Thermodynamic Requirements For Reaction - Mechanisms and Methods of Determining Them - Introduction - March's Advanced Organic Chemistry: Reactions, Mechanisms, and Structure, 7th Edition (2013)

March's Advanced Organic Chemistry: Reactions, Mechanisms, and Structure, 7th Edition (2013)

Part I. Introduction

Chapter 6. Mechanisms and Methods of Determining Them

6.C. Thermodynamic Requirements For Reaction

In order for a reaction to take place spontaneously, the free energy of the products must be lower than the free energy of the reactants (i.e., ΔG must be negative). Reactions can go the other way, of course, but only if free energy is added. Like water on the surface of the earth, which naturally flows only downhill and never uphill, molecules seek the lowest possible potential energy. Free energy is made up of two components, enthalpy (H) and entropy (S). These quantities are related by the equation

equation

The enthalpy change in a reaction is essentially the difference in bond energies (including resonance, strain,3 and solvation energies) between the reactants and the products. The enthalpy change can be calculated by totaling the bond energies of all the bonds broken, subtracting from this the total of the bond energies of all the bonds formed, and adding any changes in resonance, strain, or solvation energies. Entropy changes are quite different, and refer to the disorder or randomness of the system. The lower the order in a system, the greater the entropy. The preferred conditions in Nature are low enthalpy and high entropy, and in reacting systems, enthalpy spontaneously decreases while entropy spontaneously increases.

For many reactions, entropy effects are small and it is the enthalpy that mainly determines whether the reaction can take place spontaneously. However, in certain processes entropy is important and can sometimes dominate enthalpy. Several examples will be discussed.

1. In general, liquids have lower entropies than gases, since the molecules of gas have much more freedom and randomness. Solids, of course, have still lower entropies. Any reaction in which the reactants are all liquids and one or more of the products is a gas is therefore thermodynamically favored by the increased entropy; the equilibrium constant for that reaction will be higher than it would otherwise be. Similarly, the entropy of a gaseous substance is higher than that of the same substance dissolved in a solvent.

2. In a reaction in which the number of product molecules is equal to the number of reactant molecules (e.g., A + B → C + D), entropy effects are usually small, but if the number of molecules is increased, (e.g., A → B + C), there is a gain in entropy because more arrangements in space are possible when more molecules are present. Reactions in which a molecule is cleaved into two or more parts are likely to be thermodynamically favored by the entropy factor. Conversely, reactions in which the number of product molecules is less than the number of reactant molecules show entropy decreases, and in such cases there must be a sizable decrease in enthalpy to overcome the unfavorable entropy change.

3. Although reactions in which molecules are cleaved into two or more pieces have favorable entropy effects, many potential cleavages do not take place because of large increases in enthalpy.4 An example is cleavage of ethane into two methyl radicals. In this case, a bond of ~79 kcal mol−1 (330 kJ mol−1) is broken, and no new bond is formed to compensate for this enthalpy increase. However, ethane can be cleaved at very high temperatures, which illustrates the principle that entropy becomes more important as the temperature increases, as is obvious from the equation ΔG = ΔHTΔS. The enthalpy term is independent of temperature, while the entropy term is directly proportional to the absolute temperature.

4. An acyclic molecule has more entropy than a similar cyclic molecule because there are more conformations (cf. hexane and cyclohexane). Ring opening therefore correlates with a gain in entropy and ring closing a loss.