Determination of loads applied perpendicularly to the outer boundary of a ring using coefficients of influence

A procedure is explained to determined the amount of several pairs of diametrical loads applied to the outside boundary of a ring when stresses at selected points of the inside or outside boundaries are known. Coefficients of influence are used, following an approach similar to the one presented in a previous paper. Examples of application are given and the possible increase in precision is shown when the number of points of measurements is larger than the number of loads to be determined.     

Kinetics and mechanism of hydration of o-thioquinone methide in aqueous solution. Rate-determining protonation of sulfur

o-Thioquinone methide, 2, was generated in aqueous solution by flash photolysis of benzothiete, 1, and rates of hydration of this quinone methide to o-mercaptobenzyl alcohol, 3, were measured in perchloric acid solutions, using H2O and D2O as the solvent, and also in acetic acid and tris(hydroxymethyl)methylammonium ion buffers, using H2O as the solvent. The rate profiles constructed from these data show hydronium-ion-catalyzed and uncatalyzed hydration reaction regions, just like the rate profiles based on literature data for hydration of the oxygen analogue, o-quinone methide, of the presently examined substrate. Solvent isotope effects on hydronium-ion catalysis of hydration for the two substrates, however, are quite different: k(H)/k(D) = 0.42 for the oxygen quinone methide, whereas k(H)/k(D) = 1.66 for the sulfur substrate. The inverse nature (k(H)/k(D) < 1) of the isotope effect in the oxygen system indicates that this reaction occurs by a preequilibrium proton-transfer reaction mechanism, with protonation of the substrate on its oxygen atom being fast and reversible and capture of the benzyl-type carbocationic intermediate so formed being rate-determining. The normal direction (k(H)/k(D) > 1) of the isotope effect in the sulfur system, on the other hand, suggests that protonation of the substrate on its sulfur atom is in this case rate-determining, with carbocation capture a fast following step. A semiquantitative argument supporting this hypothesis is presented.