Significant figures empirical models

Figure 15. Empirical —aG° values for metal cation HPOj, complexes (1 = 0) plotted against t.+7.J(ym + ri/po j, with thpo = 3.15 A based on Izatt et al. (60) and Wells (27). — aG° for AlHPOj, is an estimate. The smooth plotted curve has no statistical significance. (F) Fuoss model.

Empirical models are used to correlate thermodynamic properties, unit operations, heat transfer, fluid dynamics, etc. but often the parameters in these equations also carry too many significant figures. Heat capacity, for example, is approximated by polynomials of up to three degrees and the coefficients in some models carry as many as seven significant figures (Reid et al. 1977, Himmelblau 1962, Howell and Buckius 1992, Spencer 1948 the NIST correlations, for example) ... 

Figure 3.5.2 shows the results obtained using M-5 and TS-500 samples with S/V values of 3.03 x 107 and 3.28 x 107 m 1, respectively, and porosities of 0.936 and 0.938, respectively. Note the significant deviation of the relaxation behavior from that ofbulk CF4 gas (dotted lines in Figure 3.5.2). The experimental data were first fitted to the model described above, assuming an increase in collision frequency due purely to the inclusion of gas-wall collisions, assuming normal bulk gas density. However, this model merely shifts the T) versus pressure curve to the left, whereas the data also have a steeper slope than bulk gas data. This pressure dependence can be empirically accounted for in the model via the inclusion of an additional fit parameter. Two possible physical mechanisms can explain the necessity of this parameter.

The linear relationship between log Kow and the empirically derived log BCFs reported in Table 6.1 was nonsignificant (P = 0.372). When the exceedingly low BCFs reported for NB, NTs, and 1,2-DNB for goldfish (0.01-0.1 ml/mg) [5] were excluded, a significant (P = 0.003) linear relationship (log BCF = 0.53 log Kow- 0.23, r2 = 0.37) was obtained (Figure 6.1). For compounds in the log Kow range of 0.5 to 2.5, the latter relationship predicts BCFs values lower than those predicted using the relationship of Meylan et al. [15], More studies of the bioconcentration of explosive and related compounds in other aquatic species are needed to establish more accurate predictive models for the bioconcentration of those compounds. 

Figure 9.10 tries to answer this question by direct comparisons between "Hg" and "Cs" in water, in phytoplankton (Fig. 9.1 OB), and in prey and predator (Fig. 9.10A). One can note significant differences. This is due to two factors The longer outflow rates (twice as long for "Hg") and the faster uptake for "Cs" the pelagic uptake rate is 21 3.25 10 (1/month) for "Cs" and 3.25 10 (1/year) for "Hg". So, the model and the processes accounted for in the model can describe the empirical results. But it should be stressed that similar results could also be obtained by other combinations of the rates in the model.

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