Organic Mechanisms. Xiaoping Sun

Organic Mechanisms - Xiaoping Sun


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      (1.35)equation

      On the basis of the stoichiometry for Reaction 1.28, the initial concentration of the reactant X can be formulated as

equation

      Therefore,

      (1.36)equation

      Equations show the dependence of concentrations of all the substances in Reaction 1.28 on time [2].

      1.4.3 Rate‐Laws for Stepwise Reactions

      Since Z is produced only from the k2 step which is a unimolecular process, the rate equation for Z is first order in Y.

      The steady‐state assumption is applied to the intermediate Y, and its rate equation is written as follows:

      where kobs = k1k2/(k−1 + k2) is the observed rate constant.

equation

      In this case, the first step of Reaction 1.40 is the rate‐determining step and actually irreversible.

      If k2k−1 (the intermediate Y is converted to the product Z much more slowly than going back to the reactant X), there is a fast preequilibrium between the reactant X and the intermediate Y before the product Z is formed. In this case, the Equation 1.44 can be simplified to

equation

      where Keq = (k1/k−1) is the equilibrium constant for the fast preequilibrium between X and Y (Keq = [Y]/[X]). Therefore, r = k2[Y], and the second k2 step is the rate‐determining step. Since the fast preequilibrium between X and Y is established prior to the formation of the product, the steady‐state assumption is not necessary if k2k−1.

      If the values of k2 and k−1 are comparable, the full steady‐state assumption is needed to establish the rate equation as shown in Equation 1.44.

      1.5.1 Enthalpy, Entropy, and Free Energy

      Enthalpy (H), entropy (S), and free energy (G) are all thermodynamic state functions. Enthalpy (H) is defined as the sum of internal energy (U) and the product of pressure (P) and volume (V), formulated as


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