Third Equivalence Point

In this case, the exponentials en and en exhibit very high numerical values, and before the equivalence point, 62 remains negligible. Therefore, the general equation 

This relation indicates that the sole reaction to evolve is 

After the equivalence point, the general equation may be further simplified since the 

The solution potential value is imposed by the couple Mn04 /Mn +. This last equation is equivalent to the relation 

Taking all of these considerations together, we can deduce that the possibility of the satisfactory sequential titration of the different functions of a polyfunctional compound is, above all, based on the values of the standard potential differences E° 2 — E°n, E°i2 —E°i2. These differences permit us to neglect some exponentials according to the stages of the titration. In the case of the titration of multifunctional redox derivatives, it experimentally turns out that a difference amounting to 0.24 V is sufficient to detect the successive functions. The difference AE° = 0.24 V has already been encountered. It was during the study of the titration of a monofimctional redox compound, but the difference concerned the standard potentials of the titrand and the titrant, and not only that of the titrand as here. 

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The phenolphthalein end point is basic, occurring at a pH of approximately 8.3 and can be reached only if the titration proceeds to the third equivalence point (Figure 9.19b) thus, we write... 

There is a third equivalence point, not shown in the figure, that would require an additional 10.0 mL of base to reach. Its titration reaction is represented by the following equation. 

To the third equivalence point NaOH + Na2HP04------ Na3P04 + H20... 

Another 27.50 mL of 0.020 M NaOH would be required to reach the third equivalence point. pH values at each of four equally spaced volumes of 5.50 mL additional 0.0200 M NaOH are computed as before, assuming the Henderson-Hasselbalch equation is valid. 

As noted earlier, the weaker /the acid, the shorter is the steeply rising portion of the titration curve. If the acid is very weak, the equivalence point is difficult to detect. Although H3PO4 is a triprotic acid, HPO42- is such a weak acid that the third equivalence point is not observed in the PbPC /NaOH titration curve. 

At the third equivalence point Beyond the third equivalence point... 

FIGURE 15.17 A titration curve for the titration of a polyprotic acid (phosphoric acid) by a strong base. The curve shown is for 100.0 mL of 0.1000 M H3PO4 titrated with 0.1000 M NaOH. No clear third equivalence point is seen at 300 mL because for HP04 is not much greater than for H2O in aqueous solution. 

Finally, beyond the third equivalence point, neglect of [I ], [Br ]and [CF] leads to... 

The species HP04 is such a weak acid ( as = 4.5 x 10 ) that the change in pH in the vicinity of the third equivalence point is too small to be observable. 

A 10.0 mL volume of 0.100 M NaOH is required to reach the first equivalence point. The additional volume of 0.100 M NaOH required to reach the second equivalence point is also 10.0 mL. The pH does not increase sharply in the vicinity of the third equivalence point (30 mL). 

In discussing the neutralization of phosphoric acid by a strong base, we found that the first equivalence point should come in a somewhat acidic solution and the second in a mildly basic solution. We reasoned that the third equivalence point could be reached only in a strongly basic solution. The pH at this third equivalence point is not difficult to calculate. It corresponds to that of Na3P04(aq), and P04 can ionize (hydrolyze) only as a base. 

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