Logarithmic diagrams concentration

A logarithmic concentration diagram is a plot of log concentration versus a master variable such as pH. Such diagrams are useful because they express the concentrations of all species in a polyprotic acid solution as a function of pH. This allows us to observe at a glance the species that are important at a particular pH. The logarithmic scale is used because the concentrations can vary over many orders of magnitude. 

The logarithmic concentration diagram applies only for a specific acid and for a particular initial concentration of acid. Such diagrams can be readily obtained from the distribution diagrams previously discussed. The details of... 

Logarithmic concentration diagrams can be obtained from the concentration of acid and the dissociation constants. We use as an example the maleic acid system discussed previously. The diagram shown in Figure 15F-I is a logarithmic concentration diagram for a maleic acid... 

Figure 15F-1 Logarithmic concentration diagram for 0.100 M maleic acid.

We can draw a logarithmic concentration diagram easily by noting the relationships just given. An easier method is to modify the distribution diagram so that it produces the logarithmic concentration diagram. This is the method illustrated in Applications of Microsoft Excel in Analytical Chemistry , Chapter 8. Note that the plot is specific for a total analytical concentration of 0.10 M and for maleic acid, since the acid dis.sociation constants are included. 

If we do not know the pH, the logarithmic concentration diagram can also be used to give an approximate pH value. For example, find the pH of a 0.1 M maleic acid solution. Since the log concentration diagram expresses mass balance and the equilibrium constants, we need only one additional equation such as charge balance to solve the problem exactly. The charge-balance equation for this system is... 

Discuss how you might modify the logarithmic concentration diagram so that it shows the pH in terms of the hydrogen ion activity ah-instead of the hydrogen ion concentration (pH = — log Ah instead of pH = — log Ch ). Be specific in your discussion and show what the difficulties might be. 

Below we will show how such equilibria can be visualized in logarithmic concentration diagrams. The corresponding spreadsheets are often very useful for pH calculations. 

Another graph is the logarithmic concentration diagram. Its meaning is initially... 

For the single, monoprotic acids and bases in the above example, the distribution and logarithmic concentration diagrams are rather simple, yet they clearly show the relative and absolute concentrations respectively of the various species present. Such diagrams become all the more useful when we consider more complicated systems, such as polyprotic acids and bases, where it otherwise becomes increasingly difficult to envision what happens as a function of pH. We will do so in exercises 4.5 and 4.6. 

In order to answer the above question regarding the pH of 0.1 M acetic acid, we consult the logarithmic concentration diagram for a monoprotic weak acid with C= 0.1 M and Ka 10-4 76 M, and find the pH for which (4.2-2) is satisfied. Below we will use the spreadsheet to find that pH. 

Alternatively we can use a stick diagram, which is a simplified version of the logarithmic concentration diagram, to obtain a quick-and-dirty pH estimate which, nonetheless, is usually correct to within 0.3 pH units. In the present example, either method yields a pH of 2.88. 

On the logarithmic concentration diagram for 0.1 M acetic acid made in exercise 4.1, note the above answers for the pH of 0.1 M acetic acid, and for 0.1M sodium acetate, and see whether they indeed correspond with an intersection of two curves. 

Also plot the corresponding logarithmic concentration diagram, and on it indicate the pH values just calculated. Rationalize why they again correspond with specific intersections, and note these on the plot. 

Change the chart to single-logarithmic, and plot the logarithmic concentration diagram for C = 1M, and/or... 

Change the chart to double-logarithmic, and plot a2, av and a0 versus [H+], which will also produce the logarithmic concentration diagram for C= 1 M. 

In this chapter we have encountered the most important analytical aspects of acids and bases (a) their individual speciation, as described by the mass action law, and as reflected in the distribution and logarithmic concentration diagrams, (b) their buffer action, and (c) their neutralization, as exploited in acid-base titrations. 

Plot the corresponding logarithmic concentration diagram. It should resemble Fig. 5.4-1. 

Fig. 5.4-1 The logarithmic concentration diagram for HgS. The colored line shows the solubility S of mercury and sulfur.

Fig. 5.4-2 The logarithmic concentration diagram for HgS calculated on the erroneous assumption that Hg2+ does not form hydroxy complexes.

We are now ready to plot a logarithmic concentration diagram of all silver species as a function of pCl. We will first make such a diagram for a solution in equilibrium with solid AgCl. 

Fig. 5.5-1 The logarithmic concentration diagram for the chloro complexes of Ag(I) in an aqueous solution equilibrated with solid AgCl. The colored line shows the silver solubility SAg. Note that, in this case, the solubility of the insoluble neutral species, AgCl, is quite substantial between a pCl of 2 and 3 it is the dominant component of the silver solubility SAg.

Now we are ready to make the corresponding logarithmic concentration diagram. We will use the IF statement of the spreadsheet to determine whether or not a precipitate will be present, and let the calculation selfadjust accordingly. 

Plotthe corresponding logarithmic concentration diagram, using columns A, H, andj through N. Compare with Fig. 5.5-2. 

Fig. 5.8-1 The logarithmic concentration diagram for Fe2+ /Fe3+ atC = 0.01 M, calculated with f Fe32 = 0.770V.

Fig. 5.8-3 The logarithmic concentration diagram for the Mn04 /Mn2+couple at C = 0.01 M and pH = 0 (colored line) and pH = 1 (blackline), calculated with Mn72 = 1-51 V.

LOGARITHMIC CONCENTRATION DIAGRAMS—HOW TO VIEW LARGE CONCENTRATION CHANGES... 

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