Phases, Phase Rule, and Binary Systems

For a system in thermodynamic equilibrium, J.W. Gibbs in 1875 derived the fundamental phase rule that relates the number of independent components, N, the number of coexisting phases, P, and the number of degrees of freedom, F, of the system by the following equation  

The number of independent components, N, is the minimum number of chemical species necessary to depict the existing phases completely. It is mathematically given as the difference of the sum of chemical individuals in the system and the sum of restrictive conditions such as chemical equation, electroneutrality, and stoichiometry. Examples with focus on solution equilibria are compiled in Table 3.1. On the basis of the number of independent components, a system is called to be a unary, binary, ternary, quaternary, or quinary system with N= 1,2,. . . , 5. For example, the 

The number of degrees of freedom, F, characterizes the variance of the system in the given state of equilibrium. It is defined as the number of independent variables (temperature T, pressure p, and composition x) that can arbitrarily be verified without changing the number of phases present. The number 2 in Equation 3.1 relates to the physical variables pressure and temperature. 

The phase rule is universally valid for systems in thermodynamic equilibrium and establishes the theoretical basis for all phase diagrams. 

A phase diagram graphically represents (in two or three dimensions) the equilibria between various phases of a system in a wide range of temperature, pressure, and concentration/composition. It specifies the equilibrium conditions (T p, and x) and the corresponding phases present at this state. Thus, in case of SLE, the phase diagram also tells about the solid phases occurring in a system, such as polymorphs, solvates, or intermediate compounds. 

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