Statistical product ratio

We call this outcome a statistical product ratio because it derives from the statistical fact that it is three times as likely for a chlorine atom to collide with a primary hydrogen in propane, of which there are six, as with a secondary hydrogen atom, of which there are only two. But is this the outcome that is observed Actually, no. 

For PR3/P(OR)3-stabilized nickel complexes, there are two borderline cases known from the experimental investigation of Heimbach et al. 1 which, unlike the usual behavior, redirect the cyclo-oligomerization reaction into the Ci2-cyclo-oligomer production channel. Catalysts bearing either strong a-donor ligands that must also introduce severe steric pressure (e.g., PBu Pr2) or sterically compact n-acceptors (like P(OMe)3) are known to yield CDT as the predominant product. From a statistical analysis it was concluded,8a,8c that the C8 Ci2-cyclo-oligomer product ratio is mainly determined by steric factors (75%) with electronic factors are less important. 

The product ratio a /b (statistically corrected for the number of competing H migrants), gives the relative migration rate of Ha vs. Hb, or k /kub- The rate constant for the migration of Ha corresponds to the intrinsic migratory aptitude of Ha (M[H]) multiplied by the bystander assistance factor for Y, B[Y], The carbon atom that bears Hb has no bystander substituent, so that km, is simply A/[H], We thus obtain Eq. 24. 

If radicals are unable to undergo disproportination they must react by radical combination. For example, irradiation of PhCH2COCHPh2 gives three radical combination products in the statistically-expected ratio of 1 2 1 ... 

This is a competitive reaction that compares the reactivities of toluene and cyclohexane. Br- is less reactive and more selective than C1-, and reactivity differences of the respective H s determine the product (benzyl > 2°). With the more reactive and less selective Cl, the statistical advantage of cyclohexane (12H s) over toluene (three H s) controls the product ratio. 

Alkane Methylene aource Conditions Product ratios Experimental Statistical Ref. 

These product ratios show that the orientation of substitution is not random. If each C—H position were equally reactive, there would be equal amounts of ortho and meta substitution and half as much para substitution 40% ortho, 40% meta, and 20% para. This is the statistical prediction based on the two ortho positions, two meta positions, and just one para position available for substitution. 

The nonstatistical population is the group of molecules that directly cross the diradical and produce 32x. Carpenter hypothesized that with increasing pressure, collisions will become more common such that energy will be redistributed away from the modes that lead to direct crossing of the diradical, yielding a more statistical product distribution. In other words, collisions provide the barrier so that the momentum can be redirected. The reaction of 2>l-d2 was carried out in supercritical propane in order to control the pressure. The ratio of 32x to 32n did... 

In aqueous acetone and methanol, TS-1 shows superior performance than in t-butanol or just water. The solvent has also a major effect on the catechol hydroquinone raho (see below). This varies in the range 0.5-1.3, which is some way from the value of 2 expected for a statistical attack at the ortho and para positions (Table 18.5, entries 1 and 2). Yet, under practical conditions, the main component of the reaction mixture could be phenol instead of the putative solvent and, under such conditions, the product ratio approaches unity. 

Photolysis of diazirine in the presence of a large excess of propane yielded n- and isobutane and in the presence of n-butane yielded n- and isopentane. From the relative rates of attack on the primaiy and secondary carbon-hydrogen bonds in these compounds, it was concluded that methylene derived from diazirine showed approximately the same discrimination as methylene formed by the photolysis of ketene. The results obtained, using methylene derived from the photolysis of diazomethane, gave a product ratio closer to the simple statistical ratio of the number of carbon-hydrogen bonds without correction factors for the type involved and indicated almost no differentiation between the types. 

It is apparent from Table 26 that the rate of rearrangement increases as ortho-alkyl substitution is increased. Table 27 presents these data with statistical and product ratio corrections. The rate coefficients associated with migration to the ortho and para positions are given by k and respectively. It is seen that a single ort/io-alkyl substituent is more effective in increasing the rate of rearrangement to a hydrogen occupied ortho position than is the same substituent in a para position. 

One problem is again a matter of relative component strengths in that now kyjkx, is to be sufficiently large. After this, the remaining product selectivity problem is a more subtle one relating to the statistics of position of the bond ruptures in the F2-process which determines the heavy to light product ratios of this intrinsic process (e.g., as illustrated by Fig. 12). 

The relative reactivities of various radicals for abstracting hydrogens attached to 1°, 2°, and 3° carbons are given in Table 11.10. These numbers have been corrected for statistical factors, meaning that to use these numbers to predict product ratios, you need to multiply each number by the actual number of 1° 2°, and 3° hydrogens present in your reactant. 

Therefore, the chances of attacking an ortho position should be two-thirds (or 67%), while the chances of attacking the para position should be one-third (33%). From a purely statistical point of view, we should therefore expect our product distribution to be 67% ortho and 33% para. But the product ratio is different from what we might expect, because of steric considerations. Specifically, the propyl group is fairly large, and it partially blocks the ortho positions. We do still observe ortho products, but less than 67%. In fact, the para product is the major product in this case ... 

Typically, one adopts the same total rate coefficient for each of the three reactive systems (C+ + H2O, HDO, D2O) but applies a statistical branching ratio to the products of the C+ + HDO reaction, in this case 0.5. For more complex systems, additional approximations, often having to do with the preservation of functional groups within a reaction, are made. The proton transfer reaction ... 

Selectivity with respect to reagents leads to specificity with respect to products, exemplified by non-statistical branching ratios, anisotropy of angular distribution and "surprising" product state distributions. The importance of vector correlations (from crossed beam experiments with polarized laser-induced fluorescence detection) is touched upon, as well as the subject of polarized laser photofragmentation dynamics (half-collisions) leading to (non-statistical) specificity in product polarizations. 

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