Introduction:

The study of the effect of different parameters like temperature, pressure or composition on the physical state of chemical substances is the subject matter of the phase equilibria. In this, we consider the different feature of chemical equilibria. This signifies:

a) Focusing our attention on the equilibria concerning physical state.

b) Relating the physical equilibria to different parameters like temperature, pressure and composition by employing phase rule.

Definition of the Terms:

In the year 1876, Gibbs proposed a simple relationship between the numbers of phases in equilibrium, the number of components and the number of intensive variables termed as degrees of freedom. Let us define the word phase, component and degrees of freedom.

Phase:

The Phase is a component part of the system which is immiscible by the other parts (example: solid, liquid and gas); a phase might obviously have several chemical constituents, which might or might not be shared by the other phases. The number of phases is symbolized in the relation by 'P'.

The definition as recommended by Gibbs is that a phase is a state of matter which is uniform all through, not only in the chemical composition however as well in the physical state.

Examples:

a) A gas or a gaseous mixture is a single phase as there can't be an interface between one gas and the other. Air for illustration is one phase system; however it is a mixture of numerous gases.

b) A system of completely miscible liquids will exist in one phase merely as far as the liquid phase is concerned. However as each liquid consists of its vapor above, the total number of phases in a system of miscible liquids is two, one for the liquid and the other for the vapor. These two phases are separated via the surface of the solution in the liquid phase.    

c) The system of two immiscible liquids consists of a total of three phases, two for the substances in the liquid state and the other for the vapor phase having vapors of both the liquids.

d) The crystal is a single phase. Different solids having different crystal structures comprising different phases, irrespective of the fact whether they encompass similar chemical composition or not. A mixture of graphite and diamond comprises two phases however both are only allotropic modifications of carbon.

Definition of Number of Components:

By the word component meant that the smallest number of independent variable constituents, taking part in the state of equilibrium, by mean of which the composition of each and every phase can be deduced in the form of chemical equation. For illustration:

A) In the water system:

Ice (s) ↔ Water (l) ↔ Vapor (g)

The chemical composition of all the three states or phases is H₂O. Therefore, it is one component system.

B) The sulphur system comprises of four phases, rhombic, monoclinic, liquid and vapor, the chemical composition of all the phases is 'S'. Therefore, it is one component system.

Degree of freedom or variance:

By the word degree of freedom meant that the minimum number of independently variable factors, like temperature, pressure and composition of phases, which should be randomly specified in order to represent perfectly the condition of a system. For illustration:

A) In case of water system, Ice(s) ↔ Water (l) ↔ Vapor (g), when all the three phases are present in the equilibrium, then no condition require to be specified, as the three phases can be in equilibrium only at specific pressure and temperature. If condition (example: Temperature or pressure is modified, the three phases will not remain in equilibrium and one of the phases disappears.

B)  For a system comprising of water in contact with its vapors:

Water (l) ↔ Vapor (g)

Phase Rule:

Definition of Phase rule:

The number of degrees of freedom of a system in equilibrium is equal to the number of components minus the number of phases plus the constant two (as in the system ice -liquid water- water vapor consisting of the one chemical component water and its three physical phases there are no degrees of freedom and the system can exist at only one temperature and pressure)

The phase rule was introduced by Willard Gibbs. It might be employed to find out the number of thermodynamic variables in a system at equilibrium. The thermodynamic variables are usually T, P and composition. However, the phase rule might be altered to account for pressure differences caused due to osmosis or surface tension; the given equations apply only to systems in which the pressure is uniform. The number of variables that should be fixed must equivalent the number of degrees of Freedom 'F'. The value of 'F' might be computed as:

F = C - P + 2

For a system at equilibrium the phase rule associates:

P = number of phases that coexist, to

C = number of components making up the phases, and

F = degrees of freedom.

Here these three variables are associated in the equation.

This must be remembered that the phase rule can be applied only to systems at equilibrium. The given are physical conditions that are satisfied at true equilibrium conditions.

a) The system is sensitive to changes in the external conditions.

b) Concentrations are independent of the time.

c) Equilibrium is independent of the masses of the system's phases.

d) The similar concentrations are reached in spite of the direction equilibrium is approached.

Phase diagram:

In order to record and imagine the yield of studying the effect of stage variable on a system, diagrams were introduced to exhibit the relationships between the different phases that appear in the system under equilibrium conditions, As such, the diagrams are variously termed as the constitutional diagrams, equilibrium diagrams or phase diagrams. A single-component phase diagram can be simply a one or two-dimensional plot exhibiting the phase change in the substance as temperature and/or pressure change. Most of the diagrams, though, are two or three-dimensional plots explaining the phase relationships in systems made up of two or more components, and these generally contain fields (areas) comprising of mixed-phase fields, and also single-phase fields.

Phase Diagram of Water:

Water is a unique substance in numerous ways. One of such special properties is the fact that solid water (or ice) is less dense than liquid water just above the freezing point. The phase diagram for water is illustrated in the figure shown below:

Fig: Phase Diagram of Water

Observe the one key difference between the general phase diagram and the phase diagram for water. In case of water's diagram, the slope of the line between the solid and liquid states is negative instead of positive. The main reason is that water is an unusual substance in that its solid state is less dense than the liquid state. Ice floats in the liquid water. Thus, a pressure change has the opposite effect on such two phases. When ice is relatively near its melting point, it can be transformed into liquid water via the application of pressure. The water molecules are in reality closer altogether in the liquid phase than they are in the solid phase.

Consider again the water's phase diagram (figure shown above). Notice point 'E', labeled the critical point. What does that signify? At 373.99°C, the particles of water in the gas phase are moving very, very quickly. At any temperature higher than that, the gas phase can't be made to liquefy, no matter how much pressure is exerted to the gas. The critical pressure (P_c) is the pressure that should be applied to the gas at the critical temperature in order to turn it to a liquid. For water, the critical pressure is very high, 217.75 atm. The critical point is the intersection point of the critical temperature and the critical pressure.

Merits of phases rule:

1) This is applicable to both chemical and physical equilibria.

2) It needs no information concerning molecular or micro-structure, as it is applicable to the macroscopic system.

3) This is a convenient process of categorizing equilibrium states in terms of phases, components and degrees of freedom.

4) It assists us to predict the behavior of a system, under dissimilar sets of variables.

5) It points out that various systems having similar degree of freedom behave likewise.

6) It doesn't take into cognizance of either the nature or quantities of component present in the system.

7) It assists in deciding whether beneath a given set of condition:

• Different substances would exist altogether in equilibrium.
• A few substances present would be inter-converted.
• Some of the substances present would be removed.

Limitation of phase rule:

1) This can be applied just for the system in equilibrium. As a result, it is of little value in case of very slow equilibrium state acquiring system.

2) It applies mere to a single equilibrium system: and given no information concerning any other possible equilibria in the system.

3) It needs utmost care in deciding the number of phases existing in the equilibrium sate, as it considers merely the number of phases, instead of their amounts. Therefore, even if a trace of the phase is present, it accounts in the direction of the total number of phases.

4) It limits that all the phases of the system should be present concurrently, under the similar conditions of pressure and temperature.

5) It conditions that liquid and solid phases should not be in finely divided state; or else deviations takes place.

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