Standard half-cell potentials determination

A problem that has fascinated surface chemists is whether, through suitable measurements, one can determine absolute half-cell potentials. If some one standard half-cell potential can be determined on an absolute basis, then all others are known through the table of standard potentials. Thus, if we know E for... 

The of this standard cell is +0.76 V. By international convention, the half-cell potential of the hydrogen reduction is assigned a value of exactly OV. Thus, the half-cell potential of the zinc oxidation is equal to K.n (i.e., +0.76 V). This voltage is called the standard half-cell potential and is represented by the symbol 1, to indicate that it was determined against a standard hydrogen electrode. 

If we could determine E° values for individual half-reactions, we could combine those values to obtain E° values for a host of cell reactions. Unfortunately, it s not possible to measure the potential of a single electrode we can measure only a potential difference by placing a voltmeter between two electrodes. Nevertheless, we can develop a set of standard half-cell potentials by choosing an arbitrary standard half-cell as a reference point, assigning it an arbitrary potential, and then expressing the potential of all other half-cells relative to the reference half-cell. Recall that this same approach was used in Section 8.10 for determining standard enthalpies of formation, A H°f. 

Since the values of equilibrium constants are obtained from the standard half-cell potentials, the method of obtaining the S° of a half-cell has great importance. Suppose we wish to determine the of the silver-silver ion electrode. Then we set up a cell that includes this electrode and another electrode the potential of which is known for simplicity we choose the SHE as the other electrode. Then the cell is... 

The standard cell potential of a voltaic cell, depends on the particular cathode and anode half-cells. We could, in principle, tabulate the standard cell potentials for all possible cathode/anode combinations. However, it is not necessary to undertake this arduous task. Rather, we can assign a standard potential to each half-cell and then use these half-cell potentials to determine Etea- The cell potential is the difference between two half-cell potentials. By convention, the potential associated with each electrode is chosen to be the potential for reduction at that electrode. Thus, standard half-cell potentials are tabulated for reduction reactions, which means they are standard reduction potentials, denoted Ered- The standard cell potential, ceU> is the standard reduction potential of the cathode reaction, (cathode), minus the standard reduction potential of the anode reaction, (anode) ... 

Describe the role of non-fVwork in electrochemical systems. Define the roles of the anode, cathode, and electrolyte in an electrochemical cell. Given shorthand notation for an electrochemical cell, identify the oxidation and reduction reactions. Use data for the standard half-cell potential for reduction reactions, E°, to calculate the standard potential of reaction E. Apply the Nernst equation to determine the potential in an electrochemical cell given a reaction and reactant concentrations. 

Refer to the table of half-cell potentials to determine if MnOz can oxidize Br to Br2 in acidic solution under standard conditions. 

The numerical value of an electrode potential depends on the nature of the particular chemicals, the temperature, and on the concentrations of the various members of the couple. For the purposes of reference, half-cell potentials are taken at the standard states of all chemicals. Standard state is defined as 1 atm pressure of each gas (the difference between 1 bar and 1 atm is insignificant for the purposes of this chapter), the pure substance of each liquid or solid, and 1 molar concentrations for every nongaseous solute appearing in the balanced half-cell reaction. Reference potentials determined with these parameters are called standard electrode potentials and, since they are represented as reduction reactions (Table 19-1), they are more often than not referred to as standard reduction potentials (E°). E° is also used to represent the standard potential, calculated from the standard reduction potentials, for the whole cell. Some values in Table 19-1 may not be in complete agreement with some sources, but are used for the calculations in this book. 

We have seen in Section 26.2.1 that thermodynamics (i.e., equilibrium half-cell potentials) can be used to determine which of two half-cell reactions proceeds spontaneously in the anodic or cathodic direction when the two reactions occur on the same piece of metal or on two metal samples that are in electrical contact with one another. The half-cell reaction with the higher equilibrium potential will always be at the cathode. Thus, under standard conditions any metal dissolution (corrosion) reaction with an E° less than 0.0 V vs. SHE will be driven by proton reduction while metal dissolntion reactions with an E° less than -e1.23 V vs. SHE will be driven by dissolved... 

The initial consideration in analyzing an existing or proposed metal/environment combination for possible corrosion is determination of the stability of the system. According to Eq 1.18, the criterion is whether the equilibrium half-cell potential for an assumed cathodic reaction, E x, is greater than the equilibrium half-cell potential for the anodic reaction, E M. A convenient representation of relative positions of equilibrium half-cell potentials of several common metals and selected possible corrodent species is given in Fig. 1.7. To the left is the scale of potentials in millivolts relative to the standard hydrogen electrode (SHE). The solid vertical lines identified by the name of the metal give... 

Even though we are capable of measure the galvanic cell potential by using the voltmeter placed between the two electrodes, it is not possible to ensure the two half cell potentials. We thereby have to define a half cell reaction that we may determine the other half cell potentials from. As mentioned above we have chosen to let the half cell potential for the standard hydrogen electrode be the zero point. On the basis on this it is possible to determine all the other half cell potentials. In the present case we may thereby say that the half cell reaction ... 

