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Multi-Step Reactions02:31

Multi-Step Reactions

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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 Collision Theory
Atoms, molecules, or ions must collide before they can react with each other. Atoms must be close together to form chemical bonds. This premise is the basis for a theory that explains many observations regarding chemical kinetics, including factors affecting reaction rates.
The collision theory is based on the postulates that (i) the reaction rate is proportional to the rate of reactant collisions, (ii) the reacting species collide in an orientation allowing contact between...
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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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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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Reaction Rate02:53

Reaction Rate

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The rate of reaction is the change in the amount of a reactant or product per unit time. Reaction rates are therefore determined by measuring the time dependence of some property that can be related to reactant or product amounts. Rates of reactions that consume or produce gaseous substances, for example, are conveniently determined by measuring changes in volume or pressure.
The mathematical representation of the change in the concentration of reactants and products, over time, is the rate...
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Half-life of a Reaction02:42

Half-life of a Reaction

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The half-life of a reaction (t1/2) is the time required for one-half of a given amount of reactant to be consumed. In each succeeding half-life, half of the remaining concentration of the reactant is consumed. For example, during the decomposition of hydrogen peroxide, during the first half-life (from 0.00 hours to 6.00 hours), the concentration of H2O2 decreases from 1.000 M to 0.500 M. During the second half-life (from 6.00 hours to 12.00 hours), the concentration decreases from 0.500 M to...
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Related Experiment Video

Updated: Feb 26, 2026

Modeling Fast-scan Cyclic Voltammetry Data from Electrically Stimulated Dopamine Neurotransmission Data Using QNsim1.0
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Reaction-diffusion with stochastic decay rates.

G John Lapeyre1, Marco Dentz2

  • 1Spanish National Research Council (IDAEA-CSIC), E-08034 Barcelona, Spain and ICFO-Institut de Ciències Fotòniques, Mediterranean Technology Park, 08860 Castelldefels, Spain.

Physical Chemistry Chemical Physics : PCCP
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Summary
This summary is machine-generated.

This study models anomalous transport and reaction kinetics in disordered systems. It reveals how broad distributions of transport and reaction times cause subdiffusion and power-law decay in particle density.

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Area of Science:

  • Multidisciplinary science
  • Physical chemistry
  • Geophysics
  • Biology
  • Engineering

Background:

  • Understanding anomalous transport and reaction kinetics is crucial in diverse scientific fields.
  • Microscopic physical and chemical disorder significantly impacts these processes.
  • Existing models often struggle to connect microscopic disorder to macroscopic observations.

Purpose of the Study:

  • To introduce and analyze a model framework connecting microscopic fluctuations to macroscopic descriptions of reaction-diffusion systems.
  • To investigate the effects of broad distributions in transport and reaction time scales.
  • To elucidate the origins of anomalous behavior in disordered reaction-diffusion processes.

Main Methods:

  • Development of a novel model framework for reaction-diffusion systems.
  • Explicitly linking microscopic fluctuations with mesoscopic descriptions.
  • Computation of particle density and derivation of governing evolution equations for broad time scale distributions.

Main Results:

  • Observed power-law decay in survival probability.
  • Identified spatially varying decay leading to subdiffusion.
  • Found an asymptotically stationary surviving-particle density.
  • Attributed anomalies to non-Markovian effects coupling transport and chemical properties.

Conclusions:

  • The proposed model effectively captures anomalous transport and reaction kinetics in disordered systems.
  • Non-Markovian effects are key drivers of subdiffusion and altered reaction rates.
  • The framework provides insights into complex phenomena across geophysics, biology, and engineering.