Isotope effects, equilibrium maxima

These structures were then used to generate the force fields and calculate the secondary /3-deuterium-d6 equilibrium isotope effects (EIEs) for the formation of the isopropyl carbocation (Table 30). Because the transition states for formation of the carbocation will be close to the structure of the carbocation, these KIEs should be excellent approximations of the maximum secondary /3-deuterium KIEs expected for the limiting SN1 solvolytic reaction. 

The isotope effects (both kinetic and equilibrium) that deplete deuterium, D, and 0 in evaporated water vapor must enrich these isotopes in the surface seawater left behind. This isotope effect can be seen in longitudinal transects of surface waters in both the Atlantic and Pacific Oceans (Fig. 5.12), which indicate a broad maximum of between roughly 30° north and south latitudes. Salinity maxima are evident over the same latitude band, with a slight minimum near the Equator. The parallel maxima in and salinity result because net evaporation from warm surface waters at lower latitudes preferentially leaves behind both H2 0 molecules and salt. Rainfall in excess of evaporation from atmospheric convection cells rising near the Equator is recorded by both a salinity and a minimum. 

The maximum isotope effect, k /k, will occur when the proton is completely transferred from H2O to DO, i.e. for the equilibrium reaction shown in equation 6. For reaction at 25°C, = 2.07. For a transition state in which the proton is half-transferred... 

Figure3-15. The non-equilibrium plasma (Ty To) isotopic effect dependence on translational gas temperature To temperature Tq corresponds to the maximum value of the selectivity coefficient of the inverse isotopic effect.

Many other examples could be cited which show a smooth variation of k /kP with the strength of the base, and in a few cases some indication of a maximum isotope effect when ApK (and hence the standard free energy change of the reaction) is close to zero. Such a maximum may well be concealed in the results for sodium propan-2-one-l-sulphonate in Table 25, since kP/k has almost the same value for reaction with 2,6-lutidine and hydroxide, for which ApK is -h7.4 and —2.0 respectively. One way of changing the value of Api is to modify the nature of the solvent, and in particular the addition of dimethyl sulphoxide to aqueous solutions containing hydroxide ions will displace the equilibrium SH-hOH"... 

The fractionation factor, which is the equilibrium constant Kf = [C][D]/[A][B], was calculated using the Bigeleisen equation as Kp = 1.11 at 25°C (Shiner and Hartshorn, 1972). This reaction might serve as a model for a maximum expected a-deuterium isotope effect in which a CH2=CHD group is changed to a cyclopropyl-D group. An experimental example is the equilibrium isotope effect K — 1.109 at 29°C in l,5-dimethyl-2-deuteriosemibullvalene [2] (Askani et al., 1982)... 

The equilibrium constant recalculated from the shift values reported is in reasonable agreement with the fractionation factor for a simple model reaction of isotopic exchange equilibrium (38). The fractionation factor, Kf = 1.07 (25°C), for d,-cyclopropane relative to 2-dj-propane [39] (Shiner and Hartshorn, 1972) might serve as a model value for the maximum expected a-deuterium isotope effect. 

The equilibrium isotope effect in the cation is a differential a- y-effect. Kinetic investigations have shown, however, that y-deuterium isotope effects in cyclopropylmethyl cations are small (Sunko et al., 1962) therefore neglect of the y-effect and comparison with calculated a-effects seems justified. The fractionation factor Kf = 1.11 (25°C) for an isotopic exchange equilibrium between -cyclopropane and Dj-ethene (Shiner and Hartshorn, 1972) is a model value for the maximum expected a-deuterium isotope effect and is in agreement with the experimental value in cation [9] extrapolated to 25°C (K= 1.11). 

These results have been interpreted as a direct proof of the hyperconjuga-tional origin of the dependence of the P-deuterium equilibrium isotope effect on dihedral angle in a persistent carbocation. In [153] maximum overlap between the vacant p-orbital and one of the methyl C—D or C—H bonds is always possible leading to large equilibrium isotope splittings. In [154] the dihedral angle of 90° permits no overlap of the vacant p-orbital with the... 

Two points are at once apparent in Figure 6. One is that the plot shows considerable scatter, and the other that although a maximum can clearly be seen, close to ApK = 0, there is a paucity of measurements for strongly exothermic reactions (large negative ApX). The second point is a reflection of an experimental difficulty which could in principle be remedied by determining the equilibrium isotope effects K /Ko) from measurements of the fractionation factors of reactants and products. Combination of /chAd and would... 

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