Triple point ‘A’ (96.6°C and 0.006 mm Hg) Phase equilibrium is the study of the equilibrium which exists between or within different states of matter namely solid, liquid and gas. Equilibrium is defined as a stage when chemical potential of any component present in the system stays steady with time. Phase is a region where the intermolecular interaction is spatially uniform or in other words physical and chemical properties of the system are same throughout the region. Within the same state, a component can exist in two different phases such as allotropes of an element. Also, two immiscible compounds in same liquid state can coexist in two phases. Phase equilibrium has wide range of applications in industries including production of different allotropes of carbon, lowering of freezing point of water by dissolving salt (brine), purification of components by distillation, usage of emulsions in food production, pharmaceutical industry etc. Solid-solid phase equilibrium has a special place in metallurgy and is used to make alloys of different physical and chemical properties. For instance, melting point of alloys of copper and silver is lower than melting point of either copper or silver.
2. Phase Rule:
Gibbs' phase rule was proposed by Josiah Willard Gibbs in his landmark paper titled On the Equilibrium of Heterogeneous Substances, published from 1875 to 1878. The rule applies to non-reactive multi-component heterogeneous systems in thermodynamic equilibrium and is given by the equality.
The number of degrees of freedom is the number of independent intensive variables, i.e. the largest number of thermodynamic parameters such as temperature or pressure that can be varied simultaneously and arbitrarily without determining one another. An example of one-component system is a system involving one pure chemical, while two-component systems, such as mixtures of water and ethanol, have two chemically independent components, and so on. Typical phases are solids, liquids and gases.
3. Explanation of the terms used in Phase Rule
Before studying the phase rule, it is necessary to explain the meaning of phase, component and degree of freedom.
Phase: The homogenous, physically distinct and mechanical separable parts of the heterogeneous system in equilibrium are called phases.
There are three phases in equilibrium state two solids and one is gas (CO2), water system can be expressed as
In this system there are three phases viz solid, liquid and vapours.
Component: In a heterogeneous system, in equilibrium the minimum number of variables which are necessary to explain the chemical composition of a phase, by a chemical equation, is called component, the meaning of component can be understood by taking following examples:
(a) Ice-water-vapours system
This system has three phases i.e. solid (ice) liquid (water) and gas (vapour). Chemical composition of each phase can be expressed by H2O in the form of chemical equation.
Thus water system is a one component system.
(b) When solid NH4Cl is heated in a closed vessel, following equilibrium establishes:
This system has two phases i.e. solid NH4Cl and mixture of gases NH3 and HCl. Here, although system has three components, but chemical composition of both phases can be expressed by single component i.e. NH4Cl. Since NH3 and HCl are in equimolar ratio
NH4Cl(s) = NH4Cl
NH3(g) + HCl(g) = NH4Cl
Thus, this system is also a one component system.
Note: It some additional amount of either NH3(g) or HCl(g) is added in this system at equilibrium then each phase can be not expressed by NH4Cl, then one more component will be required and number of components will be two in the system.
(c) When solid CaCO3 is heated in a closed vessel, following heterogeneous equilibrium establishes:
This system consists of three phases i.e. solid CaCO3, solid CaO and gaseous CO2. Although system has three components but they are not independent of each other. Any of these two can be independently variable. Thus out of three, two components may be selected to express the composition of any phase. Thus number of components in this system are two
(i) When CaCO3 and CaO are taken as components
CaCO3 + 0CaO
CaCO3 + CaO
CaCO3 – CaO
(ii) When CaO and CO2 are taken as components
CaCO3 + 0CO2
CaCO3 – CO2
CaCO3 + CO2
Therefore, minimum number of components which are required to express any phase is two and the system is bi-component system
(d) Sodium Sulphate-water system may have different phases as Na2SO4.7H2O, Na2SO4.10H2O, Na2SO4 solution, ice, vapurs etc. Any phase can be expressed by chemical formulae of Na2SO4 and H2O
Therefore it is also a two component system.
system also the number of components are two. Number of components may also be calculated by the following formula
When components do not ionize
C = C’ – m
Where C = number of components
C’ = total number of undissociated components
m = Number of chemical equations which correlate undissociated species with each other
Degree of Freedom: The degree of freedom or variance of a system is defined as the smallest number of independent variables such as pressure, temperature and concentration that must be specified in order to describe completely the state of a system.
Following examples will illustrate the meaning of degree of freedom in a better may:
(i) A system aqueous solution of KCl has two degrees of freedom i.e. temperature and composition (Concentration of solution). If the solution is saturated, then only one variable temperature is necessary to express the system. Thus saturated solution of KCl is monovarient and unsaturated solution is bivariant.
(b) Let there be a gas enclosed in a closed chamber. Two variables temperature and pressure are required to express this system. Third variable (composition) is not required since container has only one gas. If system has a mixture of gases then third variable i.e. composition is also required and system becomes a trivariant system.
4. Advantages of Phase Rule
(i) It gives a simple method of classifying equilibrium states of system.
(ii) Physical as well as chemical equilibria and can be studied by this rule.
(iii) The phase rule is applicable to macroscopic systems. Therefore, it is not necessary to take into account about their molecular structure.
(iv) It confirms that the different systems having the same number of degree of freedom behave in like manner.
(v) Phase rule, takes no account of nature of the reactant or products in phase reactions.
(vi) It predicts the behaviour of system when subjected in the variables such as pressure, temperature and volume.
5. Limitations of Phase Rule:
(i) In phase rule only three variables temperature, pressure and composition are considered. Phase rule does not consider the variable like electric, magnetic and radiation influence.
(ii) As the phase rule is applicable to a single equilibrium state, it does not tell about the number of other equilibrium possible in the system.
(iii) Gravitation force is not considered in phase rule.
(iv) No liquid or solid phases should be finely divided otherwise their vapour pressure and surface tension will differ from their normal values.
(v) Certain limitations are to be imposed on phase rule in some circumstances. In this state it is called phase rule under restricted condition.
6. Phase Diagram
A phase-diagram in physical chemistry, engineering, mineralogy, and materials science is a type of chart used to show conditions (pressure, temperature, volume, etc.) at which thermodynamically distinct phases occur and coexist at equilibrium.
Common components of a phase diagram are lines of equilibrium or phase boundaries, which refer to lines that mark conditions under which multiple phases can coexist at equilibrium. Phase transitions occur along lines of equilibrium.
Triple points are points on phase diagrams where lines of equilibrium intersect. Triple points mark conditions at which three different phases can coexist. For example, the water phase diagram has a triple point corresponding to the single temperature and pressure at which solid, liquid, and gaseous water can coexist in a stable equilibrium (273.16 K and a partial vapor pressure of 611.657 Pa).
The solidus is the temperature below which the substance is stable in the solid state. The liquidus is the temperature above which the substance is stable in a liquid state. There may be a gap between the solidus and liquidus; within the gap, the substance consists of a mixture of crystals and liquid (like a "slurry").
Working fluids are often categorized by on the basis of the shape of their phase diagram.