Equilibrium constants ring formation

In this mechanism, a complexation of the electrophile with the 7t-electron system of the aromatic ring is the first step. This species, called the 7t-complex, m or ms not be involved directly in the substitution mechanism. 7t-Complex formation is, in general, rapidly reversible, and in many cases the equilibrium constant is small. The 7t-complex is a donor-acceptor type complex, with the n electrons of the aromatic ring donating electron density to the electrophile. No position selectivity is associated with the 7t-complex. 

Table 2 Rate constants, equilibrium constants, and estimated Marcus intrinsic barriers for the formation and reaction of ring-substituted l-phenylethyl carbocations X-[6+] (Scheme 8)°... 

Fig. 5 Logarithmic plots of rate-equilibrium data for the formation and reaction of ring-substituted 1-phenylethyl carbocations X-[6+] in 50/50 (v/v) trifluoroethanol/water at 25°C (data from Table 2). Correlation of first-order rate constants hoh for the addition of water to X-[6+] (Y) and second-order rate constants ( h)so1v for the microscopic reverse specific-acid-catalyzed cleavage of X-[6]-OH to form X-[6+] ( ) with the equilibrium constants KR for nucleophilic addition of water to X-[6+]. Correlation of first-order rate constants kp for deprotonation of X-[6+] ( ) and second-order rate constants ( hW for the microscopic reverse protonation of X-[7] by hydronium ion ( ) with the equilibrium constants Xaik for deprotonation of X-[6+]. The points at which equal rate constants are observed for reaction in the forward and reverse directions (log ATeq = 0) are indicated by arrows.

Table 5. Rate and equilibrium constants for the formation and reaction of cyclic benzylic carbocations [18 + ] and [20+ ] and analogous ring-substituted 1-phenylethyl carbocations (Scheme 15)°... 

Equilibrium constants for some related complexes are given in Table XV (170). Chromotropic acid forms the most stable complexes, presumably with the formation of a strain-free 6-membered ring. 

An important source of experimental and theoretical studies of equilibria in ring formation is represented by the field of so-called macrocyclisation equilibria (Flory, 1969). Interest in this field appears to have been restricted so far to chemists conventionally labelled as polymer chemists. Experimental evidence of cyclic oligomer populations of ring-chain equilibrates such as those obtained in polysiloxanes (Brown and Slusarczuk, 1965) may be delated to the statistical conformation of the corresponding open-chain molecules (Jacobson and Stockmayer, 1950 Flory, 1969). In these studies experimental results are expressed in terms of molar cyclisation equilibrium constants Kx (14) related to the x-meric cyclic species Mx in equilibrium with the... 

Combining (18) and (19) one obtains (20) which shows that the molar cyclisation equilibrium constant Kx related to the cyclic x-mer coincides with the equilibrium EM for the formation of the same ring from the corresponding open-chain x-meric species. 

The equilibria involving 74 or 75 induce the formation and breaking of a PO bond and the closure and opening of one of the rings (Scheme 12). The equilibrium constants have been determined152,153 and correspond to AG = 23.8 and 24kcal mol 1, respectively. 

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