Fifty-percent rule

In sharp contrast, a plot of against AV for almost aU aqueous reactions for which both parameters are currendy available shows an excellent linear correlation of slope 0.50 0.02 and negligible intercept [16] (according to a recent reinvestigation [20], the Fe(CN)j case may be anomalous and should be excluded). For convenience, we refer to this relationship as the fifty-percent rule . The evident equivalence between and AV /2 implies that the pre-exponential factors Zei and Zex for aqueous systems are effectively independent of pressure. Such is known to be the case for Ze, from experience with the success of Eqs (5.5)-(5.8) for self-exchange reactions, and presumably it also applies to Z because the nature of a given electrode and its surface are virtually independent of pressure, even though the pre-exponential factor may differ widely from one electrode to another. 

The fifty-percent rule implies that AVJ for aqueous electrode reactions can be predicted from Eqs (5.5)-(5.8). Thus, for the Fe(diamsarH2) + couple, for which we saw in Sect. 5.2.2 that there is a detectable spin equilibrium but with AVjpin =... 

A more precise version of Eq. (5.22) for the theoretical value AV ] (calc) of AV includes a term Q representing the small, largely self-canceling pressure dependences of the factors other than r/ in Eqs (5.19) and (5.20). For the Ru(hfac)j couple in the solvents listed in Table 5.3, Qis only —0.3 to —0.4 cm mol . Furthermore, since AV.. j. is the value of AV that would be expected in the absence of solvent friction, we can use the fifty-percent rule to estimate it as AV /2 ... 

Table 5.3 shows that AV (calc) agrees with the experimentally observed to within the experimental uncertainty for the Debye solvents acetone and acetonitrile, and comes surprisingly close for methanol which, because intermolecular hydrogen-bonding contributes several frequencies to the apparent tl, is not considered to be a Debye liquid. Unfortunately, there are insufficient data for application of Eq. (5.23) to the Ru(hfac)3 electrode reaction in propylene carbonate, which is also regarded as a non-Debye liquid. In any event, the implication is that the fifty-percent rule applies to volumes of activation for electrode reactions but its effect is swamped by solvent dynamical contributions. 

FIGURE 4.25 Fifty percent majority rule consensus cladogram resulting from a Bayesian inference analysis of the complete dataset. Numbers above branches indicate the posterior probabilities as a percentage value. 

FIGURE 6.4 Fifty percent majority rule consensus tree of 2348 most parsimonious trees (L = 808, Cl = 54, RI = 79) of analysis of 86 terminals. Jackknife (in italics) and Bremer support values are shown below branches those clades that appear also in the strict consensus topology are shown with 100 above the branch. 

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