Potential ladder diagram

A "potential ladder" diagram models the potential difference. The rungs on the ladder correspond to the values of the reduction potentials. For a galvanic cell, the half-reaction at the cathode is always on the upper rung, and the subtraction... 

Ladder diagrams can also be used to evaluate equilibrium reactions in redox systems. Figure 6.9 shows a typical ladder diagram for two half-reactions in which the scale is the electrochemical potential, E. Areas of predominance are defined by the Nernst equation. Using the Fe +/Fe + half-reaction as an example, we write... 

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 ladder diagram for this system is shown in Figure 11.24a. Initially the potential of the working electrode remains nearly constant at a level near the standard-state potential for the Fe UFe redox couple. As the concentration of Fe + decreases, however, the potential of the working electrode shifts toward more positive values until another oxidation reaction can provide the necessary current. Thus, in this case the potential eventually increases to a level at which the oxidation of H2O occurs. 

Similarly, you may be presented with a diagram of a floor plan of a building, perhaps filled with smoke. Again, this is a test of your ability to remember details. As mentioned in Chapter 11, Spatial Relations, the ability of a firefighter to read a floor plan is crucial, as you may someday find yourself making your way through hallways and rooms filled with smoke. When presented with a floor plan, you will want to note the location of potential hazards and dead ends you may be asked the placement of exits or smoke alarms or where to position a ladder for rescue. 

We now turn our attention to molecular hysteresis which has two essential factors. One is that a system can be expressed a double square scheme diagram (or ladder scheme diagram ) [5], as shown in Fig. 17a. A, A, A", B, B, and B" are chemical species or states. These series of A and B vary reversibly with one another under an external perturbation such as potential, pH, ion concentration, light, etc. With A and B more stable than B" and A", respectively, A" and B" can be rapidly converted to B and A. Hence we will obtain a scheme as shown in Fig. 17b. The other important thing is that the conversion is slow between A and B. The slow rate produces a bistability, A and B, which depends on the direction of an external perturbation. This is molecular hysteresis. Some binuclear or multinuclear metal complexes with the double square scheme diagram have been reported [31]. However, because they were not designed to exhibit molecular hysteresis, their hysteresis behaviors in redox are insufficient. 

FIGURE 5.8 Schematic diagram of a ladder two-color PA experiment in Na2. The PA laser (red-detuned) is fixed on arovihrational level of either the singly-excited Ig or the 0 potential, while the photoionization (PI) laser (hlue-detuned) is scanned through the doubly-excited P3/2 + 3p3/2 asymptote. Ions produced by autoionization below this asymptote are due to excitation of doubly-excited states. (From Amehnk, A. et al., Phys. Rev. A, 61, 042707, 2000. With permission.)... 

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