Organic Mechanisms. Xiaoping Sun

if entropy of the reaction ΔS is small and negligible) (Fig. 1.4b), the energy of the transition state is most similar to that of the product. Therefore, the structure of the transition state resembles the product. Such a transition state is called late transition state.

Figure 1.5 shows examples of exothermic (ΔH < 0) and endothermic (ΔH > 0) S_N2 reactions (concerted). Usually, the entropies of simple S_N2 reactions are small relative to the reaction enthalpies, and they are negligible. According to the Hammond postulate, the exothermic S_N2 reaction has an early transition state whose structure resembles the reactants (Fig. 1.5a), while the endothermic S_N2 reaction has a late transition state whose structure resembles the products (Fig. 1.5b). Although a simple S_N2 reaction has a small entropy, the entropy of its transition state (ΔS^‡) possesses a relatively large negative value. This is because in the transition state two reactant molecules combine loosely resulting in decrease in entropy. For the exothermic S_N2 reaction (Fig. 1.5a), since the reaction has an early transition state which resembles the reactants, both breaking of the old C─I bond and formation of the new C─C bond in the transition state have only proceeded to a small extent. This gives rise to a small ΔΗ^‡ value. Therefore, the major contributor to the activation energy is the entropy effect (E_a ≈ −TΔS^‡). On the other hand, the endothermic S_N2 reaction (Fig. 1.5b) has a late transition state which resembles the products. Breaking of the old C─Cl bond and formation of the new C─I bond in the transition state are close to completion (ΔΗ^‡ ≈ ΔH). As a result, both enthalpy (ΔΗ^‡) and entropy (ΔS^‡) have substantial contributions to the activation energy (E_a = ΔΗ^‡ − TΔS^‡). Their combination makes the E_a value greater than the reaction enthalpy (ΔH).

FIGURE 1.5 The S_N2 reactions that proceed via (a) an early transition state and (b) a late transition state.

      

      1.6.3 The Bell–Evans–Polanyi Principle

      For similar concerted reactions that take place at a certain given temperature, the activation energy (E_a) can be directly correlated to the reaction enthalpy (ΔH) as follows (the Bell–Evans–Polanyi principle):

(1.55)

      where c₁ and c₂ are positive constants.

Equation 1.55 is applicable to both endothermic and exothermic reactions and can be employed to analyze the relative activation energies for similar reactions based on their reaction enthalpies. For endothermic reactions (ΔH > 0, Fig. 1.4b), the greater the energy gap (ΔH) between the reactant and product (the more endothermic), the higher is the activation energy E_a. For exothermic reactions (ΔH < 0, Fig. 1.4a), the greater the energy gap (the absolute value of ΔH) between the reactant and product (the more exothermic), the smaller is the activation energy E_a. The greater energy gap in an exothermic reaction makes the c₁ΔH more negative. As a result, the E_a becomes smaller. Using this principle, one can directly relate the kinetics (activation energy) to the thermodynamics (enthalpy of the reaction) for similar chemical reactions.

1.7 ELECTRONIC EFFECTS AND HAMMETT EQUATION

      1.7.1 Electronic Effects of Substituents

Substituents on aromatic (phenyl) rings can increase or decrease the electron density in the ring by donating or withdrawing electrons. This alters rates and/or equilibrium constants for the reactions occurring in the ring and in the side group attached to the ring. Such electronic effects of substituents can be quantitatively defined on the basis of their influence on the acidity (dissociation constant) of para‐ or meta‐substituted benzoic acid (XC₆H₄COOH) relative to benzoic acid (C₆H₅COOH) (Eq. 1.56):

(1.56)

      In Equation 1.56, K_A and K_H are the acid dissociation constants of XC₆H₄COOH and C₆H₅COOH, respectively. lg is the common logarithm (10‐based logarithm). The σ value defined in the equation is called Hammett substituent constant for a given substituent –X at para‐ or meta‐position. The para‐ or meta‐substituted benzoic acids (XC₆H₄COOH) with different –X groups are in general commercially available or easy to synthesize. The pK_A (–lgK_A) value for each XC₆H₄COOH is numerically equal to pH of a solution containing equalmolar concentrations of the acid and the sodium salt of the conjugate base and can be readily determined experimentally. Therefore, the σ constants for various substituents can be obtained readily [1].

The electron‐donating and electron‐withdrawing effects of various substituents originate from combination of inductive and conjugation effects. In general, an electron‐withdrawing group (EWG) on the phenyl ring of XC₆H₄COO⁻, such as –NO₂ (nitro), –C(O)R (acyl), –SO₃H (sulfonic acid), and –CN (cyanide), lowers the electron density in the ring facilitating delocalization of the negative charge of the carboxylate to the ring. This stabilizes the XC₆H₄COO⁻ anion, resulting in an increase in K_A relative to K_H. Therefore, the σ constants for EWGs are usually positive (σ > 0 for EWGs). On the other hand, an electron‐donating group (EDG) on the phenyl ring of XC₆H₄COO⁻, such as –R (alkyl), –OH (hydroxyl), –OR (alkoxy), and –NH₂ (amino), enhances the electron density in the ring to disfavor the delocalization of the negative charge of the carboxylate. This destabilizes the XC₆H₄COO⁻ anion, giving rise to decrease in K_A relative to K_H. Therefore, the σ constants for EDGs are usually negative (σ < 0 for EDGs). The substituents on the ortho‐position of the phenyl rings often produce steric hindrance on the side group next to them. Therefore, the electronic effects of the ortho‐substituents are usually not considered.

      For a given substituent (EWG or EDG), the extent of its electronic effects on the side group (–COO⁻) of XC₆H₄COO⁻ is different when the substituent is placed on the para‐position and on the meta‐position.