Reactions First-Order in Substrate

The concentration of the chiral auxiliary Z wiU not influence the relative rate, which is expressed as follows. d[R]/dt 

Equation 2.1 simplifies into Equation 2.2 by elimination of time t and taking r/ S Kel s (stereoselectivity factor). 

Integration of Equation 2.2 gives Equation 2.3 where [J q] and [Sq] are defined as the initial concentrations of the two enantiomers. This general equation characterizes homocompetitive reactions carried out on two different substrates. 

The reaction time t was classically used as the parameter to discuss the course of a KR [6-8, 19]. Conversion extent C gives equations that are easier to handle, especially if taken with values lying between 0 (initial state) and 1 (full transformation) [20, 21]. Conversion C is denoted by C= 1-([R]- -[S])/Xq, where Xq is the initial concentration of the racemic mixture. Enantiomeric excess of the remaining starting material (ee jj ) is defined as follows. 

By using the values from Equation 2.5, Equation 2.3 gives the stereoselectivity factor s that may be transformed into Equation 2.6. 

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Catalyst] = [substrate] = 1.00 X 10 3 M. b Second-order rate constants (reactions first-order in substrate and first-order in catalyst). c First-order, sec.-1 (substrate only) d SA2 = salicylate anion. Tiron"4 = 3,5-disulfopyrocatechol anion. f HQS 2 = 5-sulfo-8-quinolinol anion. 0 SSA 3 = 5-sulfo-8-hydroxyquinoline anion. 

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