PC-pH diagrams

Two graphical methods described here, a master variable (pC-pH) diagram and a distribution ratio diagram, are extremely useful aids for visualizing and solving acid-base problems. They help to determine the pH at which an extraction should be performed. Both involve the choice of a master variable, a variable important to the solution of the problem at hand. The obvious choice for a master variable in acid-base problems is [H+] [equations (2.9)—(2.12)], or pH when expressed as the negative logarithm of [H+]. 

Example 8.13. Chlorine Redox Equilibria Summarize in a pc-pH diagram the information contained in the equilibrium constants, I — 0, 25°C, of the following three reactions involving Cl2(aq), Cl, OCl, and HOCl. [For convenience, in addition to the equilibrium constant, the standard redox potential. 

Phosphorous can exist as H PO (i = 0, 1, 2, and 3) at different pH values. As shown in the above equation, solution pH will decrease with the release of hydrogen ions. According to the pC-pH diagram illustrated in Fig. 5, the formation of H PO and HPO contributes to the uptake of phosphorous at pH 1 to 5 and 5 to 10, respectively. The pH dependency of phosphorous removal indicates that the amount of HPO4 is higher than that of H2PO4 as shown in Fig. 6. 

This method is based on the reactions between a reagent and relevant mineral species and using solubility product values. In pC-pH diagrams, the abscissa is pH of the solution the ordinate is negative logarithm of the precipitation concentration of the metallic ions. 

The H and OH" concentration lines are common to the graphical solution of all acid-base problems (and many other types of equilibrium problems) so that it would be handy to prepare pC-pH diagrams with these lines already plotted on them. The first step would then be to plot pCx on the diagram. 

The next lines to be plotted are for fCN"] and HCNJ. To plot these quantities in the pC-pH diagram, first we must derive expressions relating each of them to pH and constants. Tackling [CN ] first, we can combine Eqs. 4-21 and 4-23 to eliminate [HCN] and produce... 

Construct a pC-pH diagram for HOCl following the procedure described previously. In the diagram. Fig. 4-2,... 

DETERMINATION OF TEMPERATURE AND IONIC STRENGTH EFFECTS ON EQUILIBRIA USING pC-pH DIAGRAMS... 

The pC-pH diagrams can be used for systems having temperatures other than 25°C and ionic strengths other than zero. The modification of a 25°C-based pC-pH diagram for temperatures other than 25 C merely entails the use of equilibrium constants for the appropriate temperature in the equilibrium expressions used to construct the diagram. The Van t Hoff relationship (Eq. 3-27) can be used to convert 25°C equilibrium constants to the values at the desired temperature. 

Construction of pC-pH diagrams for ionic strengths other than zero requires the use of activities rather than concentrations in all equilibrium... 

Effect of Temperature and Ionic Strength on Equilibria From pC-ph Diagrams 123... 

The remaining equation necessary to describe the system is either the proton condition or the charge balance. Since these equations are based on concentration rather than activity, no correction for ionic strength is necessary. The pC-pH diagram in Fig. 4-4 can now be used to obtain concentrations as previously demonstrated. 

For the general case of a multiprotic acid added to water, we can construct a pC-pH diagram in a similar fashion to that used for a monoprotic acid. The procedure is somewhat more complex because we have additional species to consider as well as additional equilibrium statements. 

It would be a useful exercise for the student to construct lines for pH versus p[HA"j and p[A "] using these equations and appropriate assumptions. These lines plot as shown in Fig. 4-5. This pC-pH diagram differs in two major ways from that for a monoprotic acid ... 

The pC-pH diagrams have so far been used only for solutions containing one acid and its conjugate base(s). These diagrams are equally applicable to mixtures of acids as is shown by the following example. 

We can plot the pC-pH diagrams for these two acid-conjugate base pairs on the same diagram (Fig. 4-8). Because = x.ac is the same for each pair, some of the lines are superimposed. The proton condition is... 

A solution contains 10 moles of acetic acid, HAc. What is the solution pH after 0.0025, 0.(K)5, and 0.01 liters of 0.1 M NaOH and 0.03 liter of 1 M NaOH have been added per liter From these data sketch a titration curve (equivalent fraction, f, added versus pH, and ml added versus pH) and show the relationship between the titration curve and the pC-pH diagram. The temperature is 25"C neglect ionic strength effects. 

We use equations (1), (3), and (4) to plot a pC-pH diagram for the acetic acid-acetate system (Ct,ac = 10 M) (Fig. 4-12). To determine the solution pH after each NaOH addition, we must first determine Na from equation (2) and then substitute this value in the charge balance, equation (5). The solution for the charge balance is obtained by inspection of the pC-pH diagram. For V 0.0025 liter From (2)... 

The titration curve was plotted in Fig. 4-12, together with the pC-pH diagram. By comparing these two plots, the following important observations can be made. 

Before HCl addition, this will be the pH of a 10 M NHajaq) solution. This can either be read from a pC-pH diagram or calculated as in Example 4-14. Roughly sketching the pC-pH diagram (Fig. 4-13), we can rapidly estimate the pH neglecting dilution, we obtain... 

After 1 equivalent fraction of strong acid has been added, we will have a 10 M NH4CI solution. Again using the pC-pH diagram (Fig. 4-13 to solve for the approximate pH, we find... 

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