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Related Concept Videos

Homogeneous Equilibria for Gaseous Reactions02:15

Homogeneous Equilibria for Gaseous Reactions

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:
Behavior of Gas Molecules: Molecular Diffusion, Mean Free Path, and Effusion03:48

Behavior of Gas Molecules: Molecular Diffusion, Mean Free Path, and Effusion

Although gaseous molecules travel at tremendous speeds (hundreds of meters per second), they collide with other gaseous molecules and travel in many different directions before reaching the desired target. At room temperature, a gaseous molecule will experience billions of collisions per second. The mean free path is the average distance a molecule travels between collisions. The mean free path increases with decreasing pressure; in general, the mean free path for a gaseous molecule will be...
Reaction Mechanisms: The Steady-State Approximation01:26

Reaction Mechanisms: The Steady-State Approximation

The steady-state approximation, also referred to as the quasi-steady-state approximation to differentiate it from a true steady state, is a widely used method for simplifying calculations in complex reaction mechanisms. This approach is particularly useful when dealing with multi-step reactions that involve reverse reactions or several steps, which can significantly increase mathematical complexity and make the reactions nearly unsolvable analytically.The steady-state approximation operates on...
Equilibrium Conditions for a Particle01:23

Equilibrium Conditions for a Particle

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...
Reaction Quotient02:35

Reaction Quotient

The status of a reversible reaction is conveniently assessed by evaluating its reaction quotient (Q). For a reversible reaction described by m A + n B ⇌ x C + y D, the reaction quotient is derived directly from the stoichiometry of the balanced equation as
First Law: Particles in Two-dimensional Equilibrium01:18

First Law: Particles in Two-dimensional Equilibrium

Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
Newton's first law tells us about the...

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Related Experiment Video

Updated: May 10, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
06:55

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

Spatial correlations in nonequilibrium reaction-diffusion problems by the Gillespie algorithm.

Jorge Luis Hita1, José María Ortiz de Zárate

  • 1Departamento de Física Aplicada I. Universidad Complutense, E-28040 Madrid, Spain.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 18, 2013
PubMed
Summary
This summary is machine-generated.

Spatial correlations in a 1D reaction-diffusion system are short-ranged at equilibrium but become long-ranged out of equilibrium. This study validates fluctuating hydrodynamics predictions for such systems.

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Last Updated: May 10, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Area of Science:

  • Physics
  • Chemistry
  • Computational Science

Background:

  • Reaction-diffusion systems are fundamental to understanding complex phenomena.
  • Spatial correlations provide insights into system behavior.
  • One-dimensional systems offer a simplified yet crucial model.

Purpose of the Study:

  • To investigate spatial correlation functions in a 1D reaction-diffusion system.
  • To compare equilibrium and non-equilibrium conditions.
  • To validate theoretical models with numerical simulations.

Main Methods:

  • Employed the Gillespie algorithm for numerical simulations.
  • Treated diffusion as a chemical process between adjacent cells.
  • Analyzed spatial correlation functions.

Main Results:

  • Observed short-ranged spatial correlations in equilibrium.
  • Found long-ranged spatial correlations out of equilibrium.
  • Results align with theoretical predictions from fluctuating hydrodynamics.

Conclusions:

  • Non-equilibrium conditions significantly alter spatial correlations in 1D reaction-diffusion systems.
  • The Gillespie algorithm effectively simulates these systems.
  • Fluctuating hydrodynamics accurately predicts system behavior under periodic boundary conditions.