Results Titration

The most obvious sensor for an acid-base titration is a pH electrode.For example, Table 9.5 lists values for the pH and volume of titrant obtained during the titration of a weak acid with NaOH. The resulting titration curve, which is called a potentiometric titration curve, is shown in Figure 9.13a. The simplest method for finding the end point is to visually locate the inflection point of the titration curve. This is also the least accurate method, particularly if the titration curve s slope at the equivalence point is small. 

In such reactions, even though the indicator electrode functions reversibly, the maximum value of AE/AV will not occur exactly at the stoichiometric equivalence point. The resulting titration error (difference between end point and equivalence point) can be calculated or can be determined by experiment and a correction applied. The titration error is small when the potential change at the equivalence point is large. With most of the reactions used in potentiometric analysis, the titration error is usually small enough to be neglected. It is assumed that sufficient time is allowed for the electrodes to reach equilibrium before a reading is recorded. 

The resulting titration curves are more or less emperical and afford a reasonably dependable and reproducible means of end-point detection. 

The advantages of using molarity are twofold (1) Stoichiometry calculations are simplified because numbers of moles are used rather than mass, and (2) amounts of solution (and therefore of solute) are measured by volume rather than by mass. As a result, titrations are particularly easy (Section 3.10). 

Another specialized form of potentiometric endpoint detection is the use of dual-polarized electrodes, which consists of two metal pieces of electrode material, usually platinum, through which is imposed a small constant current, usually 2-10 /xA. The scheme of the electric circuit for this kind of titration is presented in Figure 4.1b. The differential potential created by the imposition of the ament is a function of the redox couples present in the titration solution. Examples of the resultant titration curve for three different systems are illustrated in Figure 4.3. In the case of two reversible couples, such as the titration of iron(II) with cerium(IV), curve a results in which there is little potential difference after initiation of the titration up to the equivalence point. Hie titration of arsenic(III) with iodine is representative of an irreversible couple that is titrated with a reversible system. Hence, prior to the equivalence point a large potential difference exists because the passage of current requires decomposition of the solvent for the cathode reaction (Figure 4.3b). Past the equivalence point the potential difference drops to zero because of the presence of both iodine and iodide ion. In contrast, when a reversible couple is titrated with an irreversible couple, the initial potential difference is equal to zero and the large potential difference appears after the equivalence point is reached. 

When the equivalence point is reached, the Fe2+ will have been totally consumed (the large equilibrium constant ensures that this will be so), and the potential will then be controlled by the concentration ratio of Ce3+/Ce4+. The idea is that both species of a redox couple must be present in reasonable concentrations for a concentration to control the potential of an electrode of this kind. If one works out the actual cell potentials for various concentrations of all these species, the resulting titration curve looks much like the familiar acid-base titration curve. The end point is found not by measuring a particular cell voltage, but by finding what volume of titrant gives the steepest part of the curve. 

Indirect Titration (Method B). A weighed sample of salt was added to a flask containing methanol and a known excess of aqueous sodium hydroxide solution. The mixture was stirred and warmed on a hot plate for 1 h. After cooling, the amount of excess hydroxide present was determined by titration with standard aqueous hydrochloric acid. The titration was monitored using a pH electrode and meter, and the end point was determined from the resulting titration curve. 

Figure 1 9-4 Spreadsheet and plot for titration of 50.00 mL of 0.0500 M Fe " with 0.1000 M Ce. Prior to the equivalence point, the system potential is calculated from the and Fe + concentrations. After the equivalence point, the Ce and Ce + concentrations are used in the Nernst equation. The Fe concentration in cell B7 is calculated from the number of millimoles of Ce added, divided by the total volume of solution. The formula used for the first volume is shown in documentation cell A21. In cell Cl, [Fe- ] is calculated as the initial number of millimoles of Fe present, minus the number of millimoles of Fe formed, divided by the total solution volume. Documentation cell A22 gives the formula for the 5.00-mL volume. The system potential prior to the equivalence point is calculated in cells F7 F12 by using the Nernst equation, expressed for the first volume by the formula shown in documentation cell A23. In cell F13, the equivalence-point potential is found from the average of the two formal potentials, as shown in documentation cell A24. After the equivalence point, the Ce(lll) concentration (cell D14) is found from the number of millimoles of Fe- initially present divided by the total solution volume, as shown for the 25.10-mL volume by the formula in documentation cell D21. The Ce(IV) concentration (El 4) is found from the total number of millimoles of Ce(lV) added, minus the number of millimoles of Fe + initially present, divided by the total solution volume, as shown in documentation cell D22. The system potential in cell FI4 is found from the Nernst equation as shown in documentation cell D23. The chart is then the resulting titration curve.

