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When both temperature and pressure are held constant, and the number of particles is expressed in moles, the chemical potential is the partial molar Gibbs free energy. [1] [2] At chemical equilibrium or in phase equilibrium, the total sum of the product of chemical potentials and stoichiometric coefficients is zero, as the free energy is at a ...
In thermodynamics, the Gibbs free energy (or Gibbs energy as the recommended name; symbol ) is a thermodynamic potential that can be used to calculate the maximum amount of work, other than pressure–volume work, that may be performed by a thermodynamically closed system at constant temperature and pressure.
The Gibbs−Duhem equation applies to homogeneous thermodynamic systems. It does not apply to inhomogeneous systems such as small thermodynamic systems, [2] systems subject to long-range forces like electricity and gravity, [3] [4] or to fluids in porous media. [5] The equation is named after Josiah Willard Gibbs and Pierre Duhem.
This means that the partial molar Gibbs free energy and the chemical potential, one of the most important properties in thermodynamics and chemistry, are the same quantity. Under isobaric (constant P) and isothermal (constant T ) conditions, knowledge of the chemical potentials, (,,,), yields every property of the mixture as they completely ...
Molar Gibbs free energy is commonly referred to as chemical potential, symbolized by , particularly when discussing a partial molar Gibbs free energy for a component in a mixture. For the characterization of substances or reactions, tables usually report the molar properties referred to a standard state .
Chemical potential is the partial molar free energy. The potential, μ i, of the ith species in a chemical reaction is the partial derivative of the free energy with respect to the number of moles of that species, N i:
The pure component's molar volume and molar enthalpy are equal to the corresponding partial molar quantities because there is no volume or internal energy change on mixing for an ideal solution. The molar volume of a mixture can be found from the sum of the excess volumes of the components of a mixture:
[4]: 215 In other words, the temperature, pressure and molar Gibbs free energy are the same between the two phases when they are at equilibrium. An equivalent, more common way to express the vapor–liquid equilibrium condition in a pure system is by using the concept of fugacity. Under this view, equilibrium is described by the following equation: