D20.1 Third Law of Thermodynamics

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:

S = kB·ln(W) = kB·ln(1) = 0

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 ( \dfrac{q_\text{rev}}{\text{T}} ) 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:

ΔrS° = ∑S°(products) − ∑S°(reactants)

The thermodynamics table in the appendix lists standard entropies of select compounds at 298.15 K.

Exercise: Standard Entropy Change

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Chemistry 109 Fall 2021 by John Moore, Jia Zhou, and Etienne Garand is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.