Extent of Reaction

General Chemistry • Chemical Reactions

Written by STEM Calculators Team Published October 18, 2025 Updated February 24, 2026

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The Extent of Reaction (ξ)

For a balanced reaction, each species has a stoichiometric number \( \nu_k \): it equals the coefficient of the species with a positive sign for products and the negative of the coefficient for reactants. The extent of reaction, \( \xi \) (in moles), measures how far the reaction has progressed.

Key relations

\[ \Delta n_k \;=\; \nu_k\,\xi \] \[ n_{k,\text{final}} \;=\; n_{k,0} + \Delta n_k \;=\; n_{k,0} + \nu_k\,\xi \] \[ \xi \;=\; \frac{n_{k,\text{final}} - n_{k,0}}{\nu_k} \quad\text{(from any one species \(k\))} \]

Tabular method (Initial–Change–Final)

Consider a balanced reaction \( a\,\mathrm{A} + b\,\mathrm{B} \rightarrow c\,\mathrm{C} + d\,\mathrm{D} \). The stoichiometric numbers are \( \nu_{\mathrm{A}}=-a \), \( \nu_{\mathrm{B}}=-b \), \( \nu_{\mathrm{C}}=+c \), \( \nu_{\mathrm{D}}=+d \). Organize amounts in the table below to relate all species to the single extent \( \xi \).

Row	A	B	C	D
Initial	\( n_{\mathrm{A},0} \)	\( n_{\mathrm{B},0} \)	\( n_{\mathrm{C},0} \)	\( n_{\mathrm{D},0} \)
Changes	\( \Delta n_{\mathrm{A}} = -a\,\xi \)	\( \Delta n_{\mathrm{B}} = -b\,\xi \)	\( \Delta n_{\mathrm{C}} = +c\,\xi \)	\( \Delta n_{\mathrm{D}} = +d\,\xi \)
Final	\( n_{\mathrm{A},\text{final}} = n_{\mathrm{A},0} - a\,\xi \)	\( n_{\mathrm{B},\text{final}} = n_{\mathrm{B},0} - b\,\xi \)	\( n_{\mathrm{C},\text{final}} = n_{\mathrm{C},0} + c\,\xi \)	\( n_{\mathrm{D},\text{final}} = n_{\mathrm{D},0} + d\,\xi \)

If the final amount of any one species is known, solve for \( \xi \) directly from its column, e.g. \[ \xi=\frac{n_{\mathrm{C},\text{final}}-n_{\mathrm{C},0}}{c} \quad\text{or}\quad \xi=\frac{n_{\mathrm{A},0}-n_{\mathrm{A},\text{final}}}{a}. \] Once \( \xi \) is known, compute every other final amount using the third row.

How to use the calculator

Enter the reaction (unbalanced is fine — the tool balances it).
Enter the initial amounts \(n_{k,0}\) (mol) for any species you know. Leaving entries blank is treated as zero.
Choose how to obtain \( \xi \):
- Enter \( \xi \) directly, or
- Provide the final amount of one species; the tool uses \( \displaystyle \xi = \frac{n_{\text{final}}-n_0}{\nu} \).
The tool computes \( \Delta n_k = \nu_k\xi \), all final amounts, and the corresponding final masses.

Frequently Asked Questions

What is extent of reaction (xi) in chemistry?

Extent of reaction (xi) is a progress variable measured in moles that indicates how far a reaction has proceeded. It links all species through their stoichiometric numbers nu_k.

How do you calculate xi from one species?

For any species k, use xi = (n_k,final - n_k,0) / nu_k. Reactants have negative nu_k and products have positive nu_k, so the sign is handled by nu_k.

How do you find the change in moles for each species using xi?

Use Delta n_k = nu_k x xi. Once xi is known, every species change follows directly from its stoichiometric number.

Why does the reaction need to be balanced before using the extent method?

Balancing fixes the stoichiometric coefficients, which define nu_k for each species. Without correct nu_k values, xi and the computed mole changes and final amounts would be incorrect.

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