## What is meant by chemical and phase equilibrium?

When in a chemical reaction, both the reactants and the products do not possess any tendency to undergo a change with respect to time such that the chemical properties of the system remain constant, the condition is known as a chemical equilibrium. Hence, there is no chemical potential for the reactants and products. Under such circumstances, the chemical condition is said to be in equilibrium. The chemical potential in such a condition remains zero. The chemical equilibrium is represented by a balanced chemical equation. A chemical reaction is said to be balanced if the number of atoms on the reactant side is equal to the number of atoms on the product side.

The study of equilibrium relationships between the phases by using the principles of thermodynamics is known as phase equilibrium. A phase is defined as regions in the microstructure that remain separated from the surrounding, but have the same intensive and molar properties when the system attains the thermodynamic equilibrium. A system is said to be in a thermodynamic equilibrium when the system attains mechanical equilibrium, chemical equilibrium, and thermal equilibrium. The phase equilibrium is studied by the means of a phase diagram. For instance, the knowledge of the phase equilibrium diagram of the silicon dioxide, $Si{O}_{2}$, is primarily used in the concrete industries for the production of Portland cement.

## Phase diagram

Phase diagrams or equilibrium phase diagrams are the graphical representations that show the phase transformations of the constituting elements with respect to the pressure, temperature, and compositions. The diagrams show the conditions that limit the different phases, namely solid, liquid, and gas. The diagram can also be utilized to verify the relations between the state variables. Most of the phase diagrams are temperature-pressure phase diagrams, with the variable parameter as the composition. Usually other variables such as solubility and pressure parameters are not indicated in the phase diagram. For a one-component system (unary phase diagram), the phase diagram is generally a function of temperature and pressure as the state variables, or temperature and volume. However, for a binary system (two-phase) having two components, the phase diagram is a function of temperature and composition as the state variables only. Coexisting of the different phases of the constituting elements is indicated in the phase diagram. A ternary phase diagram can be characterized by consisting of three phases in equilibrium.

## Basic terminologies for a phase equilibrium

• Enthalpy: In thermodynamics, enthalpy is the property of a thermodynamic system. The enthalpy in thermodynamics is a function of the system's internal energy, pressure, and volume. Mathematically, represented as, $H=U+\mathrm{PV}$. Where, $H$ is the enthalpy of the system, $U$ is the internal energy of the system, $P$ is the pressure associated with the system, and $V$ is the volume of the system. The SI unit of enthalpy is Joule, $J$.
• Supercritical temperature: There is a point in the phase diagram, where the liquid and the vapor phases coexist as a single phase, this point is known as the critical point. The state of liquid beyond the critical point is termed the supercritical state. The corresponding temperature is the supercritical temperature.
• Gibbs energy: When a system is at a constant temperature and pressure, the maximum work done by the system while the system undergoes a reversible process, that can be obtained from the thermodynamic system is termed as the Gibbs energy, which is a thermodynamic potential. Mathematically, $∆G=∆H-T∆S$, where, $∆G$ is the change in the Gibbs energy, $∆H$ is the change in enthalpy, and $∆S$ is the change in entropy. The entropy is a property of the system which is derived from the second law of thermodynamics.
• Sublimation: It is a phase represented in the phase diagram when a substance undergoes a direct change to the vapor phase without reaching the liquid phase.
• Liquid-liquid critical point: It is a point in the phase diagram where two elements having the same phase as liquid coexists in the equilibrium. They have a ratio of the existence of unity.
• Metastable phase: When a phase undergoes a phase transition from a higher free energy state to a lower free energy state, it must constitute an energy barrier before that phase can be transformed. The corresponding phase transformation which occurred is termed as metastable phase transformation.
• Triple point: In the phase diagram, when the three phases of a substance, solid, liquid, and gas coexist at a point, provided the conditions of equilibrium, that point is known as the triple point.

## Gibbs phase rule

The number of degrees of freedom in a system consisting of more than one component can be related by the Gibbs phase rule. The degree of freedom of the system is a function of its number of components, $C$, and the number of phases $P$. It is represented by relation as,

$F=C-P+2$

The degree of freedom as indicated in the Gibbs phase rule indicates the number of independent intensive variables, which signify the state of equilibrium of a system.

## Solid solutions

The largest percentage of composition in a mixture can be termed as solvents and the remaining parts are known as solutes. For instance, an alloy, which is a mixture of two or more elements. Such mixtures are also termed as solid solutions. The atoms of the solute can be present in multiple ways, as the atoms can occupy the interstitial sites of the solvent atoms or can replace constituting atoms from the crystal structures and occupy their place. This kind of solute solution is also termed as a substitutional solid solution.

## Context and Applications

The following topic finds its application in the industries that deal with manufacturing, which needs intensive knowledge about the material science and needs the material properties to be altered for required processes such as in steel manufacturing industries. The topic is taught in undergraduate curriculam such as

Bachelors in Science (Chemistry)

Masters in Science (Chemistry)

Bachelors in Technology (Civil)

## Practice Problems

1. Gibbs phase rule relates to which of the following parameters?
1. Enthalpy and internal energy
2. Entropy and enthalpy
3. Number of phases and compositions
4. None of these

Correct option: c

Explanation: Gibbs phase rule indicates the number of degrees of freedom of a system. It provides a relationship between the number of phases and the number of components of a system.

2. Which of the following is true for a three-component phase diagram?

1. The phase diagram is a ternary phase diagram.
2. The phase diagram is a binary phase diagram.
3. The phase diagram is a unary phase diagram.
4. The phase diagram is a tertiary phase diagram.

Correct option: a

Explanation: A ternary phase diagram is a phase diagram that consists of three phases in equilibrium.

3. Supercritical temperature is the temperature corresponding to the supercritical point of a liquid in a phase diagram. Is it True or false?

Explanation: Supercritical point is a point beyond the critical point in a phase diagram. The corresponding temperature is termed supercritical temperature.

4. Which of the following equation is the correct expression for enthalpy?

1. $H=U-PV$
2. $H=U-P$
3. $H=U+PS$
4. $H=U+PV$

Correct option: d

Explanation: Enthalpy is a function of the internal energy, pressure, and volume of a system. Hence the equation $H=U+PV$ is correct.

5. Triple point is a point in a binary phase diagram where the three phases of the system coexist. Is it true or false?

Explanation: Triple point is a point in a single component system phase diagram, or it is a point in a unary phase diagram where the different phases of the system coexist in equilibrium.

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