Entropy of mixing

Entropy of Mixing

Entropy of mixing is a concept in thermodynamics that quantifies the increase in entropy when two or more different substances are mixed. This phenomenon is a fundamental aspect of the second law of thermodynamics, which states that the total entropy of an isolated system can never decrease over time.

Definition

The entropy of mixing can be defined for both ideal and non-ideal mixtures. For an ideal mixture, the entropy change upon mixing is solely due to the increase in the number of possible microstates of the system.

Ideal Mixtures

For an ideal mixture of two substances, A and B, the entropy of mixing (ΔS_mix) can be calculated using the formula: \[ \Delta S_{\text{mix}} = -nR \left( x_A \ln x_A + x_B \ln x_B \right) \] where:

• \( n \) is the total number of moles,
• \( R \) is the universal gas constant,
• \( x_A \) and \( x_B \) are the mole fractions of substances A and B, respectively.

Non-Ideal Mixtures

In non-ideal mixtures, interactions between different molecules must be taken into account. The entropy of mixing in such cases is more complex and requires additional terms to account for these interactions.

Applications

The concept of entropy of mixing is crucial in various fields such as chemistry, chemical engineering, and materials science. It helps in understanding processes like solution formation, alloy creation, and polymer blending.

Related Concepts

• Gibbs free energy
• Enthalpy of mixing
• Phase diagram
• Chemical potential

See Also

• Second law of thermodynamics
• Statistical mechanics
• Thermodynamic system
• Ideal gas law