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Energetics of Solution Formation02:35

Energetics of Solution Formation

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The formation of a solution is an example of a spontaneous process, which is a process that occurs under specified conditions without energy from some external source.
When the strengths of the intermolecular forces of attraction between solute and solvent species in a solution are no different than those present in the separated components, the solution is formed with no accompanying energy change. Formation of the solution requires the solute–solute and solvent–solvent...
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The experimental conditions in a gravimetric analysis should be optimized to maximize the particle size and purity of the obtained precipitate. Ideally, the concentration of the precipitating reagent should be low with effective stirring to maintain low relative supersaturation for the growth of large crystals. In homogeneous precipitation, the precipitant is slowly generated by a chemical reaction in the solution to avoid local reagent excesses. For example, urea decomposes gradually to...
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Colloidal precipitates01:09

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The high insolubility of some precipitates can result in an unfavorable relative supersaturation. This can lead to colloidal particles with a large surface-to-mass ratio, where adsorption is promoted. For instance, in the precipitation of silver chloride, silver ions are adsorbed on the surface of the colloidal particles, forming a primary layer. This layer attracts ions of opposite charge (such as nitrate ions), forming a diffuse secondary layer of adsorbed ions. This electric double layer...
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Chemical and Solubility Equilibria02:21

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The free energy change associated with dissolving a solute in a liter of solvent is called the free energy of a solution, ΔGsolution. The overall ΔGsolution is expressed as the balance of ΔGinteraction against the always-favorable free-energy of mixing, ΔGmixing. Solution formation is favorable if  ΔGsolution is less than zero, whereas it is unfavorable if ΔGsolution is greater than zero. In short, for a solution to form and complete dissolution to take place,...
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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.
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Rate laws describe the relationship between the rate of a chemical reaction and the concentration of its reactants. In a rate law, the rate constant k and the reaction orders are determined experimentally by observing how the rate of reaction changes as the concentrations of the reactants are changed. A common experimental approach to the determination of rate laws is the method of initial rates. This method involves measuring reaction rates for multiple experimental trials carried out using...
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Updated: Feb 18, 2026

Patterning of Microorganisms and Microparticles through Sequential Capillarity-assisted Assembly
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Shaken, not stirred, mixing evolves to order.

Adrian Bejan1

  • 1Duke University, Durham, NC, 27708-0300, USA.

Bio Systems
|February 16, 2026
PubMed
Summary

The constructal law and the second law are distinct principles governing natural design and irreversibility. Two mixing examples illustrate how flow configurations evolve, clarifying thermodynamic concepts and the direction of natural processes.

Area of Science:

  • Thermodynamics
  • Physics of Evolution
  • Natural Design

Background:

  • The second law of thermodynamics addresses irreversibility.
  • The constructal law addresses design and flow configuration in nature.
  • Distinguishing these laws is crucial for understanding natural phenomena.

Purpose of the Study:

  • To demonstrate the distinctness of the constructal law and the second law.
  • To clarify common thermodynamic misunderstandings using practical examples.
  • To highlight the role of design evolution in natural processes.

Main Methods:

  • Analysis of two mixing phenomena: a sinking body in liquid and stratified ball bearings.
  • Juxtaposition of the constructal law and the second law.
  • Classroom-based examples emphasizing free inquiry and common sense.
Keywords:
Constructal lawDesign in natureEvolutionMixingSecond lawTime arrow

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Main Results:

  • Mixing processes are accompanied by evolving flow configurations.
  • The sinking body example shows evolving flow design.
  • The ball bearing example demonstrates evolving stratification.
  • The constructal law governs the evolution of flow design.

Conclusions:

  • The constructal law and the second law are independent and self-standing.
  • Understanding these laws clarifies concepts like the arrow of time and universal evolution.
  • Practical, jargon-free examples are effective for scientific discovery.