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Chemical Potential: Difference between revisions

Created page with "= Chemical Potential: Definition and Mathematical Representation = == Introduction == The '''chemical potential''' is a fundamental thermodynamic quantity that plays a crucial role in understanding how particles and energy distribute in physical systems. It is particularly significant in the study of phase equilibria, chemical reactions, and processes involving the transfer of matter. In essence, the chemical potential represents the change in a system's internal energ..."
 
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In thermodynamics, the chemical potential ''μ'' of a component in a system is defined as the partial derivative of the system's Gibbs free energy ''G'' with respect to the number of moles ''nᵢ'' of the component, at constant temperature ''T'' and pressure ''P'':
In thermodynamics, the chemical potential ''μ'' of a component in a system is defined as the partial derivative of the system's Gibbs free energy ''G'' with respect to the number of moles ''nᵢ'' of the component, at constant temperature ''T'' and pressure ''P'':


:<math>\mu_i = \left( \frac{\partial G}{\partial n_i} \right)_{T, P, n_{j \ne i}}</math>
:μᵢ = (∂G/∂nᵢ) at constant T, P, and nⱼ (j ≠ i)


Alternatively, depending on the thermodynamic potential being used, chemical potential can also be defined using internal energy ''U'', enthalpy ''H'', or Helmholtz free energy ''A''. For example, in terms of internal energy:
Alternatively, depending on the thermodynamic potential being used, chemical potential can also be defined using internal energy ''U'', enthalpy ''H'', or Helmholtz free energy ''A''. For example, in terms of internal energy:


:<math>\mu_i = \left( \frac{\partial U}{\partial n_i} \right)_{S, V, n_{j \ne i}}</math>
    μᵢ = (∂U/∂nᵢ) at constant S, V, and nⱼ (j ≠ i)


Here,  
Here,  
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The chemical potential can be thought of as the "escaping tendency" of a species from a phase or a system. If two phases or systems are in equilibrium, the chemical potential of each component must be the same in both:
The chemical potential can be thought of as the "escaping tendency" of a species from a phase or a system. If two phases or systems are in equilibrium, the chemical potential of each component must be the same in both:


:<math>\mu_i^{(1)} = \mu_i^{(2)}</math>
    μᵢ^(1) = μᵢ^(2)
 


This condition ensures no net flow of particles between the phases, indicating chemical equilibrium.
This condition ensures no net flow of particles between the phases, indicating chemical equilibrium.
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