Abstract
Based on the results from potentiometric titrations carried out on polyacrylic acid and some commercially available humic acids, the equation for the proton dissociation of weak polymeric acids is proposed to be Kapp ＝ [H＋]α/(1－α) ＝ K1/2{(1－α)/α}([Na＋]/[Na＋]s), where α is the degree of dissociation, K1/2 is the dissociation constant at α ＝ 1/2, and the brackets with subscript s denote the concentration at the surface of the polymer. This equation has been derived on the assumptions: (i) Each polymer molecule is a polybasic acid (HNRN) having different acidic sites with K values from K1 to KN. (ii) Binding energies of protons on these sites are all equal. (iii) The ratios of the dissociation constants of HN－iRNi－ and HN－jRNj－ is expressed by Ki/Kj ＝ {(N－i＋1)/i}/{(N－j＋1)/j} since the probabilities to release or bind a proton are proportional to the numbers of protons or numbers of available anionic sites on the polymer. (iv) The effective concentration of protons at the surface of the polymer ([H＋]s) is related by [H＋]s/([H＋] ＝ [Na＋]s/[Na＋], where [Na＋]s can be estimated by the relation, [Na＋]s ＝ [Cl－]s＋[R－]s (where [R－]s ＝ ∑i[HN－iRNi－]). This leads to [Na＋]s ⋍ [Cl－]s, which in turn leads to [Na＋]s ⋍ [Na＋] at high ionic strength and [Na＋]s ⋍ [R－]s ＝ CRα at low ionic strength.
