What is gibbs-duhem equation?

The Gibbs-Duhem equation is an important thermodynamic identity relating the thermodynamic properties of a system. It states that for a single-phase system in equilibrium,

∑xi dμi = 0

where μi is the chemical potential of the i-th component of the system and xi is its mole fraction. In other words, the sum of all the products of the mole fractions and their corresponding chemical potentials is equal to zero.

This equation is particularly useful in the study of multi-component systems, where it allows us to infer the behavior of different components based on the behavior of the system as a whole. It also helps to describe the relationship between different thermodynamic properties, such as changes in enthalpy, entropy, and free energy, in a given system.

In engineering, the Gibbs-Duhem equation is often used to calculate the behavior of chemical reactions, such as in the design of chemical processes and synthesis of new materials.