13: Multi-Component Phase Diagrams

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We now move from studying 1-component systems to multi-component ones. Systems that include two or more chemical species are usually called solutions. Solutions are possible for all three states of matter:

Type:	Solvent	Solute	Examples:
Solid solutions	Solid	Solid	Alloys: brass, bronze
	Solid	Liquid	Dental amalgam
	Solid	Gas	Hydrogen stored in Palladium
Liquid solutions	Liquid	Solid	Saltwater, bleach
	Liquid	Liquid	Alcoholic beverages, vinegar
	Liquid	Gas	Carbonated drinks
Gaseous solutions	Gas	Solid	Smoke, smog
	Gas	Liquid	Aerosols and perfumes
	Gas	Gas	Air

The number of degrees of freedom for binary solutions (solutions containing two components) is calculated from the Gibbs phase rules at \(f=2-p+2=4-p\). When one phase is present, binary solutions require \(4-1=3\) variables to be described, usually temperature (\(T\)), pressure (\(P\)), and mole fraction (\(y_i\) in the gas phase and \(x_i\) in the liquid phase). Single-phase, 1-component systems require three-dimensional \(T,P,x_i\) diagram to be described. When two phases are present (e.g., gas and liquid), only two variables are independent: pressure and concentration. Thus, we can study the behavior of the partial pressure of a gas–liquid solution in a 2-dimensional plot. If the gas phase in a solution exhibits properties similar to those of a mixture of ideal gases, it is called an ideal solution. The obvious difference between ideal solutions and ideal gases is that the intermolecular interactions in the liquid phase cannot be neglected as for the gas phase. The main advantage of ideal solutions is that the interactions between particles in the liquid phase have similar mean strength throughout the entire phase. We will consider ideal solutions first, and then we’ll discuss deviation from ideal behavior and non-ideal solutions.

13.1: Raoult’s Law and Phase Diagrams of Ideal Solutions
The behavior of the vapor pressure of an ideal solution can be mathematically described by a simple law established by François-Marie Raoult (1830–1901). Raoult’s law states that the partial pressure of each component, i, of an ideal mixture of liquids, Pi, is equal to the vapor pressure of the pure component P∗i multiplied by its mole fraction in the mixture xi.
13.2: Phase Diagrams of Non-Ideal Solutions
Non-ideal solutions follow Raoult’s law for only a small amount of concentrations. The typical behavior of a non-ideal solution with a single volatile component is reported in the PxB plot in Figure 13.2.1.
13.3: Phase Diagrams of 2-Components/2-Condensed Phases Systems
This section discusses the equilibria between two condensed phases: liquid/liquid, liquid/solid, and solid/solid. These equilibria usually occur in the low-temperature region of a phase diagram (or high pressure). Three situations are possible, depending on the constituents and concentration of the mixture.