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Invariant points

According to Gibbs phase rule, a system with C chemically independent components and P phases in equilibrium has F=C-P+2 degrees of freedom. For a system consisting of one pure species the phase rule is F=3-P. If two phases are in equilibrium with each other in a one-component system, the system has one degree of freedom. The system is univariant. 

Pure water boils at 100°C if the pressure is one atmosphere. If the pressure is lower than one atmosphere, pure water will boil at a temperature below 100°C. If the pressure is higher than one atmosphere, pure water will boil at a temperature higher than 100°C. A one-component system consisting of water vapor in equilibrium with liquid water has only one degree of freedom. The pressure OR the temperature can be fixed. Fixing one will automatically determine the other.

At the triple point of water ice, water, and steam are in equilibrium. According to the phase rule, a one component system has no degrees of freedom when three phases are in equilibrium (F=0).The system is invariant. The triple point of water is at 273.16 K and 612 Pa.

An aqueous solution of a pure salt contains three species: water, cations and anions. Still there are only two chemically independent components as the charge of the cations has to be balanced with an equivalent charge of the anions. The solution is therefore considered a binary solution, a solution of two chemically independent components. The phase rule is F=4-P for this system. An invariant point in a binary system thus is a point where 4 phases are in equilibrium (two salts, liquid, and vapor). In a ternary system 5 phases are in equilibrium in an invariant point.