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Chemical Equilibria: Systematic Approach to Equilibrium Calculations01:21

Chemical Equilibria: Systematic Approach to Equilibrium Calculations

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Equilibrium calculations for systems involving multiple equilibria are often complex. For example, to calculate the solubility of a sparingly soluble salt in an aqueous solution in the presence of a common ion, one must consider all the equilibria in this solution. Calculations for these systems can be complicated and tedious, so a systematic approach with a series of steps is often helpful. The process is detailed below.
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A thermodynamic system is a set of objects whose thermodynamic properties are of interest. The system is considered to be embedded in its surroundings or the environment. The system and its environment can exchange heat and do work on each other through a boundary that separates them. However, the immediate surroundings of the system interact with it directly and therefore have a much stronger influence on its behavior and properties.
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The spontaneity of a process depends upon the temperature of the system. Phase transitions, for example, will proceed spontaneously in one direction or the other depending upon the temperature of the substance in question. Likewise, some chemical reactions can also exhibit temperature-dependent spontaneities. To illustrate this concept, the equation relating free energy change to the enthalpy and entropy changes for the process is considered:
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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.
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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...
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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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Nonequilibrium statistical thermodynamics of multicomponent interfaces.

Phillip M Rauscher1, Hans Christian Öttinger2, Juan J de Pablo1,3,4

  • 1Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL 60637.

Proceedings of the National Academy of Sciences of the United States of America
|June 8, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces a local equilibrium theory for nonequilibrium interfaces, validated by molecular dynamics simulations. It shows equilibrium thermodynamics accurately describes interfacial processes, even far from equilibrium.

Keywords:
interfacesmolecular dynamicsnonequilibrium thermodynamicsstatistical mechanicstransport

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Area of Science:

  • Thermodynamics
  • Interfacial Science
  • Computational Physics

Background:

  • Nonequilibrium interfacial thermodynamics is vital for biological, physical, and industrial transport processes.
  • Existing models often simplify complex interfacial phenomena, limiting their applicability.
  • A robust theoretical framework is needed for accurate descriptions of dynamic interfaces.

Purpose of the Study:

  • To develop and validate a theory of local equilibrium for multiphase, multicomponent interfaces.
  • To extend Gibbs' sharp interface concept to describe nonequilibrium interfacial processes.
  • To provide a thermodynamic foundation for studying interfacial transport phenomena.

Main Methods:

  • Developed a theory of local equilibrium for multiphase, multicomponent interfaces.
  • Utilized high-precision nonequilibrium molecular dynamics (NEMD) simulations.
  • Verified theoretical predictions against simulation data.

Main Results:

  • Demonstrated the validity of the local equilibrium hypothesis even far from equilibrium.
  • Showed that equilibrium equations of state apply to nonequilibrium conditions.
  • Confirmed that interfacial temperature and chemical potentials can be determined using generalized Clapeyron and Gibbs adsorption equations.
  • Observed that interfacial properties like temperature and chemical potential may be discontinuous far from equilibrium.

Conclusions:

  • The local equilibrium theory provides a valid thermodynamic framework for nonequilibrium interfaces.
  • NEMD simulations confirm the applicability of equilibrium thermodynamics out of equilibrium.
  • This work offers computational tools for analyzing diverse interfacial transport phenomena.