#### -Fundamentals: Thermodynamics

##### 1.2 Binary system representation

Liquid-vapor equilibrium of binary system can be graphically represented in several ways. The most common are: temperature-composition; pressure-composition; vapor-liquid mole fractions and enthalpy-composition.

One of the most convenient representation is the graph of mole fraction in gas phase versus mole fraction in liquid phase, y versus x. Generally x and y refer to the more volatile component.
In this case, the equilibrium curve is represented either at constant temperature or at constant pressure. In the latter case, the temperature changes along the curve as it is shown in the figure here below.

All the points on the equilibrium curve represent two phases (liquid and vapor) in equilibrium. All the other points in the diagram represent also two phases, but not at equilibrium.

An other useful diagram is the temperature versus composition diagram (at constant pressure). It is obtained when the above represented data on compositions are reported versus temperature. As you can see here below, actually two curves are present, respectively for the mole fraction in the liquid phase (x versus temperature) and for the mole fraction in the gas phase (y versus temperature).

Three different zones can be distinguished: a region at higher temperatures where only vapor is present; a region at lower temperatures where only liquid is present; and a biphasic region where both vapor and liquid are present at equilibrium.

Moving from a higher temperature, e.g. T1, where only vapor exists, to the biphasic region at temperature T2, a certain amount of vapor condensates.

The two phases, liquid and vapor, coexist at equilibrium with a concentration of the more volatile component respectively on liquid and vapor phase, which can be read on the liquid equilibrium line and on the gas equilibrium line.

Exactly the same type of curves is obtained in case of plotting composition versus pressure at constant temperature. This last type of diagrams is very useful for equilibrium description of ideal and non-ideal vapor-liquid systems.

Finally let's have a look to the enthalpy-composition representation. Again there are two curves: one for the saturated liquid and one for the saturated vapor.

Two points in the two curves can be connected by an equilibrium line called tie-lines . The tie-lines are curves at constant temperature because of the equilibrium condition.
The region in between the two curves is a biphasic region, where liquid and vapor coexists.

For ideal liquid mixtures:

h = h [x, T] = S xi hi[T] = S xi Cpi(T - Tref)

which for a binary system becomes:

h = xA CpA(T - Tref) + xB CpB(T - Tref)

For ideal vapor mixtures:

H = H [y, T] = S yi Hi[T] = S yi [Cvpi(T - Tref) + li]

which for a binary system becomes:

H = yA [CvpA(T - Tref) + lA] + yB [CvpB(T - Tref) + lB]

Click here to see the diagram enthalpy-composition for EtOH-Water.

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