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Mole-' , and 6~ = 13. Neither AGtx(A) nor AGtX(Tr) are well correlated by Equation (32), and hence the reasonable linear relation between log kx (and therefore of AG*X) and 6 or 6' (see Figures 1 and 2) must be due to remarkable cancellations of polar effects on the reactants and the transition state. Indeed, it is easier to deduce a value for 6Tr from a plot of log kX against 6 than it is from the theoretically better plot of AGtx("r) against VTr(6Tr - 6)'. In view of the discussion in Section IIID, it is of interest to plot AGtX(A) and AGtx(Tr) against AGtX(R4NX); this has been done in Figure 14, where the correlations are at least as good as those shown in Figures 12 and 13.
In the calculation of activation parameters from second-order rate constants, A G h f A G k # AG*m and AS& Z Ask f AS*m. * Thus in the application of Equation (13) (and of analagous equations in S) to second-order reactions, values of 6AG* must refer to the same scale as that used in the specification of the A G t values. There is no such problem in dealing with first-order reactions, since first-order rate constants are independent of any standard state. B. Solvent Effects on Nonelectrolytes The Raoult's law activity coefficient, 7 , of a solute in a given solvent is defmed by Equation (19), in which P is the vapor pressure of the solute above a solution of x mole-fraction solute, and Po is the vapor pressure of the pure solute.
63. J k f . 42. From Ref. 54 after correcting from the molar to the mole-fraction scale. eRef. 64. fValues for solute n-heptane. Ref. 64. 78 - gRef. 66. hRef. 67. Ref. 68. ]Ref. 69. kTransfers calculated from methyl alcohol to a solvent in which 6" = 1 for the solute. DMSO, nitromethane, acetonitrile, and DMF, AGtX (with methyl alcohol as the reference solvent) for benzene is about 1 kcal. mole-' more negative than for the solute n-hexane, while AGtX(p-NO2C6H4CHZC1) is about 2 kcal. mole- ' more negative than A c t X(n-C6H, 4).