Ladders

The hierarchical nature of process design has been represented in different ways by different authors. A hierarchy of decisions and a process design ladder also have been suggested. 

An LTI is a lost time incident, mentioned earlier as an accident which causes one or more days away from work. A non-LTI injury does not result in time away from work. A near hit (often called a near miss) is an incident which causes no injury, but had the potential to do so (e.g. a falling object hitting the ground, but missing personnel). An example of an unsafe act would be a poorly secured ladder, where no incident occurs, but which potentially could have been the cause of an incident. 

Figure C3.5.2. VER transitions involved in the decay of vibration Q by cubic and quartic anhannonic coupling (from [M])- Transitions involving discrete vibrations are represented by arrows. Transitions involving phonons (continuous energy states) are represented by wiggly arrows. In (a), the transition denoted (i) is the ladder down-conversion process, where D is annihilated and a lower-energy vibration cu and a phonon co are created.

For the following basis of funetions (T 2p p and F2p ), construet the matrix representation of the Lx operator (use the ladder operator representation of Lx). Verify that... 

Winning the Nobel Prize inevitably brings with it, besides a brief period of wider publicity (which in America evaporates particularly fast), a steady stream of invitations, varied honors and recognitions, as well as more general public involvement. Professors and scientists in American life are usually not exactly at the top of the social ladder, nor are they used to much recognition. Personally, I rather like this, because it helps not to attach overgrown significance to one s importance, keeps one humanized, and, most important, allows one to stay centered without much distraction from one s work. It was, therefore,... 

It would be pretty pathetic if one had to start the synthesis of a complex molecule such as X from something like phenol but it can be done. However, since ail of the intermediates listed here are legal, there is no excuse not to start as far up the ladder as... 

To see how a ladder diagram is constructed, we will use the acid-base equilibrium between HF and F ... 

Ladder diagrams are particularly useful for evaluating the reactivity of acids and bases. An acid and a base cannot coexist if their respective areas of predominance do not overlap. If we mix together solutions of NH3 and HE, the reaction... 

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... 

Using the ladder diagram in Figure 6.7, predict the result of adding 0.080 mol of Ca + to 0.060 mol of Mg(EDTA). EDTA is an abbreviation for the ligand ethylenediaminetetraacetic acid. 

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

We can also construct ladder diagrams using cumulative formation constants in place of stepwise formation constants. The first three stepwise formation constants for the reaction of + with NH3... 

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... 

Ladder diagram showing the effect of a change in pH on the areas of predominance for the U02 +/U + half-reaction. 

Ladder diagrams are a useful tool for evaluating chemical reactivity, usually providing a reasonable approximation of a chemical system s composition at equilibrium. When we need a more exact quantitative description of the equilibrium condition, a ladder diagram may not be sufficient. In this case we can find an algebraic solution. Perhaps you recall solving equilibrium problems in your earlier coursework in chemistry. In this section we will learn how to set up and solve equilibrium problems. We will start with a simple problem and work toward more complex ones. 

From the ladder diagram it appears that we may safely assume that the concentrations of H2L+ and L are significantly smaller than that for HL, allowing us to simplify the mass balance equation to... 

H.2 Representing Buffer Solutions with Ladder Diagrams... 

Ladder diagrams provide a simple graphical description of a solution s predominate species as a function of solution conditions. They also provide a convenient way to show the range of solution conditions over which a buffer is most effective. For ex-... 

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