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Extent of Reaction (ξ) Calculator

Measure of how far a reaction has proceeded.

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Extent of Rxn

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Overview

The extent of reaction is a quantitative measure of the progress of a chemical reaction that is independent of the specific chemical species chosen for calculation. It relates the change in moles of any species to its stoichiometric coefficient, allowing for a consistent tracking of mass balance across the entire system.

Symbols

Variables

\xi = Extent of Rxn, n_i = Final Moles, n_{i0} = Initial Moles, \nu_i = Stoich. Coeff.

Extent of Rxn
Final Moles
Initial Moles
Stoich. Coeff.

Apply it well

When To Use

When to use: Use this variable when performing mass balance calculations for a system where a single or multiple balanced chemical reactions occur. It is particularly helpful in identifying the equilibrium composition of a mixture when the reaction's equilibrium constant is known.

Why it matters: By using a single variable to represent the progress of a reaction, engineers can simplify the complex tracking of every individual species in a multi-component system. This concept is fundamental in designing chemical reactors and calculating thermodynamic properties like the Gibbs free energy of reaction.

Avoid these traps

Common Mistakes

  • Confusing extent of reaction (mol) with conversion (dimensionless).
  • Using the wrong sign for stoichiometric coefficients (ν).

One free problem

Practice Problem

In a Haber process reactor, 10 moles of Nitrogen (N₂) are initially present. After some time, only 4 moles of Nitrogen remain. If the stoichiometric coefficient for Nitrogen is -1 in the balanced equation N₂ + 3H₂ → 2NH₃, what is the extent of reaction in moles?

Initial Moles10 mol
Final Moles4 mol
Stoich. Coeff.-1

Solve for:

Hint: Subtract the initial moles from the final moles, then divide by the stoichiometric coefficient.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Elements of Chemical Reaction Engineering by H. Scott Fogler, 5th Edition
  2. Chemical Reaction Engineering by Octave Levenspiel, 3rd Edition
  3. Physical Chemistry by Peter Atkins and Julio de Paula, 11th Edition
  4. Wikipedia: Extent of reaction
  5. Atkins' Physical Chemistry, 11th ed., Chapter 6, Section 6.1
  6. Bird, Stewart, and Lightfoot, Transport Phenomena, 2nd ed., Chapter 1, Section 1.3
  7. IUPAC Gold Book, 'extent of reaction'
  8. Fogler, H. Scott. Elements of Chemical Reaction Engineering. 5th ed. Prentice Hall, 2016.