Consider the entropy of a pure, perfectly crystalline solid possessing no kinetic energy (that is, at a temperature of absolute zero, 0 K). This system may be described by a single microstate, as its purity, perfect crystallinity and complete lack of motion means there is but one possible location for each identical molecule comprising the crystal (W = 1). Therefore, the entropy of this system is zero:
This limiting condition for a system’s entropy represents the third law of thermodynamics: the entropy of a pure, perfect crystalline substance at 0 K is zero.
Starting with zero entropy at absolute zero, it is possible to make careful calorimetric measurements () to determine the temperature dependence of a substance’s entropy and to derive absolute entropy values at higher temperatures. (Note that, unlike enthalpy values, the third law of thermodynamics identifies a zero point for entropy. Therefore, there is no need for formation enthalpies, and every substance, including elements in their most stable states, has an absolute entropy.)
Standard entropy (S°) values are the absolute entropies per mole of substance at a pressure of 1 bar or a concentration of 1 M. The standard entropy change (ΔrS°) for any chemical process may be computed from the standard entropy of its reactant and product species:
The thermodynamics table in the appendix lists standard entropies of select compounds at 298.15 K.
Suppose an exothermic chemical reaction takes place at constant atmospheric pressure. There is heat transfer of energy from the reaction system to the surroundings, qsurr = –qsys. The heat transfer for the system is the enthalpy change of the reaction because, at constant pressure, ΔrH° = q. Because the energy transfer to the surroundings is reversible, the entropy change for the surroundings can also be expressed as:
The same reasoning applies to an endothermic reaction: qsys and qsurr are equal but have opposite sign.
Also, for a chemical reaction system, ΔSsys = ΔrS° (the standard entropy change for the reaction). Hence, ΔSuniv can be expressed as:
The convenience of this equation is that, for a given reaction, ΔSuniv can be calculated from thermodynamics data for the system only. That is, from data found in the Appendix.