Advanced Topic 406 of 1102 Thermodynamics & Energetics
Entropy of Mixing
Mixing substances increases entropy and drives spontaneous dissolution of ideal solutions.
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In-depth explanation of Entropy of Mixing
Entropy of mixing is the increase in entropy that results when different substances are combined, because the particles gain access to a larger number of arrangements. For an ideal mixture of gases, the entropy change is delta S equals minus n R times the sum of x_i times ln x_i, where x_i is the mole fraction of each component. This quantity is always positive, which means mixing is favored by entropy even when no heat is exchanged. It explains why gases and miscible liquids mix spontaneously, and why the Gibbs energy of mixing is negative for ideal solutions. The effect matters most when the components have no strong energetic preference for one another.
Going deeper: Entropy of Mixing
Key ideas: Use delta S mix equals minus R times the sum of n_i ln x_i. It is always positive for ideal mixing since mole fractions are below one. Delta H mix is zero for ideal solutions, so delta G mix equals T times minus delta S mix and is negative.
Common mistakes and connections: Mixing is not always spontaneous in real systems, because strongly unfavorable enthalpy can outweigh entropy, as in oil and water. Using concentrations instead of mole fractions is a typical error. The idea explains ideal gas mixing and ideal solution behavior.
Visualization of Entropy of Mixing
Two gases separated by a barrier mix spontaneously; the mixed state has vastly more arrangements, so entropy rises. The interactive lesson shows this as a live animation or chart.
Worked example and use case
Mixing 1 mol of helium with 1 mol of argon, both ideal gases at the same temperature and pressure, gives delta S equal to 2R ln 2, about 11.5 J/K.
Frequently asked questions about Entropy of Mixing
What is Entropy of Mixing?
Mixing substances increases entropy and drives spontaneous dissolution of ideal solutions.
Is Entropy of Mixing a beginner, intermediate or advanced topic?
Entropy of Mixing is a advanced topic in Thermodynamics & Energetics. It builds on beginner and intermediate topics, so review those first if needed.
What should I learn before Entropy of Mixing?
Study these earlier topics in Thermodynamics & Energetics first: Hess's Law Cycle Diagram, Enthalpy Level Diagram, Activation Energy Profile.
What comes after Entropy of Mixing?
The next topics in Thermodynamics & Energetics are Entropy and the Arrow of Time and Heat Death Concept.
Can I practise Entropy of Mixing with quizzes?
Yes. The interactive lesson includes a self-check question on Entropy of Mixing, and the Thermodynamics & Energetics quiz draws on every topic in this area.
Where Entropy of Mixing fits in Thermodynamics & Energetics
Entropy of Mixing is topic 78 of 91 in Thermodynamics & Energetics.