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By Lower S.K.

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For H3 PO4 the relation − [H3 PO4 ] + [H3 O+ ] = [H2 PO− 4 ] + [OH ] − yields [H2 PO2− 4 ] = [OH ] which corresponds to point 1 in Fig. 13. 3 [HPO42Ð] 5 [H3PO4] Ð2 [H+] Ð3 [OHÐ] 3 log concentration 2 Ð4 4 [PO43Ð] 1 Ð5 [HPO42Ð] Ð6 [H2PO4Ð] Ð7 Ð8 Ð9 1 2 3 4 5 6 7 8 9 10 11 12 13 pH Figure 13: Log-C diagram for the phosphate system which gives [H3 PO4 ] = [HPO2− 4 ] after smaller terms are eliminated (2). Na3 PO4 is treated straightforwardly and corresponds to point 5. The case of Na2 HPO4 is not quite so simple, however; the proton-balance expression 3− − 2[H3 PO4 ] + [H3 O+ ] + [H2 PO− 4 ] = [PO4 ] + [OH ] cannot be so greatly simplified because the two terms on the right will be comparable.

At these extremes of pH the concentrations of H3 O+ and of OH− are sufficently great that a competing buffer system (either H3 O+ /H2 O or H2 O/OH− , depending on whether the solution is highly acidic or highly alkaline) comes into play. 8 It can be shown that in the limit of large n, the ratio of K /K for a symmetrical dicarboxylic acid HOOC-(CH ) 1 2 2 n COOH converges to a value of 4. 3 Detection of the equivalence point Whether or not the equivalence point is revealed by a distinct “break” in the titration curve, it will correspond to a unique hydrogen ion concentration which can be calculated in advance.

Polyprotic acids The effect of the first point is seen by comparing the titration curves of two diprotic acids, sulfurous and succinic. The appearance of only one equivalence point in the latter is a consequence of the closeness of the first and second acid dissociation constants. 3 1 2 3 equivalent fraction of base added 1 2 3 equivalent fraction of base added Figure 9: Titration curves with end points missing monoprotic acids having the corresponding Ka s. This reflects the fact that the two acidic –OH groups are connected to the same central atom, so that the local negative charge that remains when HSO− 3 is formed acts to suppress the second dissociation step.

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Acid-base Equilibria and Calculations (1996)(en)(48s) by Lower S.K.

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