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Related Concept Videos

Heterogeneous Catalysis01:22

Heterogeneous Catalysis

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Heterogeneous catalysis involves a catalyst in a different phase from the reactants. It is a process where the catalyst and the reactants are in distinct phases, typically solid and gas or liquid.Most heterogeneous catalysts are metals, metal oxides, or acids. The list includes transition metals like iron (Fe), cobalt (Co), nickel (Ni), palladium (Pd), platinum (Pt), chromium (Cr), manganese (Mn), tungsten (W), silver (Ag), and copper (Cu). These metals possess partially vacant d orbitals that...
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Catalysis02:50

Catalysis

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The presence of a catalyst affects the rate of a chemical reaction. A catalyst is a substance that can increase the reaction rate without being consumed during the process. A basic comprehension of a catalysts’ role during chemical reactions can be understood from the concept of reaction mechanisms and energy diagrams.
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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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Catalytically Perfect Enzymes01:07

Catalytically Perfect Enzymes

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The theory of catalytically perfect enzymes was first proposed by W.J. Albery and J. R. Knowles in 1976. These enzymes catalyze biochemical reactions at high-speed. Their catalytic efficiency values range from 108-109 M-1s-1. These enzymes are also called 'diffusion-controlled' as the only rate-limiting step in the catalysis is that of the substrate diffusion into the active site. Examples include triose phosphate isomerase, fumarase, and superoxide dismutase.
 
Most enzymes...
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Turnover Number and Catalytic Efficiency01:19

Turnover Number and Catalytic Efficiency

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The turnover number of an enzyme is the maximum number of substrate molecules it can transform per unit time. Turnover numbers for most enzymes range from 1 to 1000 molecules per second. Catalase has the known highest turnover number, capable of converting up to 2.8×106 molecules of hydrogen peroxide into water and oxygen per second. Lysozyme has the lowest known turnover number of half a molecule per second.
Chymotrypsin is a pancreatic enzyme that breaks down proteins during digestion....
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Factors Influencing the Rate of Chemical Reactions01:22

Factors Influencing the Rate of Chemical Reactions

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A variety of factors influence the rate of chemical reactions. For a chemical reaction to happen, atoms must collide with enough energy to overcome the repulsion between their electrons. This energy is called activation energy. Factors influencing the rate of reaction either lower the activation energy or increase the likelihood of a successful collision.
Concentration and Pressure:
The more particles present within a given space, the more likely those particles are to bump into one another....
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Related Experiment Video

Updated: Mar 31, 2026

Synthesis of Metal Nanoparticles Supported on Carbon Nanotube with Doped Co and N Atoms and its Catalytic Applications in Hydrogen Production
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Effective rate constant for nanostructured heterogeneous catalysts.

Leila Rajabi1, S C Hendy2

  • 1School of Chemical and Physical Sciences and MacDiarmid Institute for Advanced Materials and Nanotechnology, Victoria University of Wellington, P.O. Box 600, Wellington 6140, New Zealand. Leila.Rajabibonab@vuw.ac.nz lrb.rajabi@gmail.com.

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Summary

Nanostructured catalysts can be limited by reactant diffusion. This study uses mathematical modeling and simulations to show that patterned active sites can enhance catalytic activity beyond theoretical limits under certain conditions.

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Area of Science:

  • Chemical Engineering
  • Materials Science
  • Physical Chemistry

Background:

  • Nanostructured heterogeneous catalysts offer high surface area for efficiency.
  • Precious metal catalysts are costly, driving interest in nanostructuring.
  • Diffusion limitations can reduce the effectiveness of active sites in nanostructures.

Purpose of the Study:

  • To investigate how scale and patterning affect catalytic activity under diffusion-limited conditions.
  • To develop a mathematical model for predicting catalyst performance.
  • To compare theoretical predictions with numerical simulations.

Main Methods:

  • Mathematical homogenization approach applied to heterogeneous catalysts.
  • Numerical testing using Monte Carlo simulations.
  • Analysis of catalyst patterning and reactant diffusion.

Main Results:

  • Continuum theory accurately predicts activity when mean free path is much smaller than pattern scale.
  • Effective rate constant equals the area-weighted harmonic mean of surface rate constants in the continuum limit.
  • Simulations reveal enhanced activity exceeding theoretical limits when pattern scale approaches mean free path length.

Conclusions:

  • Catalyst patterning can optimize performance under diffusion-limited conditions.
  • Mathematical homogenization provides a valid framework for understanding nanostructured catalysts.
  • Deviations from continuum theory highlight the importance of scale effects in catalysis.