chemical thermodynamics of neptunium and plutonium - U.S. ...

16 2. Standards, Conventions, and Contents of the Tablesboth β q,m and β(2.4) would be appropriate, and β q,m (2.4) is accepted, too. Note that,in general, K is used for the consecutive or stepwise formation constant, and β is usedfor the cumulative or overall formation constant. In the following outline, charges areonly given for actual chemical species, but are omitted for species containing generalsymbols (M, L). The ionization constant for water is designated by K w .2.1.6.1 Protonation of a ligandH + [H r L]+ H r−1 L Å H r L K 1,r =[H + ][H r−1 L]r H + + L Å H r L β 1,r = [H rL][H + ] r [L](2.5)(2.6)This notation has been proposed and used by Sillén and Martell [64SIL/MAR], butit has been simplified later by the same authors [71SIL/MAR] from K 1,r to K r .Thisreview retains, for the sake of consistency, cf.Eqs.(2.7)and(2.8), the older formulationof K 1,r .For the addition of a ligand, the notation shown in Eq.(2.7)isused.HL q−1 + L Å HL q K q = [HL q][HL q−1 ][L](2.7)Eq. (2.8) refers to the overall formation constant of the species H r L q .r H + + q L Å H r L q β q,r = [H r L q ][H + ] r [L] q (2.8)In Eqs. (2.5), (2.6) and(2.8), the second subscript r can be omitted if r = 1, as shownin Eq. (2.7).Example:4 ]H + + PO 3−4Å HPO 2−4β 1,1 = β 1 = [HPO2−[H + ][PO 3−2H + + PO 3−4Å H 2 PO − 4β 1,2 = [H 2PO − 4 ][H + ] 2 [PO 3−4 ]2.1.6.2 Formation of metal ion complexes4 ]ML q−1 + L Å ML q K q = [ML q][ML q−1 ][L](2.9)M + q L Å ML q β q = [ML q][M][L] q (2.10)