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

C.3 Several data at different ionic strengths 829where =N∑i=11σ 2iN∑i=1m 2 k,iσ 2i−( N∑i=1) 2m k,iσi2 . (C.12)In this way, the uncertainties σ i are not only used for the weighting of the data inEqs. (C.8) and(C.9), but also for the calculation of the uncertainties σ X◦ and σ ε inEqs. (C.10) and(C.11). If the σ i represent the 95% confidence level, σ X◦ and σ εwill also do so. In other words, the uncertainties of the intercept and the slope do notdepend on the dispersion of the data points around the straight line but rather directlyon their absolute uncertainties σ i .Example C.4:Ten independent determinations of the equilibrium constant log10 ∗ β for the reactionUO 2+2+ HF(aq) Å UO 2 F + + H + (C.13)areavailableinHClO 4 /NaClO 4 media at different ionic strengths. Uncertainties thatrepresent the 95% confidence level have been assigned by the reviewer. A weightedlinear regression, (log10 ∗β+2D)vs. m k, according to the formula log10 ∗β(C.13)+2D=log10 ∗β◦(C.13) − ε m k , will yield the correct values for the intercept log10 ∗β◦(C.13)and the slope ε. In this case, m k corresponds to the molality of ClO − 4. D is theDebye-Hückel term, cf. Appendix B.The results of the linear regression are:i m ClO−4 ,i log10 ∗βi + 2D σ i1 0.05 1.88 0.102 0.25 1.86 0.103 0.51 1.73 0.104 1.05 1.84 0.105 2.21 1.88 0.106 0.52 1.89 0.117 1.09 1.93 0.118 2.32 1.78 0.119 2.21 2.03 0.1010 4.95 2.00 0.32intercept = (1.837 ± 0.054) = log10 ∗β◦(C.13)slope = (0.029 ± 0.036) = −εCalculation of the ion interaction coefficient ε (UO2 F + ,ClO − 4 ) = ε + ε (UO 2+2 ,ClO− 4 ) −ε (H + ,ClO − 4 ): From ε (UO 2+2 ,ClO− 4 ) = (0.46 ± 0.03) kg · mol −1 , ε (H + ,ClO − 4 ) =(0.14±0.02) kg · mol −1 (see Appendix B) and the slope of the linear regression, ε =−(0.03 ± 0.04) kg · mol −1 , it follows that ε (UO2 F + ,ClO − 4 ) = (0.29 ± 0.05) kg · mol−1 .