---
title: "Chemical Potential and Gibbs Energy That Depends on Composition"
description: "Gibbs energy has been used as a fixed number per reaction. In a mixture it changes as the composition changes, and the partial derivative that describes it, the chemical potential, is what actually dr"
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source: https://lightmysky.com/learn/science/chemical-potential-and-gibbs-energy-that-depends-on-composition-mt_Tdl6K-gFO3.md
retrieved: 2026-09-12
---

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# Chemical Potential and Gibbs Energy That Depends on Composition

Gibbs energy has been used as a fixed number per reaction. In a mixture it changes as the composition changes, and the partial derivative that describes it, the chemical potential, is what actually drives matter from one place or phase to another.

Subject: Science · Area: Chemistry · Ages 20 to 21
Page: https://lightmysky.com/learn/science/chemical-potential-and-gibbs-energy-that-depends-on-composition-mt_Tdl6K-gFO3

## Ready when they can

- Defines chemical potential as the change in Gibbs energy on adding a small amount of one component
- Explains why matter flows from high chemical potential to low, and gives a phase-change example
- Writes the composition dependence for an ideal mixture and derives the entropy of mixing from it
- Shows how the equilibrium constant appears when the chemical potentials of products and reactants are set equal

## Lesson: The push that moves matter around

The activated complex you just met had its own enthalpy and entropy. A whole mixture behaves the same way: its Gibbs energy shifts with composition, so one number cannot describe it. The chemical potential of one component is the change in Gibbs energy when you add a little more of it. Chemists write it mu, and it is a partial molar Gibbs energy.

**Example.** Matter flows from high chemical potential to low. That is why gases mix, salts dissolve, and ice melts into water. When mu of a substance matches in two phases, neither direction wins and the phases sit in equilibrium.

For an ideal mixture, each chemical potential slides with the log of its fraction. Mixing raises the entropy because each component gains room, and that entropy of mixing drags the potentials down. So two miscible liquids mix on their own even when no heat is released.

Set the potentials of products and reactants equal at equilibrium and the equilibrium constant drops out. A big fall in Gibbs energy means a large constant. Note that a positive standard value describes one composition only: change the mixture and the sign can flip.

**Recap.** Chemical potential tracks how Gibbs energy answers to composition, and matter always slides from high mu to low.

## Practice

8 questions on this page, each with its working shown.

## Needs first

- [Transition State Theory and the Eyring Equation](https://lightmysky.com/learn/science/transition-state-theory-and-the-eyring-equation-mt_JVjDMcXds1)
- [Free Energy and Whether a Reaction Is Feasible](https://lightmysky.com/learn/science/free-energy-and-whether-a-reaction-is-feasible-mt_o1kZgBYWoM)
- [Partial Derivatives](https://lightmysky.com/learn/mathematics/partial-derivatives-mt_tu11fd9Xk9)

## Opens up

- [Self-Assembly: Templates, Reversibility and Error Correction](https://lightmysky.com/learn/science/self-assembly-templates-reversibility-and-error-correction-mt_6y_SNmqwYX)
- [Real Gases, Fugacity and Activity](https://lightmysky.com/learn/science/real-gases-fugacity-and-activity-mt_HzRqV-KXfN)
- [Phase Diagrams, the Clapeyron Equation and the Phase Rule](https://lightmysky.com/learn/science/phase-diagrams-the-clapeyron-equation-and-the-phase-rule-mt_U-zj6r4WFM)