Advanced Topic 419 of 1102 Thermodynamics & Energetics
Residual Entropy
Nonzero entropy at 0 K in crystals with disordered orientations, as in carbon monoxide and ice.
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In-depth explanation of Residual Entropy
Residual entropy is the entropy that remains in a substance at absolute zero because of disorder frozen into its crystal structure. It arises when a molecule or ion can adopt several orientations of nearly equal energy, so the crystal cannot settle into a single arrangement even at 0 kelvin. This does not contradict the third law, which applies to perfect crystals, but it shows that real crystals may keep disorder. Residual entropy is measured by comparing the entropy from calorimetric data with the value obtained from spectroscopic or statistical methods. Carbon monoxide and ice are classic examples.
Going deeper: Residual Entropy
Key ideas: Estimate it using S equals k ln W with W the number of equally likely frozen arrangements. For carbon monoxide, with two orientations per molecule, S per mole is R ln 2, about 5.8 J per mole kelvin. For ice, Pauling estimated about R ln 3/2, or 3.4 J per mole kelvin.
Common mistakes and connections: It does not violate the third law because the third law refers to perfect crystals. Do not mix up residual entropy with entropy at low but nonzero temperature. The existence of such disorder shows how statistical methods and calorimetry can check each other.
Visualization of Residual Entropy
Residual entropy at 0 K from frozen-in orientational disorder: CO and N2O have about 4.6 J/mol/K, while ice shows 3.4 J/mol/K; perfect crystals like Ar have none. The interactive lesson shows this as a live animation or chart.
Worked example and use case
Ice has a residual entropy of about 3.4 joules per mole per kelvin, arising from the random arrangement of hydrogen atoms among the possible water molecule orientations.
Frequently asked questions about Residual Entropy
What is Residual Entropy?
Nonzero entropy at 0 K in crystals with disordered orientations, as in carbon monoxide and ice.
Is Residual Entropy a beginner, intermediate or advanced topic?
Residual Entropy is a advanced topic in Thermodynamics & Energetics. It builds on beginner and intermediate topics, so review those first if needed.
What should I learn before Residual Entropy?
Study these earlier topics in Thermodynamics & Energetics first: Gibbs-Helmholtz Equation, Van't Hoff Equation, Maxwell Relations.
What comes after Residual Entropy?
It is the last topic in Thermodynamics & Energetics. Explore the other areas for more chemistry.
Can I practise Residual Entropy with quizzes?
Yes. The interactive lesson includes a self-check question on Residual Entropy, and the Thermodynamics & Energetics quiz draws on every topic in this area.
Where Residual Entropy fits in Thermodynamics & Energetics
Residual Entropy is topic 91 of 91 in Thermodynamics & Energetics.