Entropy and Molecular Disorder

To decide whether we need to worry about ΔS₀ with regard to any particular reaction, we have to have some idea what physical meaning entropy has. To be very detailed about this subject is beyond the scope of this book, but you should try to understand the physical basis of entropy, because if you do, then you will be able to predict at least qualitatively whether ΔH₀ will be about the same or very different from ΔG₀. Essentially, the entropy of a chemical system is a measure of its molecular disorder or randomness. Other things being the same, the more random the system is, the more favorable the system is.

Different kinds of molecules have different degrees of translational, vibrational, and rotational freedom and, hence, different average degrees of molecular disorder or randomness. Now, if for a chemical reaction the degree of molecular disorder is different for the products than for the reactants, there will be a change in entropy and ΔS0≠0.

A spectacular example of the effect of molecular disorder in contributing to the difference between ΔH₀ and ΔG₀ is afforded by the formation of liquid nonane, C9H20, from solid carbon and hydrogen gas at 25^o:

with ΔHo=−54.7kcal and ΔSo=5.0kcal.

Equations 4.5.4 and 4.5.5 can be rearranged to calculate ΔS₀ and Keq from ΔH₀ and ΔG₀

and

These ΔH₀, ΔS₀, and Keq values can be compared to those for H2+12O2⟶H2O, for which ΔH₀ is −57kcal, ΔS₀ is 8.6e.u., and Keq is 10⁴⁰. Obviously, there is something unfavorable about the entropy change from carbon and hydrogen to nonane. The important thing is that there is a great difference in the constraints on the atoms on each side of the equation. In particular, hydrogen molecules in the gaseous state have great translational freedom and a high degree of disorder, the greater part of which is lost when the hydrogen atoms become attached to a chain of carbons. This makes for a large negative ΔS₀, which corresponds to a decrease in KeqKeq. The differences in constraints of the carbons are less important. Solid carbon has an ordered, rigid structure with little freedom of motion of the individual carbon atoms. These carbons are less constrained in nonane, and this would tend to make ΔS0 more positive and ΔG0ΔG0 more negative, corresponding to an increase in Keq (Equations 4.5.4 and 4.5.5). However, this is a small effect on ΔS0 compared to the enormous difference in the degree of disorder of hydrogen between hydrogen gas and hydrogen bound to carbon in nonane.

Negative entropy effects usually are observed in ring-closure reactions such as the formation of cyclohexane from 1-hexene, which occur with substantial loss of rotational freedom (disorder) about the C−C bonds