# vapor liquid phase equilibrium

Phase is a condition or state of a system. Phase equilibrium is a condition in which the conditions and properties of a system related or in static equivalence. The condition system does not change with time. A system is said to exist in an equilibrium state if there is no tendency to deviate from a particular system condition by heat and mass transfer across the system boundary. In material transfer between system boundaries, continues till equilibrium is established. Therefore equilibrium establishes the following processes:

• Heterogeneous phase equilibrium  between system
• Displacement of a phase boundary
• Mass transfer across system boundary
• Determination of phase composition under known system condition.

In the study of thermodynamics; phase equilibrium is of great importance even to science field at large. In the field of chemical engineering, manufacturing of material involves equilibrium conditions. Biological science study involves phase equilibrium in terms of respiration. Processes such as; distillation, adsorption, leaching, gas chromatography etc. example, in a distillation colunm, assumption of equilibrium condition that exist between the vapor and liquid on a plate. It is also importance in design and analysis of reactor.

# types of system

Homogeneous system: this is a state in which the system has one phase (gas, solid & gas). It could exist as open or closed.

homogeneous closed system does not transfer materials to the surrounding. It has a uniform composition. The system properties are independent of time. The heat and entropy are related thus:

dH=Tds+VdP

For homogeneous open system, there is an exchange of material with the surrounding.

Heterogeneous system: this is a multi component phase system. The relations are summarized under closed system:

T(1)=T(2)=…T(π)

P(1)=P(2)=…P(π)

µ(1)(2)(π)

µm(1)m(2)m(π)

## phase rule ( Duhem equation)

This can be called Gibbs-Duhem equation. It is used for non reacting system. Considering the homogeneous and heterogeneous; the internal equilibrium is described by it’s temperature, pressure and chemical potential. The phase rule is use to determine the degree of freedom of a chemical species. The degree of freedom is the number of independent variables that is arbitrarily fixed so as to establish the intensive state of that system.

The phase rule is given buy:

F=2-π+N

Duhem equation is given by:

Sdt-vdp+ summation=0

The above relation is important in thermodynamics studies

### Azeotropes

Azeotropes are constant boiling mixtures. It is condition in which the vapor and liquid has the composition at the a particular temperature. The equilibrium temperature is brought about by the variation of bubble and dew point. The Azotropic temperature is the same until the entire liquid vaporizes.

PHASE DIAGRAM

Phase diagram shows the relationship and coexistence between a vapor and liquid phases. This is a practical application of Duhem equation and phase rule. Consider the binary system represented below. The component of liquid is xi and vapor yi  as shown:

When a binary mixture (benzene and toluene) is heated in a closed system and at atmospheric pressure (constant); the plot of the more volatile against temperature gives the above graph along (ABCJ). The vapor component is plotted as (ADEJ).  The line LN represents the tie line. The point C represents the bubble point. Bubble point is the temperature at which the first vapor drops on heating. The point D represents the dew point. Dew point is the temperature at which the first liquid drops on condensation.

Therefore; an increase in temperature reduces the less volatile component. As the temperature increases from T3,T2 T1; the vapor component becomes richer while the liquid component reduces. A close observation shows that the composition of vapor and liquid are of alternating; that is if x1 is 0.4 y1 is 0.6. But at temperature T΄ and line LMN, there was no alternation. Therefore the proportion of liquid to vapor is given as

$\frac{liquid}{vapor}=\frac{MN}{ML}$

This is normally seen in distillation processes .

Since increase in pressure decreases temperature, but increases the liquid composition, the graph below is obtained.

The relationship was given by Dalton law of partial pressure and Henry’s law

PA=YAP          PA=XAA     PA=нX

References

J.M. Smith, H.C. Van Ness, M.M. Abbott, chemical engineering thermodynamics. MCGraw-Hill international edition. 2001

K.V. Narayanan, chemical engineering thermodynamics. Second edition; PHI learning private limited 2013

M.P.John, N.L.Rudiger, A.G Edumundo; molecular thermodynamics of fluid phase equilibra. Prentice Hall PTR 1999