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Reactions at Equilibrium and the Equilibrium Constant01:24

Reactions at Equilibrium and the Equilibrium Constant

103
Reactions at equilibrium are characterized by equal rates of forward and reverse reactions. This state of equilibrium does not mean that the reactions have stopped, but rather that they are occurring at identical rates. As a result, the concentrations of reactants and products remain constant over time.The equilibrium constant, denoted as 'K', is a key factor in understanding this state of equilibrium. 'K' is the ratio of the rate constant of the forward reaction to the rate constant of the...
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Homogeneous Equilibria for Gaseous Reactions
For gas-phase reactions, the equilibrium constant may be expressed in terms of either the molar concentrations (Kc) or partial pressures (Kp) of the reactants and products. A relation between these two K values may be simply derived from the ideal gas equation and the definition of molarity. According to the ideal gas equation:
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Equilibrium Conditions for a Particle01:23

Equilibrium Conditions for a Particle

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When an object is in equilibrium, it is either at rest or moving with a constant velocity. There are two types of equilibrium: static and dynamic. Static equilibrium occurs when an object is at rest, while dynamic equilibrium occurs when an object is moving with a constant velocity. In both cases, there must be a balance of forces acting on the object.
To understand the concept of equilibrium, let us first consider the forces acting on an object. When different forces act on an object, they can...
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Thermodynamic Potentials01:26

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Thermodynamic potentials are state functions that are extremely useful in analyzing a thermodynamic system. They have dimensions of energy. The four important thermodynamic potentials are internal energy, enthalpy, Helmholtz free energy, and Gibbs free energy. These thermodynamic potentials can be expressed using two of the following variables: pressure, volume, temperature, and entropy. These two variables are expressed as the rate of change of the thermodynamic potential with respect to other...
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Calculating the Equilibrium Constant02:46

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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:
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The Equilibrium Constant03:10

The Equilibrium Constant

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Consider the oxidation of sulfur dioxide:
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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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Equilibrium molecular thermodynamics from Kirkwood sampling.

Sandeep Somani1, Yuko Okamoto2,3,4,5, Andrew J Ballard1

  • 1†University Chemical Laboratories, Lensfield Road, Cambridge CB2 1EW, United Kingdom.

The Journal of Physical Chemistry. B
|April 28, 2015
PubMed
Summary

We introduce two novel methods for molecular system equilibrium sampling using Kirkwood sampling. These techniques enhance conformational space exploration for molecular simulations, improving computational efficiency.

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Area of Science:

  • Computational Chemistry
  • Molecular Dynamics
  • Statistical Mechanics

Background:

  • Molecular simulations require efficient methods to explore high-dimensional conformational space.
  • Traditional sampling methods can be limited by potential energy landscapes and computational cost.
  • The Kirkwood method offers a geometry-based approach for sampling molecular conformations.

Purpose of the Study:

  • To present two new barrierless equilibrium sampling methods based on the Kirkwood method.
  • To demonstrate the application of these methods for molecular systems.
  • To evaluate their efficiency in exploring conformational space.

Main Methods:

  • Developed a biased Monte Carlo variant using Kirkwood sampling for generating trial moves.
  • Implemented a reservoir replica exchange variant incorporating Kirkwood sampling for enhanced conformational exchange.
  • Utilized low-order correlations of internal coordinates for sampling.

Main Results:

  • Proof-of-concept results were obtained for a model nine-atom linear molecule and alanine dipeptide.
  • The biased Monte Carlo method allows generation of equilibrium distributions at different temperatures and potentials.
  • The reservoir replica exchange method facilitates global conformational jumps, enhancing sampling.

Conclusions:

  • The presented methods offer efficient, barrierless equilibrium sampling strategies for molecular systems.
  • These approaches are suitable for massively parallel computing and can accelerate molecular simulations.
  • Method efficiency is contingent on the overlap between Kirkwood and target equilibrium distributions.