Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Mass Spectrometry: Isotope Effect01:13

Mass Spectrometry: Isotope Effect

Most elements exist in nature as a mixture of isotopes. The isotopes differ in weight due to their respective number of neutrons. The molecular weight of a molecule is different depending on the specific isotope of its elements involved. As a result, the mass spectrum of the molecule exhibits peaks from the same fragment at multiple positions. The positions of these mass signals depend on the mass differences between isotopes. Furthermore, the intensity of these signals is dependent on the...
The Equilibrium Constant03:10

The Equilibrium Constant

Consider the oxidation of sulfur dioxide:
Le Chatelier's Principle: Changing Temperature02:19

Le Chatelier's Principle: Changing Temperature

Consistent with the law of mass action, an equilibrium stressed by a change in concentration will shift to re-establish equilibrium without any change in the value of the equilibrium constant, K. When an equilibrium shifts in response to a temperature change, however, it is re-established with a different relative composition that exhibits a different value for the equilibrium constant.
To understand this phenomenon, consider the elementary reaction:
Homogeneous Equilibria for Gaseous Reactions02:15

Homogeneous Equilibria for Gaseous Reactions

Homogeneous Equilibria for Gaseous Reactions
For gas-phase reactions, the equilibrium constant may be expressed in terms of either the molar concentrations (Kc) or partial pressures (Kp) of the reactants and products. A relation between these two K values may be simply derived from the ideal gas equation and the definition of molarity. According to the ideal gas equation:
Reaction Quotient02:35

Reaction Quotient

The status of a reversible reaction is conveniently assessed by evaluating its reaction quotient (Q). For a reversible reaction described by m A + n B ⇌ x C + y D, the reaction quotient is derived directly from the stoichiometry of the balanced equation as
Calculating the Equilibrium Constant02:46

Calculating the Equilibrium Constant

The equilibrium constant for a reaction is calculated from the equilibrium concentrations (or pressures) of its reactants and products. If these concentrations are known, the calculation simply involves their substitution into the Kc expression.
For example, gaseous nitrogen dioxide forms dinitrogen tetroxide according to this equation:

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Labelling of subpleural pulmonary nodules with blue dye and contrast agents under CT-guided control and subsequent video-assisted thoracoscopic resection: the BLUEPAT prospective randomised study.

Trials·2026
Same author

Precise Localization of the Subsolid Lesion by Colour Marking under CT-Guided Control before Video-Assisted Surgery Resection: A Case Report.

Case reports in oncology·2025
Same author

What factors affect a patient's subjective perception of MRI examination.

Scientific reports·2024
Same author

Subpleural pulmonary nodule marking with patent blue V dye prior to surgical resection.

Frontiers in oncology·2024
Same author

Hippocampal subfield volumetric changes after radiotherapy for brain metastases.

Neuro-oncology advances·2024
Same author

Efficient Semiclassical Evaluation of Electronic Coherences in Polyatomic Molecules.

Chimia·2023

Related Experiment Video

Updated: Jun 21, 2026

Cellular Lipid Extraction for Targeted Stable Isotope Dilution Liquid Chromatography-Mass Spectrometry Analysis
09:26

Cellular Lipid Extraction for Targeted Stable Isotope Dilution Liquid Chromatography-Mass Spectrometry Analysis

Published on: November 17, 2011

Path integral evaluation of equilibrium isotope effects.

Tomás Zimmermann1, Jirí Vanícek

  • 1Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland.

The Journal of Chemical Physics
|July 17, 2009
PubMed
Summary

This study introduces a new quantum method for calculating isotope effects, accurately including vibrational and rotational motions. The approach significantly speeds up computations and reveals anharmonicity effects up to 30% in reactions.

More Related Videos

Isotopic Effect in Double Proton Transfer Process of Porphycene Investigated by Enhanced QM/MM Method
05:51

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

Published on: July 19, 2019

Workflow Based on the Combination of Isotopic Tracer Experiments to Investigate Microbial Metabolism of Multiple Nutrient Sources
12:47

Workflow Based on the Combination of Isotopic Tracer Experiments to Investigate Microbial Metabolism of Multiple Nutrient Sources

Published on: January 22, 2018

Related Experiment Videos

Last Updated: Jun 21, 2026

Cellular Lipid Extraction for Targeted Stable Isotope Dilution Liquid Chromatography-Mass Spectrometry Analysis
09:26

Cellular Lipid Extraction for Targeted Stable Isotope Dilution Liquid Chromatography-Mass Spectrometry Analysis

Published on: November 17, 2011

Isotopic Effect in Double Proton Transfer Process of Porphycene Investigated by Enhanced QM/MM Method
05:51

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

Published on: July 19, 2019

Workflow Based on the Combination of Isotopic Tracer Experiments to Investigate Microbial Metabolism of Multiple Nutrient Sources
12:47

Workflow Based on the Combination of Isotopic Tracer Experiments to Investigate Microbial Metabolism of Multiple Nutrient Sources

Published on: January 22, 2018

Area of Science:

  • Computational Chemistry
  • Physical Chemistry
  • Quantum Mechanics

Background:

  • Standard methods for calculating quantum equilibrium isotope effects often rely on approximations like separability of motions and harmonic potentials.
  • These approximations can limit accuracy, particularly for understanding the full quantum mechanical behavior of isotopes in chemical reactions.

Purpose of the Study:

  • To develop and implement a general, rigorous methodology for computing quantum equilibrium isotope effects without standard approximations.
  • To accurately account for zero-point energy and anharmonicity effects in isotopic calculations.

Main Methods:

  • Utilized thermodynamic integration with respect to isotope mass and Feynman path integral representation of the partition function.
  • Developed an efficient free energy derivative estimator, independent of imaginary time slices, significantly accelerating calculations.
  • Implemented the methodology within the AMBER 10 molecular dynamics package.

Main Results:

  • Anharmonicity corrections were found to contribute up to 30% of the symmetry-reduced reaction free energy in [1,5] sigmatropic hydrogen shift reactions.
  • The new method demonstrated a computational speed-up factor of approximately 60 at 500 K compared to standard approaches.
  • Calculations confirmed experimental results for specific pentamethylnaphthacene and bicyclo[4.4.0]decene systems, highlighting the importance of anharmonicity.

Conclusions:

  • The developed quantum method provides a more accurate and efficient way to compute equilibrium isotope effects.
  • Accurate treatment of anharmonicity is crucial for understanding and predicting isotope effects in chemical reactions.
  • The methodology offers a valuable tool for theoretical and experimental chemists studying isotopic phenomena.