Statistical weight isotope effect

A second example of an inverse statistical weight isotope effect is that of the secondary H/D KIE on C-C bond rupture during the gas phase unimolecular isomerization of cyclopropane to propene. Theory and experiment are compared in Fig. 14.2 for reactions 14.37 and 14.38. 

Schneider, F.W. and Rabinovitch, B. S., The unimolecular isomerization of methyl-d3 isocyanide. Statistical-weight inverse secondary intermolecular kinetic isotope effects in nonequilibrium thermal systems. J. Am. Chem. Soc. 85, 2365 (1963). 

Thermally Activated Systems. The equilibrium (high pressure) kinetic isotope effect in thermal activation systems is the one conventionally measured and the theoretical basis for this limiting case has been well formulated.3 In the low-pressure non-equilibrium regime, very large inverse statistical-weight secondary isotope effects can occur. 20 b These effects are dependent on the ambient temperature and the thermal energy distribution function the latter is considered in Sec. III-E, and discussion of these effects is postponed until Sec. III-E,4. 

Next we examine the effect described in Sec. II-E, 5 for C—C rupture of C4 and C4-d6. This is a pure secondary effect at p = when Ae0 = 0 at 300°C., (fcH/fcn)< = 0.93. At p = 0, this becomes a combined primary-secondary effect the collisional reaction coordinate again involves the (negligible) primary isotopic reduced molecular mass ratio in wh/wd, but an important secondary effect, associated with the quantum statistical weight difference of the ratio of eq. (36), still remains. 

It is important to look into the implications of Eq. (1) since the development of the quantum-statistical mechanical theory of Isotope chemistry from 1915 until 1973 centers about the generalization of this equation and the physical interpretation of the various terms in the generalized equations. According to Eq. (1) the difference in vapor pressures of Isotopes is a purely quantum mechanical phenomenon. The vapor pressure ratio approaches the classical limit, high temperature, as t . The mass dependence of the Isotope effect is 6M/M where 6M = M - M. Thus for a unit mass difference in atomic weights of Isotopes of an element, the vapor pressure isotope effect at the same reduced temperature (0/T) falls off as M 2. Interestingly the temperature dependence of In P /P is T 2 not 6X0/T where 6X.0 is the heat of vaporization of the heavy Isotope minus that of the light Isotope at absolute zero. In fact, it is the difference between 6, the difference in heats of vaporization at the temperature T from (> that leads to the T law. 

However, the half width of this MALDI peak is relatively broad. As natural gadolinium consists of several isotopes the 24mer Gadomer has a statistical distribution of molecular weights. Figure 13 shows a simulation of flus effect. The theoretical half width is approximately 25 Da but experimentally, peaks with half widths of > 100 Da have been found. This has of course some consequences for the structure elucidation of byproducts which show only minor differences in mass. Simulation experiments show that dendrimers which differ in about 40 Da will even show an overlap of the peaks if the experimental half width is only 25 Da. 

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