Relative rate

In order to fit solvolytic reactions into the above framework it is important to establish the magnitude of nucleophilic solvent assistance, the extent to which nucleophilic attack by solvent assists heterolytic cleavage of the bond to the leaving group. 2-Adamantyl tosylate [6] was selected as a model for SN 1 behaviour because non-bonded interactions [7] would reduce the possibility of nucleophilic attack (Fry et al., 1970a) extensive experimental evidence 

The above evidence firmly establishes that 2-adamantyl tosylate behaves very much like a tertiary substrate in its lack of response to changes in solvent nucleophilicity. As shown by correlations using eqn (9)—Section 6, Table 9—and by the relative rates in Table 1, other secondary tosylates are more responsive to solvent nucleophilicity. Schleyeret al. (1970) proposed that the magnitude of 

Solvent Tosylate EtOH ch3co2h hco2h 97 wt% (CF3)2CHOH cf3co2h 

8 Unpublished results from three independent laboratories. 

2-propyl tosylate appears to be nucleophilically assisted by a factor of 13/0-028 = 470 whereas the more hindered cyclopentyl tosylate is assisted by afactor of 280/2-7 = 105. An extensive tabulation is given in Table 2. As Schadt et al. (1976) have noted, the above argument and calculations are based on the following assumptions. 

Although detailed kinetic studies are not yet available, qualitative observations regarding the addition of RTi(OCHMe2)3 to carbonyl compounds point to the following approximate reactivity scale 77) 

Allyl cyanomethyl benzyl methyl phenyl cyclopropyl ethyl n-butyl o-fluorophenyl trimethylsilylmethyl per-fluorophenyl 

Increasing the number of alkyl groups at titanium increases the rate of addition dramatically  

A final point regards the effect of lithium salts. Methyltitanium triisopropoxide 6, prepared from methyllithium and 3, reacts in situ with carbonyl compounds lightly slower than the distilled compound. However, this has no effect on chemoselectivity6. The only exception noted so far concerns allyl derivatives, as discussed in the following Section C.VII. 

When the reactants and products are described by Morse curves, the value of Q can be obtained from eq. (6.69). For simplicity, in this section we employ harmonic oscillators, and the barrier is, by analogy with eq. (6.68) 

The location of the transition state for asymmetric reactions is given by the first derivative of eq. (6.90), 

The functional dependence of these parameters can be further simplified using eq. (6.95) together with eqs. (6.57) and (6.59), 

In earlier empirical applications of the ISM, a different nomenclature was employed, which is related to the present parameters via 

Both sets of eqs. (6.100)-(6.102) and (6.104)-(6.106) give the same activation free energy, but through a different reactant bond extension, d, = In principle, for 

---

If adsorption occurs via a physisorbed precursor, then the sticking probability at low coverages will be enhanced due to the ability of the precursor to diflfiise and find a lattice site [30]. The details depend on parameters such as strength of the lateral interactions between the adsorbates and the relative rates of desorption and reaction of the precursor. In figure Al.7,8 an example of a plot of S versus 0 for precursor mediated adsorption is presented. 

Quack M 1979 Quantitative comparison between detailed (state selected) relative rate data and averaged (thermal) absolute rate data for complex forming reactions J. Phys. Chem. 83 150-8... 

Many experimental methods may be distinguished by whether and how they achieve time resolution—directly or indirectly. Indirect methods avoid the requirement for fast detection methods, either by detemiining relative rates from product yields or by transfonuing from the time axis to another coordinate, for example the distance or flow rate in flow tubes. Direct methods include (laser-) flash photolysis [27], pulse radiolysis [28]... 

Quack M and Thdne H J 1987 Absolute and relative rate coefficients in the IR-laser chemistry of bichromophoric fluorobutanes tests for inter- and intra-molecular selectivity Chem. Rhys. Lett. 135 487-94... 

Let us illustrate this with the example of the bromination of monosubstituted benzene derivatives. Observations on the product distributions and relative reaction rates compared with unsubstituted benzene led chemists to conceive the notion of inductive and resonance effects that made it possible to explain" the experimental observations. On an even more quantitative basis, linear free energy relationships of the form of the Hammett equation allowed the estimation of relative rates. It has to be emphasized that inductive and resonance effects were conceived, not from theoretical calculations, but as constructs to order observations. The explanation" is built on analogy, not on any theoretical method. 

Kinetic enolate- deprotonation of the most accessable proton (relative rates of deprotonation). Reaction done under essentially irreversible conditions. 

Table 1.2. Relative rate constants of some selected Diels-Alder reactions in water compared to organic solvents of different hydrogen bond donor capacities.

There are a few cases where the rate of one reaction relative to another is needed, but the absolute rate is not required. One such example is predicting the regioselectivity of reactions. Relative rates can be predicted from a ratio of Arrhenius equations if the relative activation energies are known. Reasonably accurate relative activation energies can often be computed with HF wave functions using moderate-size basis sets. 

TABLE 2.1 Relative rates of nitration in aqueous nitric acid ... 

Unfortunately, insufficient data make it impossible to know whether the activity coefficients of all aromatic compounds vary slightly, or whether certain compounds, or groups of compounds, show unusual behaviour. However, it seems that slight variations in relative rates might arise from these differences, and that comparisons of reactivity are less sound in relatively concentrated solutions. 