The half cell potential (s° values) corresponding to the given half cell reactions are sometimes referred to as standard reduction potentials and may be found in tables. Typically one of the half cell reactions should be turned around as each redox reaction contains one reduction reaction and one oxidation reaction. This means that one of the signs from the table must be turned around. Further may the half cell reaction from the table typically be multiplied with an integer in order to make sure that the number of electrons fits the number of consumed electrons from the overall cell reaction. These integer multiplications are associate with the determination of the free energy of Gibb s for a half cell reaction ... 

Determining Ehaif-ceii The Standard Hydrogen Electrode What portion of ceii for the zinc-copper reaction is contributed by the anode half-cell (oxidation of Zn) and what portion by the cathode half-cell (reduction of Cu ) That is, how can we know half-cell potentials if we can only measure the potential of the complete cell Half-cell potentials, such as Ezine and °opper. are not absolute quantities, but rather are values relative to that of a standard. This standard reference halfcell has its standard electrode potential defined as zero (E fereiice — 0.00 V). The standard reference half-cell is a standard hydrogen electrode, which consists of a specially prepared platinum electrode immersed in a 1 M aqueous solution of a strong acid, H (fl ) [or H30 (a )], through which H2 gas at 1 atm is bubbled. Thus, the reference half-reaction is... 

By measuring the cell potential at various concentrations of Cu ", we can determine < cu2+/cu = 0cu2+/cu- This standard potential is tabulated along with the standard potentials of other half-cells in Table 17.1. Such a table of half-cell potentials, or electrode potentials, is equivalent to a table of standard Gibbs energies f rom which we can calculate values of equilibrium constants for chemical reactions in solution. Note that the standard potential is the potential of the electrode when all of the reactive species are present with unit activity, a = 1. 

In addition, the Pt serves as the electrical conductor to the external circuit. Under standard state conditions, that is, when the H2 pressure equals 1 atm and the ideal concentration of the HCl is 1 M, and the system is at 25°C, the reduction potential for the reaction given in Eq. (15.8) is exactly 0 V. (The potential actually depends on the chemical activity of the HCl, not on its concentration. The relationship between activity and concentration is discussed subsequently. For an ideal solution, concentration and activity are equal.) The potential is symbolized by where the superscript zero means standard state conditions. The term standard reduction potential means that the ideal concentrations of all solutes are 1 M and all gases are at 1 atm other solids or liquids present are pure (e.g., pure Pt solid). By connecting the SHE half-cell with any other standard half-cell and measuring the voltage difference developed, we can determine the standard reduction potential developed by the second half-cell. 

The standard reduction potentials for other half-reactions can be determined in a fashion analogous to that used for the Zx " jZvr half-reaction. TABLE 20.1 lists some standard reduction potentials a more complete list is found in Appendix E. These standard reduction potentials, often called half-cell potentials, can be combined to calculate values for a large variety of voltaic cells. 

A note on half-cell potential values The electrode (or the half-cell) potentials in the example above, -0.76 V for the Zn /Zn and +0.34 V for Cu /Cu, are not some numbers that we know as a fact of nature but relative potentials determined by comparison to the electrochemical potential of the so-called standard hydrogen electrode, SHE,... 

The emf or cell pofenfial of a voltaic cell depends on the particular cathode and anode half-cells involved. We could, in principle, tabulate the standard cell potentials for all possible cafhode/anode combinations. However, it is not necessary to undertake this arduous task. Rather, we can assign a standard potential to each individual half-cell, and fhen use these half-cell potentials to determine Eceii ... 

The standard hydrogen electrode is the universal and internationally agreed lUPAC (International Union of Pure and Applied Chemistry) reference for reporting relative half-cell potentials. It is a type of gas electrode and was widely used in early studies as a reference electrode, and as an indicator electrode (Chapter 18) for the determination of pH values. It is an arbitrary reference and in principle any metal/metal ion system could be used as reference electrode. To use an analogy, heights are measured using sea level as an arbitrary zero. Any level above or below sea level could be used as the reference point. 

The potential difference measured across the complete voltaic cell is easily measured and equals the sum of the electrode potentials for the two half-reactions. Individual electrode potential cannot be measured directly, because there can be no transfer of electrons unless both the anode and the cathode are connected to form a complete circuit A relative value for the potential of a half-reaction can be determined by connecting it to a standard half-cell as a reference. This standard halfcell, shown in Figure 2.8, is called a standard hydrogen electrode, or SHE. 

A suitable potential is applied between a standard half-cell and the micro-electrode and the current flowing through the electrode system during the course of the titration is noted. The current, after the addition of each increment of titrant, is plotted against volume of reagent on each side of the end-point and the latter determined by the intersection of the two straight lines thus produced. The points obtained often give a curve... 

There have been a number of theoretical approaches to the determination of absolute electrode potentials (relative to the electric potential at a location infinitely distant from all charges). All of them require the use of nonthermodynamic theories. One work cites a value of —4.43 V (absolute) for the standard hydrogen electrode. Other workers have come up with values ranging from this value to —4.73 V. We will use only half-cell potentials relative to the standard hydrogen electrode. 

Not only can equation (19.15) be used to determine Afi° from E eU/ as in Example 19-5, but the calculation can be reversed and an E eu value determined from Aj-G . Moreover, equation (19.15) can be applied to half-cell reactions and half-cell potentials—that is, to standard electrode potentials, E°. That is what we must do, for example, to determine E for the half-cell reaction... 

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