Analyte half-reaction, 702

The potential difference between the titrant and the analyte half-reaction should be 0.2-0.3 V for a sharp end point. 

We can use our understanding of redox equihbria to describe titration curves for redox titrations. The shape of a titration curve can be predicted from the E° values of the analyte half-reaction and the titrant half-reaction. Roughly, the potential change in going from one side of the equivalence point to the other will be equal to the difference in the two values the potential will be near E° for the analyte half-reaction before the equivalence point and near that of the titrant half-reaction beyond the equivalence point. 

Before the equivalence point the titration mixture consists of appreciable quantities of both the oxidized and reduced forms of the analyte, but very little unreacted titrant. The potential, therefore, is best calculated using the Nernst equation for the analyte s half-reaction... 

Although EXo /ATcd is standard-state potential for the analyte s half-reaction, a matrix-dependent formal potential is used in its place. After the equivalence point, the potential is easiest to calculate using the Nernst equation for the titrant s half-reaction, since significant quantities of its oxidized and reduced forms are present. 

At the equivalence point, the moles of Fe + initially present and the moles of Ce + added are equal. Because the equilibrium constant for reaction 9.16 is large, the concentrations of Fe and Ce + are exceedingly small and difficult to calculate without resorting to a complex equilibrium problem. Consequently, we cannot calculate the potential at the equivalence point, E q, using just the Nernst equation for the analyte s half-reaction or the titrant s half-reaction. We can, however, calculate... 

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. 

Standard Hydrogen Electrode The standard hydrogen electrode (SHE) is rarely used for routine analytical work, but is important because it is the reference electrode used to establish standard-state potentials for other half-reactions. The SHE consists of a Pt electrode immersed in a solution in which the hydrogen ion activity is 1.00 and in which H2 gas is bubbled at a pressure of 1 atm (Figure 11.7). A conventional salt bridge connects the SHE to the indicator half-cell. The shorthand notation for the standard hydrogen electrode is... 

Analytical methods based upon oxidation/reduction reactions include oxidation/reduction titrimetry, potentiometry, coulometry, electrogravimetry and voltammetry. Faradaic oxidation/reduction equilibria are conveniently studied by measuring the potentials of electrochemical cells in which the two half-reactions making up the equilibrium are participants. Electrochemical cells, which are galvanic or electrolytic, reversible or irreversible, consist of two conductors called electrodes, each of which is immersed in an electrolyte solution. In most of the cells, the two electrodes are different and must be separated (by a salt bridge) to avoid direct reaction between the reactants. 

To understand potentiometric methods, those that measure electrical potentials and determine analyte concentrations from these potentials, it is necessary that numerical values for these tendencies be known under conventional standard modes and conditions. What are these modes and conditions First, all halfreactions must be written as either reductions or oxidations. Scientists have decided to write them as reductions. Second, the tendencies for half-reactions to proceed depend on the temperature, the concentrations of the chemical species involved, and, if gases are involved, the pressure in the half-cell. Scientists have defined standard conditions to be a temperature of 25°C, a concentration of exactly 1 M for all dissolved chemical species involved, and a pressure of exactly 1 atm. Third, because every cell consists of two half-cells, it is not possible to measure the value directly. However, if we were to assign the tendency of a certain half-reaction to be zero, then the tendencies of all other half-reactions can be determined relative to this reference half-reaction. 

The potential at which half the maximum current is reached in Figure 17-16a, called the half-wave potential ( 1/2). is characteristic of a given analyte in a given medium and can be used for qualitative analysis. For electrode reactions in which reactants and products are both in solution, such as Fe3+ + e Fe2+, Em is nearly equal to E° for the half-reaction. 

For a reaction to be applicable in kinetic analysis, its rate must be neither too high nor too low. We may define fast reactions as those that approach equilibrium (several half-lives) during the time of mixing. For analytical measurements, reaction... 

Note then that E of equation (A.2.1) is a known quantity (i.e., we dial in a specified /iappi). Through the processes of mass transfer and diffusion of the analyte, Q will be properly maintained. The establishment of Q in response to varying wl will be reflected in the current (e-flow to and from the working electrode) response. A cyclic voltammogram is simply the current measured as a function of the applied potential (/iappi)- From the voltammogram we can extract what we are after, E° for the [Fe3+(CN)5F]"-/ [Fe2+ (CN)5F](n+1) half reaction. 

Most analytical oxidation/reduction reactions are carried out in solutions that have such high ionic strengths that activity coefficients cannot be obtained via the Debye-Hiickel equation (see Equation 10-1, Section lOB-2). Significant errors may result, however, if concentrations are used in the Nernst equation rather than activities. For example, the standard potential for the half-reaction... 

Formal potentials are empirically derived potentials that compensate for the types of activity and competing equilibria effects that we have just described. The formal potential of a system is the potential of the half-cell with respect to the standard hydrogen electrode measured under conditions such that the ratio of analytical concentrations of reactants and products as they appear in the Nernst equation is exactly unity and the concentrations of other species in the system are all carefully specified. For example, the formal potential for the half-reaction... 

A formal potential Is the electrode potential when the ratio of analytical concentrations of reactants and products of a half-reaction is exactly 1.00 and the molar concentrations of any other solutes are specified. 

Q Spreadsheet Summary In the first exercise in Chapter 10 of Applications of Microsoft Excel in Analytical Chemistry, a spreadsheet is developed for use in calculating electrode potentials for simple half-reactions. Plots are made of the potential versus the ratio of the reduced species to the oxidized species and of the potential versus the logarithm of this ratio. 

There are many examples of redox processes in which all components are in the electrolyte solution. An example of a complex reaction which is used in analytical chemistry is the reduction of Mn04 to Mn " " in acidic solution. The half-reaction is... 

To construct a titration curve, we are interested in the equilibrium electrode potential (i.e., when the cell potential is zero—after the titrant and analyte have reacted). The two electrodes have identical potentials then, as determined by the Nemst equation for each half-reaction. 

In Chapter 12, we mentioned measurement of the potential of a solution and described a platinum electrode whose potential was determined by the half-reaction of interest. This was a special case, and there are a number of electrodes available for measuring solution potentials. In this chapter, we hst the various types of electrodes that can be used for measuring solution potentials and how to select the proper one for measuring a given analyte. The apparatus for making potentiomet-ric measurements is described along with limitations and accuracies of potentio-metric measurements. The important glass pH electrode is described, as well as standard buffers required for its calibration. The various kinds of ion-selective electrodes are discussed. The use of electrodes in potentiometric titrations is described in Chapter 14. 

FIGURE 25-6 Linear-sweep voltammogram for Ihe reduction of a hypothetical species A to give a product P. The limiting cunent i, is proportionai to the analyte concentration and is used for quantilative analysis. The half-wave potential is related to the standard potential for the half-reaction and is often used for qualitative identification of species. The half-wave potenlial is the applied potential at which the current i is i,/2. 

Electrochemistry is ranked by teachers and students as one of the most difficult curriculum domains taught and learnt in secondary school chemistry (cf. Davies, 1991 Griffiths, 1994). For that reason, in this chapter, we primarily discuss this domain at the secondary level but also make connections to the tertiary level. In many chemistry curricula and textbooks, it is common to divide electrochemistry into two topics redox reactions (oxidation and reduction) and electrochemical cells (galvanic and electrolytic). The usual rationale for this distinction is that students need an understanding of oxidation-reduction to apply it to electrochemical cells. This analytical distinction, based on differences in the location of the half reactions, is used throughout the chapter. 

Thus, the analytical solution of the Michaelis-Menten equation (eqn (4.9) and (4.10)) together with one of the cases in eqn (4.23) presents a possibility to even kinetically evaluate coupled half-reactions accurately. Since the... 

Addition of the two half-reactions gives the expression for respiration on explicitly including the statement for the chemical energy obtained. The analytical simplicity of the halfreactions lays out the underlying essential result of the biological electron transport chain. Indeed, the electron transport chain of the mitochondrion achieves the separation into protons, ff, and electrons, e". (For the structure of the mitochondrion, refer to Figure 8.5, below.)... 

The stoichiometry of the reaction between one of these titrants and a particular analyte is established by combining the appropriate half-reactions. For the titrants above, the half-reactions are as follows ... 

The different results of the estimated parameters at the two rotation speeds could be due to interfering reactions in the supporting electrolyte or, more likely, to the oxidation of hexaamineruthenium (II) to hexaamineruthenium (III), occurring at the initial potentials of the polarization curve. The oxidation half-reaction is not taken in consideration in the formulation of the analytical current-potential expression this could have an influence on the parameter estimation. According to our modeling strategy, a better estimation of the model parameters needs further investigation on the treatment of the experimental data and/or the formulation of the reaction mechanism. Present research is devoted to this topic. 

Indicator and reference electrodes. Complete analytical electrochemical cells are composed of combinations of an indicator and a reference electrode. Each of these electrodes contributes half-reaction chemistry in combination they provide a complete redox reaction. The indicator electrode is the analyte activity sensing element and develops a potential Eind relative to the reference electrode, which represents a constant known potential Ref independent of the composition of the sample solution. The measured ceU potential Eceii can be written... 

The earliest examples of analytical methods based on chemical kinetics, which date from the late nineteenth century, took advantage of the catalytic activity of enzymes. Typically, the enzyme was added to a solution containing a suitable substrate, and the reaction between the two was monitored for a fixed time. The enzyme s activity was determined by measuring the amount of substrate that had reacted. Enzymes also were used in procedures for the quantitative analysis of hydrogen peroxide and carbohydrates. The application of catalytic reactions continued in the first half of the twentieth century, and developments included the use of nonenzymatic catalysts, noncatalytic reactions, and differences in reaction rates when analyzing samples with several analytes. 

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