Standardization of potentials

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Although it is not yet possible to determine with certainty the absolute value of the potential difference between a metal and a solution, we can determine its value relative to an arbitrarily fixed standard of potential difference by determining the E.M.F. of the cell... 

The H /H2 redox couple is used as a standard of potential often called the hydrogen electrode . Cathode half reaction ... 

Standardization of Potentials. The increasing interest in potentiometry stressed the need for standard values of electrode potentials. In 1890, Ostwald introduced the calomel electrode, calibrating this against a dropping mercury electrode. Nernst chose the normal hydrogen electrode, assigning to it a potential of zero. The upshot was a confrontation between the two scientists as the 19th century ended. 

The UV-visible absorption spectrum of Ru(2,2 -bipyridine)3 maximum at about 450 nm, from which the energy in volts for process XI-39 may be estimated. The standard reduction potential for the R" /R couple is about 1.26 V at 25°C. Estimate from this information (and standard reduction potentials) the potential in volts for processes XI-40 and XI-41. Repeat the calculation for alkaline solutions. 

For example, for iron in aqueous electrolytes, tlie tliennodynamic warning of tlie likelihood of corrosion is given by comparing tlie standard electrode potential of tlie metal oxidation, witli tlie potential of possible reduction reactions. 

Both the BO dynamics and Gaussian wavepacket methods described above in Section n separate the nuclear and electronic motion at the outset, and use the concept of potential energy surfaces. In what is generally known as the Ehrenfest dynamics method, the picture is still of semiclassical nuclei and quantum mechanical electrons, but in a fundamentally different approach the electronic wave function is propagated at the same time as the pseudoparticles. These are driven by standard classical equations of motion, with the force provided by an instantaneous potential energy function... 

STANDARD REDOX POTENTIALS OF SOME COMMON METALS... 

For many purposes the hydrogen electrode is not convenient and it can be replaced by another cell of known standard electrode potential. A well-known example is the calomel cell shown in Figure 4.5. 

Iodine has the lowest standard electrode potential of any of the common halogens (E = +0.54 V) and is consequently the least powerful oxidising agent. Indeed, the iodide ion can be oxidised to iodine by many reagents including air which will oxidise an acidified solution of iodide ions. However, iodine will oxidise arsenate(lll) to arsenate(V) in alkaline solution (the presence of sodium carbonate makes the solution sufficiently alkaline) but the reaction is reversible, for example by removal of iodine. 

Generally the solubility of a given metal halate decreases from chlorate(V) to iodatef and many heavy metal iodates(V) are quantitatively insoluble. Like their parent acids, the halates(V) are strong oxidising agents, especially in acid solution their standard electrode potentials are given below (in volts) ... 

To determine the vibrational motions of the system, the eigenvalues and eigenvectors of a mass-weighted matrix of the second derivatives of potential function has to be calculated. Using the standard normal mode procedure, the secular equation... 

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The standard redox potentials of inorganic oxidants used in organic synthesis are generally around or above + 1.0 V. Organic substrates do not have such high potentials. The values for the CH4/CH3OH and CjHj/CjHjOH couples are at +0,59 V and 0.52 V, respectively. The oxidation of alcohols and aldehydes corresponds to values around 0.0 V (W.M. 

Calculations of the interaction energy in very fine pores are based on one or other of the standard expressions for the pair-wise interaction between atoms, already dealt with in Chapter 1. Anderson and Horlock, for example, used the Kirkwood-Miiller formulation in their calculations for argon adsorbed in slit-shaped pores of active magnesium oxide. They found that maximum enhancement of potential occurred in a pore of width 4-4 A, where its numerical value was 3-2kcalmol , as compared with 1-12, 1-0 and 1-07 kcal mol for positions over a cation, an anion and the centre of a lattice ceil, respectively, on a freely exposed (100) surface of magnesium oxide. 

Since the potential for a single half-reaction cannot be measured, a reference halfreaction is arbitrarily assigned a standard-state potential of zero. All other reduction potentials are reported relative to this reference. The standard half-reaction is... 

For potentials more positive than the standard-state potential, the predominate species is Fe +, whereas Fe + predominates for potentials more negative than E°. When coupled with the step for the Sn +/Sn + half-reaction, we see that Sn + can be used to reduce Fe +. If an excess of Sn + is added, the potential of the resulting solution will be near -1-0.154 V. 

Using standard-state potentials to construct a ladder diagram can present problems if solutes are not at their standard-state concentrations. Because the concentrations of the reduced and oxidized species are in a logarithmic term, deviations from standard-state concentrations can usually be ignored if the steps being compared are separated by at least 0.3 A trickier problem occurs when a half-reaction s potential is affected by the concentration of another species. For example, the potential for the following half-reaction... 

The most common strong base for titrating acidic analytes in aqueous solutions is NaOH. Sodium hydroxide is available both as a solid and as an approximately 50% w/v solution. Solutions of NaOH may be standardized against any of the primary weak acid standards listed in Table 9.7. The standardization of NaOH, however, is complicated by potential contamination from the following reaction between CO2 and OH . 

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. 

The scale of operations, accuracy, precision, sensitivity, time, and cost of methods involving redox titrations are similar to those described earlier in the chapter for acid-base and complexometric titrimetric methods. As with acid-base titrations, redox titrations can be extended to the analysis of mixtures if there is a significant difference in the ease with which the analytes can be oxidized or reduced. Figure 9.40 shows an example of the titration curve for a mixture of Fe + and Sn +, using Ce + as the titrant. The titration of a mixture of analytes whose standard-state potentials or formal potentials differ by at least 200 mV will result in a separate equivalence point for each analyte. 

Despite the apparent ease of determining an analyte s concentration using the Nernst equation, several problems make this approach impractical. One problem is that standard-state potentials are temperature-dependent, and most values listed in reference tables are for a temperature of 25 °C. This difficulty can be overcome by maintaining the electrochemical cell at a temperature of 25 °C or by measuring the standard-state potential at the desired temperature. 

Another problem is that the Nernst equation is a function of activities, not concentrations. As a result, cell potentials may show significant matrix effects. This problem is compounded when the analyte participates in additional equilibria. For example, the standard-state potential for the Fe "/Fe " redox couple is +0.767 V in 1 M 1TC104, H-0.70 V in 1 M ITCl, and -H0.53 in 10 M ITCl. The shift toward more negative potentials with an increasing concentration of ITCl is due to chloride s ability to form stronger complexes with Fe " than with Fe ". This problem can be minimized by replacing the standard-state potential with a matrix-dependent formal potential. Most tables of standard-state potentials also include a list of selected formal potentials (see Appendix 3D). 

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... 

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