Ladder diagrams for

The ladder diagram for HF/F- also can be used to evaluate the effect of pH on other equilibria that include either HF or F-. For example, the solubility of CaF2... 

Ladder diagram for metal-ligand complexes of ethylenediaminetetraacetic add (EOTA) with Ca + and Mg +. 

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... 

Construct ladder diagrams for the following diprotic weak acids (H2L), and estimate the pH of 0.10 M solutions of H2L, HL , and Using the systematic approach, calculate the pH of each of these solutions. 

Construct ladder diagrams for the following systems, and describe the information that can be obtained from each... 

The extraction efficiency, therefore, is almost 75%. When the same calculation is carried out at a pH of 5.00, the extraction efficiency is 60%, but the extraction efficiency is only 3% at a pH of 7.00. As expected, extraction efficiency is better at more acidic pHs when HA is the predominate species in the aqueous phase. A graph of extraction efficiency versus pH for this system is shown in Figure 7.23. Note that the extraction efficiency is greatest for pHs more acidic than the weak acid s piQ and decreases substantially at pHs more basic than the pi A- A ladder diagram for HA is superimposed on the graph to help illustrate this effect. 

Solubility of AgCI as a function of pCI. The dashed line shows the predicted SAgci, assuming that only reaction 8.1 and equation 8.2 affect the solubility of AgCI. The solid line is calculated using equation 8.7, and includes the effect of reactions 8.3-8.5. A ladder diagram for the AgCI complexation equilibria is superimposed on the pCI axis. 

Also shown in Figure 8.1 is a ladder diagram for this system. Note that the increase in solubility begins when the higher-order soluble complexes, AgCb" and AgCb ", become the dominant species. 

The first four values are for the carboxyl protons, and the remaining two values are for the ammonium protons. A ladder diagram for EDTA is shown in figure 9.26. The species Y becomes the predominate form of EDTA at pH levels greater than 10.17. It is only for pH levels greater than 12 that Y becomes the only significant form of EDTA. 

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. 

Ladder diagrams for the controlled-current coulometric analysis of Fe + (a) without the addition of Ce +, and (b) with the addition of Ce +. The matrix is 1 M H2SO4 in both cases. 

There are two types of third-order cascades that can lead to an overall fifth-order signal. Ladder diagrams for the two types of cascades are shown in Fig. 2a and b, and we label them sequential and parallel. A sequential cascade (Fig. 2a) involves the emission of a field from the first vibrational coherence that then participates in driving a vibrational coherence on a different chromophore. A parallel cascade (Fig. 2b) begins with the preparation of vibrational coherences on separate chromophores as a result of interactions with the first and second pairs of laser fields. The probing interaction on one of the chromophores then results in a field that is involved in a probing interaction on the other chromophore. 

Figure 2 Representative ladder diagrams for the possible cascading fifth-order pathways, (a) The sequential cascade pathway, (b) The parallel cascade pathways.

The details of a very similar calculation of the ladder and crossed ladder diagrams for n = 2 excited states of helium, which differs only in angular momentum factors, can be found in Ref. [31]. The technique used is that of a Wick rotation, in which the transformation z iu is carried out and the to> integration carried out numerically. In the present case, while this basic approach is used, significant complications from the photon cuts are encountered, which requires the use of a somewhat complicated contour integration. The results of a rather involved calculation are tabulated as 2 in Tables 2 and 3. 

Figure 14. Ladder eind crossed ladder diagrams for second-order correlation energies.

Figure 14. (a) The contributing ladder diagrams for A thick line corresponds to... 

Many permutation algorithms have been proposed such as Heap Method, Johnson-Trotter Method, Loopless Johnson-Trotter Method, Ives Method, Alternate Ives Method, Langdon Method, Fischer-Krause Method, etc. The heap method runs faster and is simpler than other methods as presented in [5]. A ladder diagram for heap algorithm is depicted in Fig. 4.5. 

The fixed ladder standard does not address the depth of ladder steps however, OSHA provides in 1910.27 several fixed ladder diagrams for reference to which employers should refer for specific design suggestions. Specifically, Figure D-1 shows a minimum... 

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