Isotope rate ratios

Using the terminology of Wolfsherg and Stem (1964), the isotopic rate ratio may be expressed as equation (11) ... 

Brown and McDonald (1966) provided another type of kinetic evidence for these size relationships by determining secondary kinetic isotope effects in reactions of pyridine-4-pyridines with alkyl iodides. For example, the isotopic rate ratio in the reaction between 4-(methyl-d3)-pyridine and methyl iodide at 25-0 C in nitrobenzene solution was determined to be kjyfk = l-OOl, while that in the corresponding reaction with 2,6-(dimethyl-d6)-pyridine was 1-095. (Brown and McDonald (1966) estimate an uncertainty of 1% in the k jk values.) Furthermore, the isotopic rate ratio in the case of the 2-(methyl-d3)-compound increased from 1 030 to 1-073 as the alkyl group in the alkyl iodide was changed from methyl to isopropyl, i.e. the isotope effect increased with increasing steric requirements of the alkyl iodide. 

The molecules most profitably studied in connection with purely steric isotope effects have been isotopically substituted biphenyl derivatives. Mislow et al. (1964) reported the first more or less clearcut example of this kind in the isotope effect in the configurational inversion of optically active 9,10-dihydro-4,5-dimethylphenanthrene (7), for which an isotopic rate ratio ( d/ h) of 1-17 at 295-2°K in benzene solution was determined. The detailed conformation of the transition state is not certain in this case, as it involves the mutual passage of two methyl groups, and thus it is difficult to compare the experimental results with... 

Combining Equations 4.77, 4.140 and 4.145 we obtain a useful expression for the isotopic rate ratio... 

Variation of Primary lntermoleoular Isotopic Rate Ratio with Some Parameters of... 

Variation of Primary Intermolecular Isotopic Rate Ratio with Some Parameters of Case 6 ( oh = 35 kcal. mole-1)... 

Distribution Functions and Hydrogen-Deuterium Isotope Effects in Nonthermal Activation Systems. In Sec. II-D, hydrogen-deuterium isotopic rate ratios for monoenergetic systems were discussed. In practice, the measured effects are ratios modified by the energy distribution functions and should be compared to kan/kaD rather than to k,n/ktn. A s appropriate for the system under investigation, one of eqs. (19)-(22) is written for each of the isotopic species and a ratio, kttn/kaD, is thus constructed for comparison of isotope effects. These need not be listed in detail. It should be noted that the distribution function for the normal and isotopically substituted systems will usually be somewhat different (Fig. SB). 

In the limiting low-pressure non-equilibrium system, the rate constant is given by eq. (30) the isotopic rate ratio is ... 

Isotopic Rate Ratio for Decomposition of the Pairs, sec-Butyl and sec-Butyl-dg. see-Butyl-di and aec-Butyl-do ... 

For most organic molecules, the substitution of hydrogen for its heavier isotopes materially has little influence on the molecular mass or moment of inertia. The isotopic rate ratio thus reduces, essentially, to a dependence on the vibrational partition functions, viz. 

If all the zero-point energy is lost in the stretching of the C—H bond in the transition state, then the calculated primary isotope effect should be around 7 at room temperature (6). This means the isotope rate ratio, h/ d, where kn is the... 

Isotopic Rate Ratios for Various Compounds Hydrolyzing in Water ... 

A theoretical expression for the isotopic rate ratio v/v can be derived using the general rate equation (203.HI) for a given (endothermic or exothermic) reaction. Omitting the indices, we write... 

Very often, one assumes that the vibrational frequencies in the reacting molecule are identical with those in the activated complex with the exception of the vibrational frequency corresponding to the rupture of the bond (vn-). In this approximation, and at low temperatures or high vibrational frequency for the bond of interest, the logarithm of the isotopic rate ratio k /k is given by... 

The isotopic rate ratio is ll 3, and the difference of activation energies (E - E ) is ih 2.6 kJ mol"" both values suggest that tunnelling is important. Moreover the Arrhenius plot for the proton-transfer reaction deviates from linearity at low temperatures, and indeed below about 200 K it becomes horizontal this indicates that tunnelling occurs from one energy-level only. 

Reactions of thiophenols have been studied by Lewis (37) the isotopic rate ratios are increased by substitution near the reaction site, suggesting (since the solvent takes little part) that steric repulsion does increase the barrier height, rather than merely exclude solvent (cf, above). An intramolecular reaction of this type is the exchange of H atoms in the phenoxy1-type radical formed from 1,2-dihydroxybenxene (equation 7), which has been studied by e.s.r. line-broadening methods (9) the... 

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