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Related Concept Videos

Free Energy Changes for Nonstandard States03:25

Free Energy Changes for Nonstandard States

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The free energy change for a process taking place with reactants and products present under nonstandard conditions (pressures other than 1 bar; concentrations other than 1 M) is related to the standard free energy change according to this equation:
 
where R is the gas constant (8.314 J/K·mol), T is the absolute temperature in kelvin, and Q is the reaction quotient. This equation may be used to predict the spontaneity of a process under any given set of conditions.
Reaction Quotient...
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Chemical reactions often occur in a stepwise fashion involving two or more distinct reactions taking place in a sequence. A balanced equation indicates the reacting species and the product species, but it reveals no details about how the reaction occurs at the molecular level. The reaction mechanism (or reaction path) provides details regarding the precise, step-by-step process by which a reaction occurs. Each of the steps in a reaction mechanism is called an elementary reaction. These...
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The Integrated Rate Law: The Dependence of Concentration on Time02:39

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While the differential rate law relates the rate and concentrations of reactants, a second form of rate law called the integrated rate law relates concentrations of reactants and time. Integrated rate laws can be used to determine the amount of reactant or product present after a period of time or to estimate the time required for a reaction to proceed to a certain extent. For example, an integrated rate law helps determine the length of time a radioactive material must be stored for its...
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Chemical Reactions02:26

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A balanced chemical equation provides the information of chemical formulas of the reactants and products involved in the chemical change. A reaction’s stoichiometry helps predict how much of the reactant is needed to produce the desired amount of product, or in some cases, how much product will be formed from a specific amount of the reactant.
The relative amounts of reactants and products represented in a balanced chemical equation are often referred to as stoichiometric amounts.
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Concentration and Rate Law03:03

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The rate of a reaction is affected by the concentrations of reactants. Rate laws (differential rate laws) or rate equations are mathematical expressions describing the relationship between the rate of a chemical reaction and the concentration of its reactants.
For example, in a generic reaction aA + bB ⟶ products, where a and b are stoichiometric coefficients, the rate law can be written as:
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Dynamic Equilibrium02:20

Dynamic Equilibrium

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A reversible chemical reaction represents a chemical process that proceeds in both forward (left to right) and reverse (right to left) directions. When the rates of the forward and reverse reactions are equal, the concentrations of the reactant and product species remain constant over time and the system is at equilibrium. A special double arrow is used to emphasize the reversible nature of the reaction. The relative concentrations of reactants and products in equilibrium systems vary greatly;...
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Related Experiment Video

Updated: Sep 13, 2025

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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Universal limiting behavior of reaction-diffusion systems with conservation laws.

Joshua F Robinson1,2, Thomas Machon2, Thomas Speck3

  • 1STFC Daresbury Laboratory, The Hartree Centre, Warrington WA4 4AD, United Kingdom.

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Summary

A new theory simplifies complex many-species systems using conservation laws, linking phase separation to coexistence. This framework aids understanding of biomolecular condensates and reaction-diffusion systems.

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Area of Science:

  • Physical Chemistry
  • Theoretical Biology
  • Complex Systems

Background:

  • Understanding complex inhomogeneous systems with many interacting species is a major scientific challenge.
  • Phase separation and pattern formation in reaction-diffusion systems are typically studied as distinct phenomena.

Purpose of the Study:

  • To establish a unified theoretical framework for many-species reaction-diffusion systems.
  • To link phase separation and pattern formation under conservation laws.
  • To simplify the description of complex systems at coarse spatiotemporal scales.

Main Methods:

  • Developed a geometrical framework using the nullcline (line of homogeneous steady states).
  • Utilized a conservation law to derive a Cahn-Hilliard-like equation for conserved quantities.
  • Analyzed the elimination of fast nonconserved degrees of freedom.

Main Results:

  • Demonstrated that conservation laws in many-species systems lead to Cahn-Hilliard-like equations.
  • Established a direct link between phase separation, coexistence, and active field theories.
  • Showed that a simplified yet accurate description emerges for complex systems at larger scales.

Conclusions:

  • The developed theory provides a unified approach to complex many-species systems.
  • The geometrical framework offers new insights into chemical space and system dynamics.
  • This work is expected to significantly advance the understanding of biomolecular condensates.