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Radical Reactivity: Concentration Effects01:20

Radical Reactivity: Concentration Effects

1.9K
In a radical reaction, the concentration of starting materials governs the selectivity of a radical. For example, the reaction between an alkyl halide and an alkene, in the presence of tin hydride and AIBN, begins with the generation of a tin radical. The generated radical then abstracts halogen from the alkyl halide, producing an alkyl radical. This alkyl radical can either react with tin hydride, yielding an alkane, or add to an alkene, generating a nitrile-stabilized radical, eventually...
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Concentration Cells02:41

Concentration Cells

25.9K
A concentration cell is a type of a  voltaic cell constructed by connecting two almost identical half-cells, both based on the same half-reaction and using the same electrode, differing only in the concentration of one redox species. A concentration cell's potential, therefore, is determined only by the concentration difference of the particular redox species.
Consider the following voltaic cell:
25.9K
Concentration and Rate Law03:03

Concentration and Rate Law

38.3K
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:
38.3K
Calculating Equilibrium Concentrations02:05

Calculating Equilibrium Concentrations

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Being able to calculate equilibrium concentrations is essential to many areas of science and technology—for example, in the formulation and dosing of pharmaceutical products. After a drug is ingested or injected, it is typically involved in several chemical equilibria that affect its ultimate concentration in the body system of interest. Knowledge of the quantitative aspects of these equilibria is required to compute a dosage amount that will solicit the desired therapeutic effect.
A more...
53.3K
Determining Order of Reaction02:53

Determining Order of Reaction

62.0K
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...
62.0K
The Integrated Rate Law: The Dependence of Concentration on Time02:39

The Integrated Rate Law: The Dependence of Concentration on Time

41.4K
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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Related Experiment Video

Updated: Jan 30, 2026

CO2 Photoreduction to CH4 Performance Under Concentrating Solar Light
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CO2 Photoreduction to CH4 Performance Under Concentrating Solar Light

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Reactive SINDy: Discovering governing reactions from concentration data.

Moritz Hoffmann1, Christoph Fröhner1, Frank Noé1

  • 1Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 6, 14195 Berlin, Germany.

The Journal of Chemical Physics
|January 17, 2019
PubMed
Summary

This study introduces "reactive SINDy," a new machine learning method to accurately identify essential reactions in complex biological and chemical systems from observed data, avoiding spurious pathways.

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Area of Science:

  • Systems Biology
  • Chemical Kinetics
  • Machine Learning

Background:

  • Understanding complex biological cells and chemical reactors relies on mapping their reaction networks, which are often unknown and difficult to compute.
  • Standard methods like least-squares regression can identify reaction networks but frequently include non-existent or spurious reactions.
  • Accurate estimation of effective reaction networks from observational data, such as time-series measurements, is crucial for deciphering system mechanisms.

Purpose of the Study:

  • To develop a novel machine learning approach for estimating parsimonious reaction networks from observational data.
  • To extend the Sparse Identification of Nonlinear Dynamics (SINDy) method for application to vector-valued functions representing reaction processes.

Main Methods:

  • Extension of the Sparse Identification of Nonlinear Dynamics (SINDy) algorithm to handle vector-valued ansatz functions.
  • Development of a sparse tensor regression technique, termed 'reactive SINDy', for parsimonious reaction network inference.
  • Application and validation of the reactive SINDy method using time-series data from complex systems.

Main Results:

  • The reactive SINDy method successfully estimates parsimonious (minimal and essential) reaction networks.
  • The method effectively identifies the true underlying reaction structure, distinguishing from spurious reactions.
  • Demonstrated accurate estimation of a gene regulation network from observed time-series data.

Conclusions:

  • Reactive SINDy provides a powerful and accurate tool for inferring reaction mechanisms in complex systems.
  • This approach overcomes limitations of standard regression techniques by minimizing spurious reactions.
  • The method holds significant potential for advancing research in systems biology, chemical engineering, and other fields reliant on network analysis.