Organic Mechanisms. Xiaoping Sun

Equation 1.45, the change in enthalpy (ΔH) can be calculated as

(1.46)

At constant pressure (P), Equation 1.46 becomes

      According to the first law of thermodynamics, q_P = ΔU − w (heat).

Therefore,

(1.47)

The physical meaning of Equation 1.47 is that the enthalpy change in a process (including a chemical reaction) at constant pressure is equal to the heat evolved. Since most of the organic reactions are conducted at constant pressure, the reaction heat can be calculated on the basis of the enthalpy change for the reaction.

      Entropy (S) is considered as the degree of disorder. In thermodynamics, the infinitesimal change in entropy (dS) is defined as the reversible heat (dq_rev) divided by the absolute temperature (T), formulated as

      For a finite change in state,

      (1.48)

      Free energy (G) is defined as

      At constant temperature and pressure, the change in free energy (ΔG) can be calculated as

(1.49)

      1.5.2 Reversible and Irreversible Reactions

      In general, chemical reactions in thermodynamics can be classified as two types, reversible and irreversible reactions. An irreversible reaction is such a reaction that proceeds only in one direction. As a result, the reactant is converted to the product completely (100%) in the end of the reaction. In contrast, a reversible reaction is such a reaction that can proceed to both forward and backward directions. In other words, there is an interconversion between the reactants and the products in a reversible reaction. As a result, all the reactants and the products coexist in the end of the reaction, and the conversion is incomplete.

      The reversibility of a chemical reaction can be judged by the second law of thermodynamics. Originally, the second law is stated based on the entropy criterion as follows: A process (including a chemical reaction) is reversible if the universal entropy change (ΔS_UNIV) associated to the process is zero; and a process is irreversible if the universal entropy change (ΔS_UNIV) associated to the process is positive (greater than zero). ΔS_UNIV = ΔS + ΔS_SURR, the sum of the entropy change in the system (ΔS) and the entropy change in surroundings (ΔS_SURR).

      Since it is difficult to calculate the entropy change in surroundings (ΔS_SURR), very often the free energy criterion is used to judge reversibility for any processes that take place at constant temperature and pressure. By employing the free energy change (ΔG) in a system, the second law can be modified as: At constant temperature and pressure, a process (including a chemical reaction) is irreversible (spontaneous) if the free energy change (ΔG) of the process is negative (ΔG < 0), a process is reversible (at equilibrium) if the free energy change (ΔG) of the process is zero (ΔG = 0), and a process is nonspontaneous if the free energy change (ΔG) of the process is positive (ΔG > 0). The free energy criterion is widely used in organic chemistry because most of the organic reactions are conducted in open systems at constant temperature and pressure.

According to Equation 1.49, both enthalpy (ΔΗ) and entropy (ΔS) effects need to be considered when judging reversibility of a reaction using the free energy criterion. The spontaneity of a reaction is favored by a negative enthalpy (ΔΗ < 0, exothermic) or a positive entropy (ΔS > 0, increase in disorder), while a positive enthalpy (ΔΗ > 0, endothermic) or a negative entropy (ΔS < 0, decrease in disorder) works against a reaction. Variations in temperature (T) can change the extent of the entropy effect (TΔS), and therefore they affect the reversibility accordingly. High temperatures favor reactions with a positive entropy change (ΔS > 0), and low temperatures favor reactions with a negative entropy change (ΔS < 0). The effects of enthalpy and entropy on reversibility of the chemical reactions conducted at constant temperature and pressure are summarized in Figure 1.3.

      1.5.3 Chemical Equilibrium

Many organic reactions are reversible, namely that the conversion of the reactant to the product is incomplete. When the rate of the forward process is equal to the rate of the backward process for a reversible reaction, the concentrations of all the reactants and products cease to change, and the reaction has reached a dynamic equilibrium.

FIGURE 1.3 The effects of enthalpy and entropy on reversibility of the chemical reactions conducted at constant temperature and pressure.

      While the rate constant of a reaction serves as the quantitative measure of how fast the reaction proceeds (Section 1.4), the equilibrium constant (K) is used as a quantitative measure for the extent of a reversible reaction, which is defined as follows:

(1.50)

Equation 1.50 represents a balanced chemical equation for a reversible reaction (concerted or stepwise). A, B, C, and D represent chemical formulas of different substances (reactants or products). a, b, c, and d represent the corresponding stoichiometric coefficients. [A], [B], [C], and [D] represent the molar concentrations of the species A, B, C, and D, respectively. At a certain given temperature, the K value remains constant, and it is independent of the concentrations of any reactants or products.

      The equilibrium constant expression indicates that having one of the reactants (such as B) in excess can increase the percentage of conversion of the other reactant (such as A) to the products. On the other hand, removal of one product (decrease in its concentration) from the reaction system can also increase the percentage of the conversion of the reactants to the products. In the case that one reactant is in very large