Use of PBE to Derive Titration Curves

Strong acid - strong base. Let us add a specified volume, mL, of a solution of M HCl to a vessel and titrate this with Cg M NaOH. The PBE can be written that describes the titration mixture for any volume, Vg mL, of base that is added  

The quantity F, titration fraction, defined as the number o f moles o f titrant added, CgVg, per mole of analyte acid, is another useful way to 

Vg is plotted from 0 to 100 mL on the X axis against pH on the Y axis for 50 mL of various concentrations of HCl with equal concentrations of NaOH as titrant. Notice how the pH changes slowly both well before and well after the region of the equivalence point, and changes very rapidly near the equivalence point. Further, it can be seen that the region of rapid pH change near the endpoint decreases with the acid concentration. The pH 

The corresponding PBE when H B, a weak polyprotic acid, replaces HCl is  

Notice the S-shaped region (from about 10 to 90% neutralization of the acid) before the equivalence point corresponding to the buffer region (mixture of HOAc andNaOAc). The close resemblance of these segments of the curve demonstrates the independence of buffer pH from absolute acid concentration when HOAc is very dilute (10 M), however, its dissociation is essentially complete so that its titration curve is like that of HCl at the same concentration. 

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