Second Law of Thermodynamics: Entropy

The second law of thermodynamics states that the universe (i.e. all systems) tend to the greatest degree of randomization. This concept is defined by the term entropy, S.

S = klnW

where k = Boltzmann constant (the gas constant, R, divided by Avagadros\' number) and W = the number of substrates. For an isothermal reversible reaction the change in entropy can be reduced to the term:

ΔS = ΔH/T

Whereas, enthalpy is a term whose value is largely dependent upon electronic internal energies, entropy values are dependent upon translational, vibrational and rotational internal energies. Entropy also differs from enthalpy in that the values of enthalpy that indicate favored reactions are negative and the values of entropy are positive. Together the terms enthalpy and entropy demonstrate that a system tends toward the highest entropy and the lowest enthalpy.

In order to effectively evaluate the course (spontaneity or lack there of) of a reaction and taking into account both the first and second laws of thermodynamics, Josiah Gibbs defined the term, free energy which is defined as:

ΔG = ΔH – TΔS

Free energy is a valuable concept because it allows one to determine whether a reaction will proceed and allows one to calculate the equilibrium constant of the reaction which defines the extent to which a reaction can proceed. The discussion above indicated that a decrease in energy, a negative ΔH, and an increase in entropy, a positive ΔS, are indicative of favorable reactions. These terms would, therefore, make ΔG a negative value. Reactions with negative ΔG values are termed exergonic and those with positive ΔG values endergonic. However, when a system is at equilibrium:

ΔG = 0

Gibbs\' free energy calculations allows one to determine whether a given reaction will be thermodynamically favorable. The sign of ΔG states that a reaction as written or its reverse process is the favorable step. If ΔG is negative then the forward reaction is favored and visa versa for ΔG values that are calculated to be positive.