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Related Concept Videos

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.
The first step is to identify all the chemical reactions involved, The...
1.3K
Recrystallization: Solid–Solution Equilibria01:10

Recrystallization: Solid–Solution Equilibria

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Recrystallization is a purification technique used to separate impurities from solid compounds. In this technique, no chemical reactions occur. Instead, it exploits physical properties only, specifically, the solubility differences between the desired compound and impurities, either at a single temperature or at different temperatures, and under other selected conditions. The solid-solution equilibrium (solubility equilibrium) of each component in the solution represents a binary phase...
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Phase Transitions: Melting and Freezing02:39

Phase Transitions: Melting and Freezing

14.3K
Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy becomes large enough to partially overcome the forces holding the molecules or ions of the solid in their fixed positions, and the solid begins the process of transitioning to the liquid state or melting. At this point, the temperature of the solid stops rising, despite the continual input of heat, and it remains constant until all of the solid is...
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Calculating Equilibrium Concentrations02:05

Calculating Equilibrium Concentrations

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Being able to calculate equilibrium concentrations is essential to many areas of science and technology—for example, in the formulation and dosing of pharmaceutical products. After a drug is ingested or injected, it is typically involved in several chemical equilibria that affect its ultimate concentration in the body system of interest. Knowledge of the quantitative aspects of these equilibria is required to compute a dosage amount that will solicit the desired therapeutic effect.
A more...
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Phase Transitions: Sublimation and Deposition02:33

Phase Transitions: Sublimation and Deposition

19.4K
Some solids can transition directly into the gaseous state, bypassing the liquid state, via a process known as sublimation. At room temperature and standard pressure, a piece of dry ice (solid CO2) sublimes, appearing to gradually disappear without ever forming any liquid. Snow and ice sublimate at temperatures below the melting point of water, a slow process that may be accelerated by winds and the reduced atmospheric pressures at high altitudes. When solid iodine is warmed, the solid sublimes...
19.4K
Calculating the Equilibrium Constant02:46

Calculating the Equilibrium Constant

37.1K
The equilibrium constant for a reaction is calculated from the equilibrium concentrations (or pressures) of its reactants and products. If these concentrations are known, the calculation simply involves their substitution into the Kc expression.
For example, gaseous nitrogen dioxide forms dinitrogen tetroxide according to this equation:
37.1K

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High-pressure Sapphire Cell for Phase Equilibria Measurements of CO2/Organic/Water Systems
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Efficient determination of solid-state phase equilibrium with the multicell Monte Carlo method.

Edwin Antillon1, Maryam Ghazisaeidi1

  • 1Department of Materials Science at The Ohio State University, Columbus, Ohio 43210, USA.

Physical Review. E
|July 22, 2020
PubMed
Summary

This study enhances the multicell Monte Carlo (MC)^2 method for solid phase equilibria. A new predictor-corrector algorithm ensures accurate phase equilibrium determination by guiding the system towards equilibrium.

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Area of Science:

  • Materials Science
  • Computational Chemistry
  • Thermodynamics

Background:

  • The multicell Monte Carlo (MC)^2 method models phase coexistence by simulating mass transfer between cells.
  • A key challenge is the lack of a robust stopping condition, risking convergence to non-equilibrium solutions.

Purpose of the Study:

  • To introduce significant improvements to the (MC)^2 method for efficient determination of phase equilibria in solids.
  • To address the issue of non-equilibrium solutions by developing a reliable stopping condition.

Main Methods:

  • A predictor-corrector algorithm is introduced to penalize non-equilibrium solutions and guide the system towards equilibrium.
  • The most general acceptance criteria for (MC)^2 are derived from the isothermal-isobaric Gibbs ensemble.
  • Translational and volume Monte Carlo moves are incorporated to handle vibrational excitations and maintain constant pressure and temperature.

Main Results:

  • The enhanced (MC)^2 method successfully steers the system towards equilibrium, overcoming the previous limitation of potentially trapping in non-equilibrium states.
  • The method was validated on binary alloys with miscibility gaps and a model quaternary alloy.

Conclusions:

  • The improved (MC)^2 method provides a more efficient and reliable approach for calculating solid phase equilibria.
  • This advancement enables accurate phase diagram predictions using classical interatomic potentials.