Ring-chain equilibrium constants

Ring-Chain and Ring-Ring Equilibrium. Constants... 

When there are simple rings of several sizes, each size of ring may be related to the chain distribution by an equilibrium constant of the form of Eq. (b). Likewise, the rings may be related to each other by a ring-ring equilibrium constant, of the usual form... 

The best-known equation of the type mentioned is, of course, Hammett s equation. It correlates, with considerable precision, rate and equilibrium constants for a large number of reactions occurring in the side chains of m- and p-substituted aromatic compounds, but fails badly for electrophilic substitution into the aromatic ring (except at wi-positions) and for certain reactions in side chains in which there is considerable mesomeric interaction between the side chain and the ring during the course of reaction. This failure arises because Hammett s original model reaction (the ionization of substituted benzoic acids) does not take account of the direct resonance interactions between a substituent and the site of reaction. This sort of interaction in the electrophilic substitutions of anisole is depicted in the following resonance structures, which show the transition state to be stabilized by direct resonance with the substituent ... 

An interesting ring-chain tautomerism between 2-azidothiazole (328) and thiazolotetrazole (328a) has been reported (597, 618, 619), the 328 structure predominating (Scheme 190). The solvent polarity and basicity influences this equilibrium constant significantly (1592). 

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. 

In solution, the aminoketone 29a is in equilibrium with the heterocyclic carbinolamine 29b. The equilibrium constant varies with the substituents the various compounds of the series are, as far as is known, monomorphic, some giving crystals having the molecules in open-chain form, others giving crystals with ring-closed molecules (75). 

The most powerful method currently available for the quantitative determination of ring-chain equilibrium constants is H-NMR spectroscopy. Often, two pairs of indicator signals of both tautomeric forms have been used, thereljy increasing the accuracy of equilibrium-constant determination. For structural analysis of the tautomers and quantitative measure-... 

Ring-chain equilibrium constants for 7A 7B have been measured by H-NMR as a function of pressure (1-2000 bar) to obtain the volumes of the intramolecular cyclization reaction and to compare them with those of the corresponding intermolecular analog [87JCS(P2)1477]. 

Ring-chain equilibrium constants Ky have been determined by using IR and H-NMR spectroscopy [93JCS(P2)635] for a series of 2-phenylacetylbenzoic (9) and benzyl-2-carboxylic (10) acids substituted in the phenyl group. A good linear correlation between Ky and the constants a or ct for the substituents X was obtained. As shown in Table I, for acids... 

Correlation Parameters of Ring-Chain Equilibrium Constants of 2-Phenylacetylbenzoic (9) AND Benzil-2 carboxylic (10) Acids"... 

UKZ746) for 2-hydroxy-2-methyl-l,4-dioxane. The ring-chain equilibrium constants for the A -aroylmethyl-A/-(2-hydroxyethyl)-/V,/V-dimethyl-ammonium (aroylcholinium) salts 30A 30B (Y = NMc2, R = XQH4)... 

The H-NMR spectra were recorded at different temperatures to determine the ring-chain equilibrium constants in solutions of 2-N- 2-hydroxyethyl)amino-5-methyl-l,4-benzoquinones 33 (93M1053). Greater... 

Ring-Chain Equilibrium Constants" for 2-(2-Hydroxyethoxy)benzaldehydes (37A 37B) in Various Solvents... 

Ring-Chain Equilibrium Constants for 2-Hydroxy Indolines 58 AND 59 ... 

The only example of kinetic considerations dealing with the ring-opening polymerization was published by Ballard and Bamford. The authors examined polymerization of N-carboxy-amino acid anhydrides proceeding onto polysacrosine. The authors assumed the equilibrium between adsorbed molecules of monomer, E, and free monomer, M, described by equilibrium constant, K, independent of the position in the template chain ... 

Acid-base equilibrium constants have been used to calculate the a-values of azoles as substituents on an aromatic ring or on an aliphatic chain. An example of this last case is the determination of ct, values of 1- (acetic acids 740,741, and 721 (Table 11-5) (82KGS264). 

The molar cyclization equilibrium constants, Kx, of PDMS are measured. Using the Jacobson and Stockmayer equilibrium theory of macrocyclization, the dimensions of PDMS chains with 40-80 chemical bonds in the bulk polymer at 383 K are deduced. Dilution effects in the PDMS systems are contrasted with predictions of the Jacobson-Stockmayer theory, and the experimental molar cyclization equilibrium constants of the smallest siloxane rings are discussed in terms of the statistical properties of the corresponding oligomeric chains using tire RIS model of PDMS of Flory, Crescemi, and Mark [S 116]. 

More quantitative chemical evidence for random coil configuration comes from cyclization equilibria in chain molecules (49). According to the random coil model there must be a very definite relationship among the concentrations of x-mer rings in an equilibrated system, since the cyclization equilibrium constant Kx should depend on configurational entropy and therefore on equilibrium chain and ring dimensions. Values of /Af deduced from experimental values on Kx for polydimethylsiloxane, both in bulk and in concentrated solution, agree very well with unperturbed dimensions deduced from dilute solution measurements(49). 

A ring-chain tautomeric equilibrium between the pyranopyrandione (254) and the 4-pyranonecarboxylic acid (255 equation 9) in CDC13 solution has been investigated by H NMR spectroscopy (73AC(R)29l). The equilibrium constant Ki was calculated as 1.7 at 298 K and AH° for the equilibrium reaction as 16.2 kJ mol-1. 

Ring-Chain Equilibrium Constants in Methyl-Terminated... 

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