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

806 B. Ionic strength correctionsof (∂ε/∂T ) p are usually ≤ 0.005 kg · mol −1 · K −1 for temperatures below 200 ◦ C.Therefore, if values of ε ( j,k,Im ) obtained at 25 ◦ C are used in the temperature range 0 to50 ◦ C to perform ionic strength corrections, the error in (log 10 γ j )/I m will be ≤ 0.13.It is clear that in order to reduce the uncertainties on solubility calculations at t ̸= 25 ◦ ,studies on the variation of ε ( j,k,Im )-values with temperature should be undertaken.B.1.3B.1.3.1Estimation of ion interaction coefficientsEstimation from mean activity coefficient dataExample B.1:The ion interaction coefficient ε (H + ,Cl − ) can be obtained from published values ofγ ±,HCl vs. m HCl .2log 10 γ ±,HCl = log 10 γ H + + log 10 γ Cl −= −D + ε (H + ,Cl − )m Cl − − D + ε (Cl − ,H + )m H +log 10 γ ±,HCl = −D + ε (H + ,Cl − )m HClBy plotting log 10 γ ±,HCl + Dvs. m HCl a straight line with the slope ε (H + ,Cl − ) is obtained.The degree of linearity should in itself indicate the range of validity of thespecific ion interaction approach. Osmotic coefficient data can be treated in an analogousway.B.1.3.2Estimations based on experimental values of equilibrium constants atdifferent ionic strengthsExample B.2:Equilibrium constants are given in Table B.2 for the reactionUO 2+2+ Cl − Å UO 2 Cl + . (B.12)The following formula is deduced from Eq. (B.5) for the extrapolation to I = 0:log 10 β 1 + 4D = log 10 β ◦ 1 − εI m (B.13)The linear regression is done as described in Appendix C. The following results areobtained:log 10 β1 ◦ = 0.170 ± 0.021ε(B.12) = −(0.248 ± 0.022) kg · mol −1The experimental data are depicted in Figure B.1, where the dashed area representsthe uncertainty range that is obtained by using the results in log 10 β1 ◦ and ε andcorrecting back to I ̸= 0.