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

B.1 The specific ion interaction equations 801Assumption 1: The activity coefficient γ j of an ion j of charge z j in the solution ofionic strength I m may be described by Eq. (B.1).log 10 γ j = −z 2 j D + ∑ kε ( j,k,Im )m k(B.1)D is the Debye-Hückel term:D =A √ I m1 + Ba j√Im(B.2)where I m is the molal ionic strength:I m = 1 ∑m i zi2 2A and B are constants which are temperature and pressure dependent, and a j is an ionsize parameter (“distance of closest approach”) for the hydrated ion j. The Debye-Hückel limiting slope, A, has a value of (0.509 ± 0.001) kg 1/2 · mol −1/2 at 25 ◦ Cand1bar,(cf. Section B.1.2). The term Ba j in the denominator of the Debye-Hückelterm has been assigned a value of Ba j = 1.5kg 1/2 · mol −1/2 at 25 ◦ Cand1bar,asproposed by Scatchard [76SCA] and accepted by Ciavatta [80CIA]. This value hasbeen found to minimise, for several species, the ionic strength dependence of ε ( j,k,Im )between I m = 0.5 mandI m = 3.5 m. It should be mentioned that some authors haveproposed different values for Ba j , ranging from Ba j = 1.0 [35GUG] toBa j = 1.6[62VAS]. However, the parameter Ba j is empirical and as such correlated to the valueof ε ( j,k,Im ). Hence, this variety of values for Ba j does not represent an uncertaintyrange, but rather indicates that several different sets of Ba j and ε ( j,k,Im ) may describeequally well the experimental mean activity coefficients of a given electrolyte. The ioninteraction coefficients at 25 ◦ C listed in Tables B.3 through B.5 have thus to be usedwith Ba j = 1.5kg 1/2 · mol −1/2 .The summation in Eq. (B.1) extends over all ions k present in solution. Theirmolality is denoted m k , and the specific ion interaction parameters, ε ( j,k,Im ), in generaldepend only slightly on the ionic strength. The concentrations of the ions of the ionicmedium is often very much larger than those of the reacting species. Hence, the ionicmedium ions will make the main contribution to the value of log 10 γ j for the reactingions. This fact often makes it possible to simplify the summation ∑ k ε ( j,k,I m )m k sothat only ion interaction coefficients between the participating ionic species and theionic medium ions are included, as shown in Eqs. (B.4)to(B.8).Assumption 2: The ion interaction coefficients ε ( j,k,Im ) are zero for ions of the samecharge sign and for uncharged species. The rationale behind this is that ε,whichdescribes specific short-range interactions, must be small for ions of the samecharge since they are usually far from one another due to electrostatic repulsion.This holds to a lesser extent also for uncharged species.i