Ladder diagrams

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-... 

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. 

Calculate the solubility of CaF2 in a solution buffered to a pH of 7.00. Use a ladder diagram to help simplify the calculations. How would your approach to this problem change if the pH is buffered to 2.00 What is the solubility of CaF2 at this pH ... 

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. 

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