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When pressure and temperature are variable, only of components have independent values for chemical potential and Gibbs' phase rule follows. 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 ...
The relative activity of a species i, denoted a i, is defined [4] [5] as: = where μ i is the (molar) chemical potential of the species i under the conditions of interest, μ o i is the (molar) chemical potential of that species under some defined set of standard conditions, R is the gas constant, T is the thermodynamic temperature and e is the exponential constant.
The concept of thermodynamic potentials was introduced by Pierre Duhem in 1886. Josiah Willard Gibbs in his papers used the term fundamental functions. Effects of changes in thermodynamic potentials can sometimes be measured directly, while their absolute magnitudes can only be assessed using computational chemistry or similar methods. [3]
Josiah Willard Gibbs Born (1839-02-11) February 11, 1839 New Haven, Connecticut, U.S. Died April 28, 1903 (1903-04-28) (aged 64) New Haven, Connecticut, U.S. Nationality American Alma mater Yale College (BA, PhD) Known for List Statistical mechanics Chemical thermodynamics Chemical potential Cross product Dyadics Exergy Principle of maximum work Phase rule Phase space Physical optics Physics ...
Differentiating the Euler equation for the internal energy and combining with the fundamental equation for internal energy, it follows that: = + which is known as the Gibbs-Duhem relationship. The Gibbs-Duhem is a relationship among the intensive parameters of the system.
Chemical potentials can be used to explain the slopes of lines on a phase diagram by using the Clapeyron equation, which in turn can be derived from the Gibbs–Duhem equation. [9] They are used to explain colligative properties such as melting-point depression by the application of pressure. [10]
Chemical thermodynamics is the study of the interrelation of heat and work with chemical reactions or with physical ... and sometimes the Gibbs-Duhem equation is used.
The Gibbs adsorption isotherm for multicomponent systems is an equation used to relate the changes in concentration of a component in contact with a surface with changes in the surface tension, which results in a corresponding change in surface energy. For a binary system, the Gibbs adsorption equation in terms of surface excess is