Half-reaction potentials

Applying Concepts Write the half-reactions for the anode and cathode in each of the voltaic cells in the data table. Look up the half-reaction potentials from the standard reduction potentials table (Table 21-1) and record these in the data table. 

The calculation of the standard cell potential using these standard half-reaction potentials is as follows. 

Since neither of the two half-reaction potentials is known absolutely, it is necessary to propose an arbitrary /cm, relative to which all half-reaction potentials may be quoted. The half-reaction chosen to represent the arbitrary zero is the hydrogen electrode1 in which the half-reaction is the reduction of the aqueous hydrogen ion to gaseous dihydrogen ... 

The sign of the chromium half-reaction potential is reversed because the half-reaction itself is reversed to make up the overall equation. 

This is obtained by doubling reaction (4.17) before the addition, so that Cr3 (aq) is eliminated. The simple addition of the two half-reaction potentials gives 1.33-0.41 —+0.92 V, which is not correct for the potential of the half-reaction (4.18). Calculation of i (4. 18) via the value of ArG illustrates why the correct answer is not the arithmetic sum of the two half-reaction potentials. 

Calculations ol the reduction potential of a half-reaction from I two other half-reaction potentials were described. 

Because (like AG) refers to a difference in a state property, it can be evaluated in additive fashion along many alternative pathways. For this purpose, it is convenient to assign conventional ° values to each half-cell reaction [e.g., standard oxidation potentials as compiled in W. M. Latimer. Oxidation Potentials, 2nd edn (Prentice-Hall, New York, 1952)], such that the algebraic sum of the two half-reaction potentials equals the overall cell °. Such half-reaction ° values can in turn be obtained by choosing some standard electrode reaction as the conventional zero of the scale [such as the standard hydrogen electrode (SHE) for the l/2H(g) —> H+ aq) + e oxidation reaction, with she = 0]. Sidebar 8.2 illustrates a simple example of this procedure. 

First, decide whether an electron-transfer reaction is possible, using approximate half-reaction potentials (p 301) and/or the characteristics of electron-transfer reactions (p 300). If it is possible, follow the equation-balancing procedure outlined on pp 295-299. 

Potentiometry has found extensive application over the past half-century as a means to evaluate various thermodynamic parameters. Although this is not the major application of the technique today, it still provides one of the most convenient and reliable approaches to the evaluation of thermodynamic quantities. In particular, the activity coefficients of electroactive species can be evaluated directly through the use of the Nemst equation (for species that give a reversible electrochemical response). Thus, if an electrochemical system is used without a junction potential and with a reference electrode that has a well-established potential, then potentiometric measurement of the constituent species at a known concentration provides a direct measure of its activity. This provides a direct means for evaluation of the activity coefficient (assuming that the standard potential is known accurately for the constituent half-reaction). If the standard half-reaction potential is not available, it must be evaluated under conditions where the activity coefficient can be determined by the Debye-Hiickel equation. 

Standard cell potentials are calculated from the sum of the two half-reaction potentials for the reduction and oxidation reactions occurring in the cell ... 

All half-reaction potentials are relative to the reduction of H+ to form H2. This potential is assigned a value of zero ... 

At 25°C the standard half reaction potential for the process 2H20 + 2e - H2 + 20H is -0.8277 V determine the dissociation constant for water at that temperature. 

Since in a redox reaction electrons are transferred, and since electrons have charge, there is an electric potential E associated with any redox reaction. The potentials for the oxidation component and reduction component of a reaction can be approximated separately based upon a standard hydrogen electrode (SHE) discussed later in this lecture. Each component is called a hall reaction. Of course, no half reaction will occur by itself any reduction half reaction must be accompanied by an oxidation half reaction. There is only one possible potential for any given half reaction. Since tire reverse of a reduction half reaction is an oxidation half reaction, it would be redundant to list potentials for both the oxidation and reduction half reactions. Therefore, half reaction potentials are usually listed as reduction potentials To find the oxidation potential for the reverse half reaction, the sign of the reduction potential is reversed. Below is a list of some common reduction potentials. 

Warning Since reduction potentials are intensive properties, we do not multiply the half reaction potential by the number of times it occurs. 

B. The reduction half reaction potential is greater than die oxidation half reaction potential,... 

C is correct. The two half reaction potentials must be added after they have been rearranged to represent the galvanic cell. This means that the first half reaction is reversed. If this potential is applied, the cell can be recharged back to this potential which is the standard potential. 

The N03 /N0 reduction half-reaction has the more positive value, so we write it first and write the Sn +/Sn + half-reaction as an oxidation. We balance the electron transfer and add the two half-reactions to obtain the equation for the spontaneous reaction. Then we add the half-reaction potentials to obtain the overall cell potential. 

The standard reduction potential for the Sn +/Sn + couple is +0.15 volt that for the Cr +/Cr couple is —0.74 volt. The equation for the reaction shows Cr being oxidized to Cr +, so the sign of the value for the Cr +/Cr couple is reversed. The overall reaction, the sum of the two half-reactions, has a cell potential equal to the sum of the two half-reaction potentials. 

To determine the potential for the cell, the hydrogen electrode is by convention assigned a half-reaction potential E of 0.00 volt (V) under standard state conditions. This means that if the H ion activity and the H2 gas activity are both 1.00, for the hydrogen electrode is 0.00 volt. This convention can be symbolized as... 

HALF-REACTION POTENTIALS—THEY ARE lyiEASURED RELATIVE TO EACH OTHER... 

Before we discuss redox titration curves based on reduction-oxidation potentials, we need to learn how to calculate equilibrium constants for redox reactions from the half-reaction potentials. The reaction equilibrium constant is used in calculating equilibrium concentrations at the equivalence point, in order to calculate the equivalence point potential. Recall from Chapter 12 that since a cell voltage is zero at reaction equilibrium, the difference between the two half-reaction potentials is zero (or the two potentials are equal), and the Nemst equations for the halfreactions can be equated. When the equations are combined, the log term is that of the equilibrium constant expression for the reaction (see Equation 12.20), and a numerical value can be calculated for the equilibrium constant. This is a consequence of the relationship between the free energy and the equilibrium constant of a reaction. Recall from Equation 6.10 that AG° = —RT In K. Since AG° = —nFE° for the reaction, then... 

The above two methods of indication do not depend on the half-reaction potentials, although the completeness of the titration reaction and hence the sharpness of the end point do. Examples of these first two methods of visual indication are few, and most types of redox titrations are detected using redox indicators. These are highly colored dyes that are weak reducing or oxidizing agents that can be oxidized or reduced the colors of the oxidized and reduced forms are different. The oxidation state of the indicator and hence its color will depend on the potential at a given point in the titration. A half-reaction and Nemst equation can be written for the indicator ... 

Construct a cell using a standard hydrogen electrode and an electrode designed around the redox couple of interest. The cel potential E is measured with a high impedance voltmeter under zero current conditions. When using SHE as a reference electrode, E is the desired half-reaction potential [7.13], Should the redox couple have one or more electroaclive species (i) that are solvated with concentration b, E must be measured over a range of b values. 

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