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      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.