. 3a). The experimental p/sTa s of model analogs of HBI in aqueous solutions have been studied. Titration curves follow two macroscopic transitions at pH 1.8 and pH 8.2, each corresponding to a single proton release [69]. Comparison of theoretical... 

To use this method, the sample is dissolved in a system containing two phases (e.g., water and octanol) such that the solution is at least about 5 x 10-4 M. The solution is acidified (or basified) and titrated with base (or acid) under controlled conditions. The shape of the ensuing titration curve is compared with the shape of a simulated curve, which is created in silico. The estimated p0Ka values (together with other variables used to construct the simulated curve such as substance concentration factor, CO2 content of the solution and acidity error) are allowed to vary systematically until the simulated curve fits as closely as possible to the experimental curve. The p0Ka values required to achieve the best fit are assumed to be the correct measured p0Ka values. This computerized calculation technique is called refinement , and is described elsewhere [14, 15]. 

To select an indicator for an acid-base titration it is necessary to know the pH of the end point before using equation (5.5) or standard indicator tables. The end point pH may be calculated using equations (3.27), (3.29) or (3.30). Alternatively, an experimentally determined titration curve may be used (see next section). As an example, consider the titration of acetic acid (0.1 mol dm 3), a weak acid, with sodium hydroxide (0.1 mol dm-3), a strong base. At the end point, a solution of sodium acetate (0.05 mol dm 3) is obtained. Equation (3.28) then yields... 

Theoretical (dotted line) and experimental (continuous line) titration curves for such a mixture are shown in Figure 6.8(b). The formation of mixed crystals and solid solutions limits the accuracy to 1-2% when the halides are present in similar concentrations. 

We will demonstrate how the surface charge of a hydrous oxide (a-FeOOH) can be calculated from an experimental titration curved (e.g., Fig. 2.2). 

Fig. 3.4a gives plots of charge resulting from surface protonation vs pH for various oxides. Dots represent experimental data from different authors (Table 3.1a) from titration curves at ionic strength I = 0.1 M (hematite = 0.2 M). It is interesting to note that the data "of different oxides" can be "normalised" i.e., made congruent, if we chose the master variable... 

Surface protonation isotherms. Dots represent experimental data from titration curves at ionic strength I = 0.1 (Hematite, I = 0.2). References are indicated in Table 3.1. The concentration of protonated sites MOH is given in moles nr2. BET surface data were used to calculate the surface concentration. 

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... 

In Figs. 2.10a and b experimental data on the shift in the titration curves were given and in Example 2.4 it was shown how these effects are quantified, and that the extent of adsorption can be determined from the displacement of the titration curve. 

Method I. To illustrate the application of these methods, the experimental data for the adsorption of H+/OH on TiC (32 ) are considered (Figure 5). Use of Method I involves the approximations in the material balance equations that, on the acidic branch of the titration curve,... 

The experimental titration curve is normally the pH as a function of the added number of moles of base. This is the inverse function of Eq. (2.6.5). 

The actual values of gjj determined experimentally depend, of course, on the method used to extract the effective fej and 2 from the titration curve. Figure 4.32 shows the BI (transformed into -20 + 2 to conform with the titration curve, see Appendix G) and its derivative, along with the corresponding titration curves for the values of k, Ajj, and k with = 1/2. It is clear that the BI has four... 

Titration curve for seawater. The shape of the curve is dependent upon experimental conditions. The top curve is produced when seawater is titrated in an open container so that CO2 generated after incremental acid addition can escape into the atmosphere. The bottom curve is generated when seawater is titrated in a closed container. In this case, the pH drops faster during the initial part of the titration because of the build-up of CO2 as acid is added. Once the carbonate/carbonic acid equivalence point is reached, both curves converge upon the same pH for the same volume of acid added, but extensive laboratory work has demonstrated that better accuracy is achieved with the closed container method. Source From Pilson, M. E. Q. (1998). An Introduction to the Chemistry of the Sea. Prentice-Hall, p. 119. 

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