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Related Concept Videos

Chemical Equilibria: Systematic Approach to Equilibrium Calculations01:21

Chemical Equilibria: Systematic Approach to Equilibrium Calculations

Equilibrium calculations for systems involving multiple equilibria are often complex. For example, to calculate the solubility of a sparingly soluble salt in an aqueous solution in the presence of a common ion, one must consider all the equilibria in this solution. Calculations for these systems can be complicated and tedious, so a systematic approach with a series of steps is often helpful. The process is detailed below.
The first step is to identify all the chemical reactions involved, The...
¹H NMR: Complex Splitting01:13

¹H NMR: Complex Splitting

A proton M that is coupled to a proton X results in doublet signals for M. However, NMR-active nuclei can be simultaneously coupled to more than one nonequivalent nucleus. When M is coupled to a second proton A, such as in styrene oxide, each peak in the doublet is split into another doublet.
Splitting diagrams or splitting tree diagrams are routinely used to depict such complex couplings. While drawing splitting diagrams, the splitting with the larger coupling constant is usually applied first.
π Molecular Orbitals of 1,3-Butadiene01:24

π Molecular Orbitals of 1,3-Butadiene

Conjugated dienes have lower heats of hydrogenation than cumulated and isolated dienes, making them more stable. The enhanced stabilization of conjugated systems can be understood from their π molecular orbitals.
The simplest conjugated diene is 1,3-butadiene: a four-carbon system where each carbon is sp2-hybridized and has an unhybridized p orbital that contains an unpaired electron. According to molecular orbital theory, atomic orbitals combine to form molecular orbitals such that the number...
π Molecular Orbitals of the Allyl Cation and Anion01:18

π Molecular Orbitals of the Allyl Cation and Anion

An allyl group is a three-carbon conjugated system where the sp³-hybridized allylic carbon is bonded to a CH=CH2 group via a single bond. Allyl anions can be obtained by treating propene with a strong base that can deprotonate methyl groups. Allyl cations are formed as intermediates during substitution reactions involving allylic halides. In both cases, the hybridization of the allylic carbon changes from sp3 to sp2, giving rise to a carbon chain with three sp2-hybridized carbons, each with an...
¹H NMR: Pople Notation01:09

¹H NMR: Pople Notation

The Pople nomenclature system classifies spin systems based on the difference between their chemical shifts. Coupled spins are denoted by capital letters with subscripts indicating the number of equivalent nuclei. When the coupled nuclei have well-separated chemical shifts, they are assigned letters that are far apart in the alphabet, such as A and X. When the difference in chemical shifts is small, coupled nuclei are named using adjacent letters of the alphabet (AB, MN, or XY).
A proton...
Weak Base Solutions03:21

Weak Base Solutions

Some compounds produce hydroxide ions when dissolved by chemically reacting with water molecules. In all cases, these compounds react only partially and so are classified as weak bases. These types of compounds are also abundant in nature and important commodities in various technologies. For example, global production of the weak base ammonia is typically well over 100 metric tons annually, being widely used as an agricultural fertilizer, a raw material for chemical synthesis of other...

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Isotopic Effect in Double Proton Transfer Process of Porphycene Investigated by Enhanced QM/MM Method
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Isotopic Effect in Double Proton Transfer Process of Porphycene Investigated by Enhanced QM/MM Method

Published on: July 19, 2019

Master equation methods for multiple well systems: application to the 1-,2-pentyl system.

Struan H Robertson1, Michael J Pilling, Luminita C Jitariu

  • 1School of Chemistry, University of Leeds, Leeds, UK.

Physical Chemistry Chemical Physics : PCCP
|August 10, 2007
PubMed
Summary

The master equation models complex chemical reactions with multiple energy wells and products. This technique extracts rate constants for combustion models and reveals indirect dissociation pathways in systems like pentyl radicals.

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Curtain Flow Column: Optimization of Efficiency and Sensitivity
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Curtain Flow Column: Optimization of Efficiency and Sensitivity

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Isotopic Effect in Double Proton Transfer Process of Porphycene Investigated by Enhanced QM/MM Method
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Curtain Flow Column: Optimization of Efficiency and Sensitivity

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Area of Science:

  • Chemical Kinetics
  • Theoretical Chemistry
  • Computational Chemistry

Background:

  • The master equation (ME) is a robust method for modeling chemical reactions involving potential energy wells.
  • It is applicable to complex reaction systems with multiple wells and product channels.

Purpose of the Study:

  • To review the application of the master equation technique for extracting phenomenological rate constants.
  • To extend the ME approach to systems with multiple sinks and demonstrate detailed balance.
  • To analyze the pentyl radical system, including isomerization and dissociation pathways.

Main Methods:

  • Analysis of eigenvalues and eigenvectors of the collision matrix (M) for reaction systems.
  • Application of the master equation to the H + SO(2) reaction to model adduct formation, energy transfer, and product channels.
  • Extension of the ME to the 1- and 2-pentyl radical system to study isomerization and dissociation.

Main Results:

  • Phenomenological rate constants were extracted for the H + SO(2) reaction, suitable for combustion models.
  • Macroscopic rate coefficients derived from the ME were shown to obey detailed balance.
  • The importance of indirect dissociation channels was highlighted in the pentyl radical system.
  • Convergence of chemically significant and internal energy relaxation eigenvalues was observed above 1000 K.

Conclusions:

  • The master equation is a versatile tool for modeling complex chemical reactions and extracting meaningful kinetic parameters.
  • The study confirms the validity of the ME for systems with multiple reaction pathways and sinks.
  • Indirect dissociation pathways play a crucial role in the overall reaction dynamics of systems like pentyl radicals.