Definition:
Chemical potential (μ\muμ) is the measure of the change in the free energy of a system when an additional particle is introduced, while keeping temperature, pressure, and other particles constant. It determines the direction of mass transfer in a system and plays a crucial role in phase equilibrium, chemical reactions, and thermodynamics.
Mathematical Representation:
The chemical potential is mathematically expressed as:μ=(∂G∂n)T,P\mu = \left( \frac{\partial G}{\partial n} \right)_{T, P}μ=(∂n∂G)T,P
where:
- GGG is the Gibbs free energy,
- nnn is the number of particles (or moles) of the substance,
- TTT is the temperature,
- PPP is the pressure.
Alternatively, in terms of Helmholtz free energy (FFF):μ=(∂F∂n)T,V\mu = \left( \frac{\partial F}{\partial n} \right)_{T, V}μ=(∂n∂F)T,V
where:
- FFF is the Helmholtz free energy,
- VVV is the volume.
In an ideal gas, the chemical potential is given by:μ=μ0+RTlnPP0\mu = \mu^0 + RT \ln \frac{P}{P^0}μ=μ0+RTlnP0P
where:
- μ0\mu^0μ0 is the standard chemical potential,
- RRR is the universal gas constant,
- TTT is the temperature in Kelvin,
- PPP is the partial pressure of the gas,
- P0P^0P0 is the reference pressure.
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