The phenomenon was established firmly by determining the rates of reaction in 68-3 % sulphuric acid and 61-05 % perchloric acid of a series of compounds which, from their behaviour in other reactions, and from predictions made using the additivity principle ( 9.2), might be expected to be very reactive in nitration. The second-order rate coefficients for nitration of these compounds, their rates relative to that of benzene and, where possible, an estimate of their expected relative rates are listed in table 2.6. 

TABLE 2.6 Second-order rate coefficients and relative rates for nitration at 2 -0 °C in 68- % sulphuric acid and 6i-o % perchloric acid ° ... 

Compound nitrated t5% aqueous sulpholan (K) Sulpho- lan (C) 15% aqueous nitromethane (K) Nitromethane (C) 61-05 % perchloric acid (K) 68-3% sulphuric acid (K) 68-3 % sulphuric acid (C) Estimated relative rates ... 

TABLE 4.1 Nitration of aromatic compounds relative rates at 25 °C... 

In all other cases the observed result will depend upon both the speed of mixing and the speed of nitration. The relative rate will be greater than unity by an amount peculiar to the conditions of the experiment. Again, if the alkylbenzene is sufficiently reactive to be nitrated upon encounter, whilst benzene is not, the relative rate will be greater than unity and, for the experimental conditions, will be a limiting upper value no matter what aromatic is used. 

Molar ratio of alkylbenzene to benzene No. of equivs. of aromatics in solution in which nitrating agent is consumed Products Relative rate... 

Relative rate meaning, here, simply the ratio of nitro-alkylbenzene to nitrobenzene, multiplied by the initial ratio of alkylbenzene to benzene. This is not precisely the same as the ratio of rate constants for nitration. ... 

It has been necessary to comment upon these various studies because Olah and his co-workers have suggested that whilst nitrations, like those with nitronium salts, which give a relative rate of reaction of toluene with respect to benzene not much greater than unity involve the nitronium ion as the electrophile, this is not so in other cases. It is important to consider these opinions closely. In the earlier of the two relevant papers it is agreed that since nitrations of toluene with nitronium tetrafluoroborate in sulpholan show no abnormal o -ratio there... 

Substituents in pyridinium salt Relative rates Isomer proportions (partial rate factors) i 0 p-ratio... 

The relative basicities of aromatic hydrocarbons, as represented by the equilibrium constants for their protonation in mixtures of hydrogen fluoride and boron trifluoride, have been measured. The effects of substituents upon these basicities resemble their effects upon the rates of electrophilic substitutions a linear relationship exists between the logarithms of the relative basicities and the logarithms of the relative rate constants for various substitutions, such as chlorination and... 

The heats of formation of Tt-complexes are small thus, — A//2soc for complexes of benzene and mesitylene with iodine in carbon tetrachloride are 5-5 and i2-o kj mol , respectively. Although substituent effects which increase the rates of electrophilic substitutions also increase the stabilities of the 7r-complexes, these effects are very much weaker in the latter circumstances than in the former the heats of formation just quoted should be compared with the relative rates of chlorination and bromination of benzene and mesitylene (i 3 o6 x 10 and i a-Sq x 10 , respectively, in acetic acid at 25 °C). 

The fact that the ratios of rates were much greater in chlorination than in nitration, prompted Dewar to suggest that the actual transition state was intermediate between the Wheland model and the isolated molecule model. He accommodated this variation in the relative rates within his discussion by treating yS as a variable whose value depended on the nature of the reaction. With the notation that y ) is the... 

Irrespective of the precision of these quantitative correlations, this approach is useful in emphasizing that relative rates depend on the nature of the reaction as well as of the aromatic compound. 

Streitwieser pointed out that the eorrelation whieh exists between relative rates of reaetion in deuterodeprotonation, nitration, and ehlorination, and equilibrium eonstants for protonation in hydrofluorie aeid amongst polynuelear hydroearbons (ef. 6.2.3) constitutes a relationship of the Hammett type. The standard reaetion is here the protonation equilibrium (for whieh p is unity by definition). For eon-venience he seleeted the i-position of naphthalene, rather than a position in benzene as the referenee position (for whieh o is zero by definition), and by this means was able to evaluate /) -values for the substitutions mentioned, and cr -values for positions in a number of hydroearbons. The p -values (for protonation equilibria, i for deuterodeprotonation, 0-47 for nitration, 0-26 and for ehlorination, 0-64) are taken to indieate how elosely the transition states of these reaetions resemble a cr-eomplex. 

Relative rates and isomer ratios for substitution in benzene and toluene ... 

Reaction Relative rate hffks Product distribution ... 

Nitrating system Relative rate Isomer proportions (%) Partial rate factors ... 

Ratio toluene- /-f-butylbenzene. The partial rate factors are based on the relative rates for toluene benzene of ref. i. 

If this electrostatic treatment of the substituent effect of poles is sound, the effect of a pole upon the Gibbs function of activation at a particular position should be inversely proportional to the effective dielectric constant, and the longer the methylene chain the more closely should the effective dielectric constant approach the dielectric constant of the medium. Surprisingly, competitive nitrations of phenpropyl trimethyl ammonium perchlorate and benzene in acetic anhydride and tri-fluoroacetic acid showed the relative rate not to decrease markedly with the dielectric constant of the solvent. It was suggested that the expected decrease in reactivity of the cation was obscured by the faster nitration of ion pairs. 

---