it is difficult to calculate the entropy change in surroundings (ΔSSURR), 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:
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 excess, the conversion of the other reactant (limiting reagent) can be essentially complete (~100%). Therefore, a reversible reaction has been essentially converted to an irreversible reaction.
In organic chemistry, the strategy of using a certain reactant in excess is employed for many reversible reactions to increase the product yields. For example, most of the acid–catalyzed esterification reactions (Reaction 1.51) have the equilibrium constants K ~ 5–10.
When the carboxylic acid (RCO2H) and the alcohol (R′OH) are used in 1:1 molar ratio, the conversion of the reactants to the products is 70–75%. If R′OH is used in 10‐folds of excess, the conversion of RCO2H (limiting reactant) to the ester product will be ~99%. In this case, the reversible reaction has been almost transformed into an irreversible reaction. For some esterification reactions, the essential quantitative conversion of the reactants to the ester product can also be obtained by removal of water from the reaction system once it is formed.
The relationship between the equilibrium constant (K) and standard free energy (ΔG°) is formulated as
Substituting Equation 1.49 for Equation 1.52 leads to
Therefore,
Equation 1.53 describes the dependence of the equilibrium constant on temperature. Very often, for an exothermic reaction, the standard enthalpy ΔH° < 0 (−ΔH°/R is positive). The equilibrium constant (K) decreases as a function of the temperature (T). On the other hand, an endothermic reaction often has ΔH° > 0 (−ΔH°/R is negative). The equilibrium constant (K) increases as a function of the temperature (T). Therefore, in many cases (exceptions exist) high temperatures facilitate endothermic reactions and low temperatures facilitate exothermic reactions.
Equation 1.53 also shows that plot of lnK versus 1/T defines a straight line, from which both the standard enthalpy (ΔH°) and standard entropy (ΔS°) can be obtained from the slope and intercept, respectively, for an unknown reaction.
1.6 THE TRANSITION STATE
1.6.1 The Transition State and Activation Energy
The transition state is the
