Entropy Change of Reaction

General Chemistry • Spontaneous Change Entropy and Gibbs Energy

Written by STEM Calculators Team Published October 25, 2025 Updated February 24, 2026

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Theory — Reaction Entropy from Standard Molar Entropies

At a fixed temperature (usually \(298.15\ \mathrm{K}\)), the standard reaction entropy, \( \Delta_r S^{\circ} \), is obtained from the absolute standard molar entropies of the participating species, \(S^{\circ}\) (units \( \mathrm{J\,mol^{-1}\,K^{-1}} \)), by a Hess–law style sum over the balanced chemical equation. For a reaction written with stoichiometric coefficients \( \nu_i \) (positive for products, negative for reactants),

\[ \begin{aligned} \Delta_r S^{\circ} &= \sum_i \nu_i\, S_i^{\circ} \\ &= \sum_{\text{products}} \nu\, S^{\circ} \;-\; \sum_{\text{reactants}} \nu\, S^{\circ} \end{aligned} \]

Unlike enthalpy, there is no “standard entropy of formation”. We use absolute \(S^{\circ}\) values (Third Law) that depend on temperature and phase.

Using the relation

Balance the reaction first; the coefficients are the \(\nu\) used in the sums.
Insert \(S^{\circ}\) values for each species in its stated phase at the same temperature (typically \(298.15\ \mathrm{K}\)).
The result \(\Delta_r S^{\circ}\) is per the reaction as written (i.e., per “mole of reaction”).

Solving for an unknown \(S^{\circ}\)

If one species’ \(S^{\circ}\) is unknown but \(\Delta_r S^{\circ}\) and the other \(S^{\circ}\) values are known, rearrange the same equation. For a chosen unknown species “\(u\)” with coefficient \(\nu_u\),

\[ \begin{aligned} \nu_u\,S_u^{\circ} &= \Delta_r S^{\circ} - \sum_{\substack{\text{products}\\ j\neq u}} \nu_j S_j^{\circ} + \sum_{\text{reactants}} \nu\, S^{\circ} \\[6pt] S_u^{\circ} &= \frac{1}{\nu_u}\! \left( \Delta_r S^{\circ} - \sum_{\substack{\text{products}\\ j\neq u}} \nu_j S_j^{\circ} + \sum_{\text{reactants}} \nu\, S^{\circ} \right) \end{aligned} \]

Sign and trends

\(\Delta_r S^{\circ} > 0\) typically when the reaction increases the number of gas molecules, generates gaseous products from condensed phases, or increases disorder.
\(\Delta_r S^{\circ} < 0\) when gas moles decrease or order increases (e.g., association reactions).

Worked template

\[ \begin{aligned} \text{Balanced:}\quad &a\,\mathrm{A} + b\,\mathrm{B} \;\longrightarrow\; c\,\mathrm{C} + d\,\mathrm{D} \\ \Delta_r S^{\circ} &= c\,S^{\circ}(\mathrm{C}) + d\,S^{\circ}(\mathrm{D}) \;-\; \big[a\,S^{\circ}(\mathrm{A}) + b\,S^{\circ}(\mathrm{B})\big] \end{aligned} \]

Notes & pitfalls

\(S^{\circ}\) values are absolute at the stated temperature and standard state (usually \(1\ \mathrm{bar}\)); they are generally non-zero even for elements.
Always match the phase (g, l, s, aq) of the species to the tabulated \(S^{\circ}\).
Report units: \(\Delta_r S^{\circ}\) in \( \mathrm{J\,K^{-1}} \) per reaction as written.

Frequently Asked Questions

How do you calculate the entropy change of a reaction from standard molar entropies?

Use Delta_r S° = sum(nu x S°) for products minus sum(nu x S°) for reactants, using the balanced equation coefficients nu. The S° values are absolute standard molar entropies (Third Law), not entropies of formation.

Do elements in their standard state have S° equal to zero?

No. Standard molar entropy S° is generally non-zero even for elements in their standard state because it is an absolute entropy referenced to 0 K.

Why do I need a balanced chemical equation for Delta_r S°?

The stoichiometric coefficients determine how many moles of each species contribute to the entropy sum. If the equation is not balanced, the computed Delta_r S° will not correspond to the reaction as written.

Can I include charges, electrons, or state symbols in the reaction entry?

State symbols are optional and may be ignored during parsing, but the phase still matters for choosing the correct S° value. Charges and electrons are not supported for this reaction entry format.

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