Now let us assign values to terms in these equations and calculate the titration curve. First, assume = 1.0 L, and that acid-solution and titrant base concentrations are both 0.01 eq/L as above or, in other words, that Cl, = Na = 0.01 eq/L. With these substitutions into Eqs. (5.77) and (5.78) and for different volumes of added base titrant, V, we can solve for the solution pH. Now because Q = Na and Na is given by Eq. (5.73), we can calculate Cg. The resultant titration curve of Cg versus pH is... 

One-electrode potentiometry involves the measurement of the potential of an indicator electrode with respect to a reference (nonpolarizable) electrode either at open circuit or with a small anodic or cathodic current applied to the indicator electrode. These three possibilities are shown in Figure 11.5.2 for the Fe -Ce titration, and the resulting titration curves are shown in Figure 11.5.3. The i = 0 curve, a), is the usual potentiometric titration curve, showing the equilibrium potential of the solution (F gq) as a function of/ When a small anodic current is impressed on the indicator electrode, the measured potential at a given/will be somewhat more positive than Fgq [curve (c)]. When a small cathodic cur-... 

Based on the curves in Figure 11.10.1, consider the titration of Sn with I2 using one-electrode amperometry. Sketch the resulting titration curves for a platinum indicator electrode maintained at... 

With the ability to detect and resolve the C-2 proton resonances of histidine residues in protein NMR experiments came the development of NMR-based methods to study the microenvironment and protonation state of histidine residues in proteins. In one strategy, the pH dependence of the chemical shifts observed for either the C-2 or C-4 protons in the imidazole side chain of histidine residues in protein NMR experiments is detamined the data in the resulting titration curve are used to determine the value of histidine residues in proteins [9,10,12]. Over the decades since its first use in the late 1960s, the earlier NMR strategy has become the method of choice for measuring the pK values of histidine residues in proteins. Such NMR measurements of histidine p T values in... 

For optimal results titrate the ampholytes. Mix in various proportions, maintaining the final percentage fixed, and run first and second dimensions. Select the combination that gives the best separation (well-focused spots, no streaking, etc.). Store them at —20°C in 1- or 2-ml aliquots. Ampholytes can be stored for many years at —20°C. 

The azocompound formed in the coupling reaction between a phenol or aniline derivative and a diazonium salt, is reduced at more negative potentials than the corresponding diazonium salt. If the current is measured at potentials corresponding to the limiting current of the diazonium salt, but more positive than the reduction of the azocompound, it is possible to measure the excess of the diazonium salt from the equivalence point. The resulting titration curve possesses the form given in Fig. 47. 

Plot the absorbance versus added mL of EDTA (see Fig. 11-1) and determine the volume of EDTA needed to reach the endpoint from the resulting titration curve. The intersection of the straight lines indicates the endpoint. 

The optimum Calcein concentration was determined by titrating 20 ml of 0.0002 M EDTA with 0.00025 M calcium chloride and the resulting titration curves recorded at four different calcein levels. One-fourth gram of Calcein was dissolved in 4 ml of IN NaOH and 30 ml of water was added. This solution was then diluted 1 100 and 0.1, 0.5, 1, and 2.5 ml of the dilute solution was added to the EDTA for each titration. The titration curves are shown in Fig. 7. The curve labeled "0.5 ml Calcein" is steepest at the equivalence point, consequently this concentration (approximately 2 /ig/ml) was used for subsequent titrations. 

A 0.229 g sample of an unknown monoprotic acid is titrated with 0.112 M NaOH. The resulting titration curve is shown here. Determine the molar mass and pKa of the acid. 

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