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Related Concept Videos

Third Law of Thermodynamics02:38

Third Law of Thermodynamics

A pure, perfectly crystalline solid possessing no kinetic energy (that is, at a temperature of absolute zero, 0 K) 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 atom or molecule comprising the crystal (W = 1). According to the Boltzmann equation, the entropy of this system is zero.
Entropy and the Second Law of Thermodynamics01:20

Entropy and the Second Law of Thermodynamics

The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
The relation  between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...
Entropy and the Second Law of Thermodynamics01:26

Entropy and the Second Law of Thermodynamics

Consider an isolated system in which a hot object is placed in contact with a cold one. This is an irreversible process that eventually leads both objects to reach the same equilibrium temperature. It is crucial to note that the constituents of any substance exhibit increased disorder at higher temperatures. As a cold substance absorbs heat, its constituents become more disordered. The energy transfer from a hotter object to a cooler one increases the system's disorder or randomness. This...
Entropy02:39

Entropy

Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
Entropy01:18

Entropy

The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
Standard Entropy Change for a Reaction03:00

Standard Entropy Change for a Reaction

Entropy is a state function, so the standard entropy change for a chemical reaction (ΔS°rxn) can be calculated from the difference in standard entropy between the products and the reactants.

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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
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Published on: April 8, 2020

Systematic Molecularity-Dependent Entropy Errors in Continuum/RRHO Solution Thermochemistry: Origin and Correction.

Aida Rebollar-Zepeda1, Mirzam Carreon-Gonzalez1, Leonardo Muñoz-Rugeles2

  • 1Departamento de Física y Química Teórica, Facultad de Química, Universidad Nacional Autónoma de México, México City 04510, Mexico.

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|July 1, 2026
PubMed
Summary

Continuum solvation models can lead to inconsistent reaction free energies due to artificial entropy penalties for molecularity changes. Applying condensed-phase corrections resolves this issue for association and activation processes.

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Published on: June 8, 2022

Area of Science:

  • Computational Chemistry
  • Physical Chemistry
  • Chemical Thermodynamics

Background:

  • Continuum solvation models accurately predict solvation free energies but may not ensure thermodynamic consistency for reaction free energies.
  • Common workflows combine continuum solvation with gas-phase rigid rotor harmonic oscillator (RRHO) thermochemical corrections.
  • Molecularity-changing processes (e.g., association, clustering) are particularly sensitive to the cancellation of translational and rotational entropy terms.

Purpose of the Study:

  • To analyze the impact of gas-phase RRHO thermochemical corrections on solution-phase reaction free energies.
  • To investigate the artificial penalty imposed on associated species in molecularity-changing processes.
  • To evaluate confinement-based corrections for improving thermodynamic consistency.

Main Methods:

  • Decomposition of solution-phase association free energies into electronic, differential solvation, and RRHO contributions.
  • Analysis of carbon tetrachloride self-association in liquid CCl4 as a diagnostic case.
  • Examination of water and chloroform clusters to assess the accumulation of RRHO penalty.
  • Application of confinement-based corrections (Martin-Pratt density scaling, Benson's free-volume formulation).

Main Results:

  • Gas-phase RRHO corrections impose an artificial penalty against associated species in molecularity-changing processes.
  • Carbon tetrachloride self-association shows a positive association free energy despite favorable electronic contributions.
  • The RRHO penalty increases with the degree of association in water and chloroform clusters.
  • Confinement-based corrections effectively reduce artificial destabilization without altering electronic or solvation energies.

Conclusions:

  • The primary limitation in calculating solution-phase reaction free energies lies in the use of gas-phase RRHO corrections for molecularity-changing processes.
  • Condensed-phase translational entropy corrections are physically justified for association and activation thermochemistry.
  • Accurate thermodynamic consistency requires accounting for condensed-phase effects on entropy for reactions involving changes in the number of molecules.