text: For a two-phase system consisting of the  and  phase in equilibrium with a surface  dividing the phases, the total Gibbs free energy of a system can be written as:
  where  is the Gibbs free energy.
  The equation of the Gibbs Adsorption Isotherm can be derived from the “particularization to the thermodynamics of the Euler theorem on homogeneous first-order forms.”  The Gibbs free energy of each phase , phase , and the surface phase can be represented by the equation:
  where  is the internal energy,  is the pressure,  is the volume,  is the temperature,  is the entropy, and  is the chemical potential of the -th component.
  By taking the total derivative of the Euler form of the Gibbs equation for the  phase,  phase and the surface phase:
  where  is the area of the dividing surface, and  is the surface tension.
  For reversible processes, the first law of thermodynamics requires that:
  where  is the heat energy and  is the work.
  Substituting the above equation into the total derivative of the Gibbs energy equation and by utilizing the result  is equated to the non-pressure volume work when surface energy is considered:
  by utilizing the fundamental equation of Gibbs energy of a multicomponent system:
  The equation relating the  phase,  phase and the surface phase becomes:
  When considering the bulk phases ( phase,  phase), at equilibrium at constant temperature and pressure the Gibbs–Duhem equation requires that:
  The resulting equation is the Gibbs adsorption isotherm equation:
  The Gibbs adsorption isotherm is an equation which could be considered an adsorption isotherm that connects surface tension of a solution with the concentration of the solute.
  For a binary system containing two components the Gibbs Adsorption Equation in terms of surface excess is: