Gibbs Phase Rule

INTRODUCTION:

Josiah Willard Gibb is an American scientist who had the upper hand in the applications of thermodynamics. He had been a man behind the invention of various rules and formulas that are useful in science. He postulated the theory of the Gibbs phase rule. This rule is one of the most important relationships between the number of the components of a chemical in their respective phase, under the influence of various variables, i.e., temperature and pressure to determine the characteristics of the equilibrium of that Particular chemical composition. The formula of the Gibbs Phase rule is a direct derivative from the fundamental thermodynamic principles.

WHAT IS GIBBS PHASE RULE?

Gibbs Phase rule was posted by an American scientist named Josiah Willard Gibb in the 1870’s. It is one of the important aspects of the physics, chemistry and mathematics field. It determines a relationship between the chemical constituents in their respective phase, i.e., solid, liquid, or vapor, under the influence of variables which are termed as pressure and temperature, to find out the characteristics of the equilibrium of that chemical composition. Gibbs Phase rule had played a vital role in geothermal barometry and determining the acidity or the oxygen state of a chemical. The Gibbs Phase rule works, and a general principle, that if the number of components is increasing, the variance should also increase, and The number of variances should decrease in correspondence to the increase in the number of the phase of a system.

AN INSIGHT OF GIBBS PHASE RULE:

Gibbs phase rule is an important aspect of the relationship between the chemical compositions. It was postulated so as to detail down the studies of geological history and their processes of the minerals found in nature. Several naturally occurring minerals and components have different reactions under the influence of pressure and temperature changes. Whereas the acidity and basicity of the chemicals also change their characteristics. Gibbs Phase Rule was a foundation. Towards the advancement in the studies of these geological aspects. It paved a path to characterize the chemical reaction of the minerals, determining the equilibrium system. as well as the effects of pressure and temperature change.

EXAMPLE

There are several examples related to Gibbs phase rule. Here, taking water (H2O) as a component, that is present in all 3 phases. Considering the water in its pure form, i.e, liquid, it will be determined as a single compound under a certain pressure, suppose 1 atm, similarly the temperature could have a definite value. Here, s is 1 and r is 0, that gives the degree of freedom equals to 2. 

As, F represents that the values of p and T can be chosen independently.

DETAILED TERMINOLOGY:

Gibbs Phase rule had been useful in the field of geothermal-barometry, Physico-chemical conditions, observation of behavior change of temperature and pressure, determination of the equilibrium of chemical components, as well as to figure out a phase diagram to represent the interconnection. The basic formula of the Gibbs Phase rule is:

P+F=C+2

Here,

P denotes the number of phases in the system. Compounds can be in one or two different phases at the same time. The phase can be determined as solid, liquid, or vapor.

C denotes the number of the chemical components in reaction, for example, SiO2, CaO, etc. There can be two components present in equal proportion or a combination of several multi-phase constituents into a single component.

F denotes the number of degrees of freedom in a system, also called a variance. The variance in chemical composition occurs due to the change in the temperature and pressure or their interconnected behavior.

GIBBS PHASE RULE DERIVATION:

Gibbs Phase rule for the General System is determined by the derivation of the fundamental thermodynamics principle. The Gibbs-Duhem equation represents a relationship between temperature, pressure, and the chemical potential of the components. 

dG=Vdp-Sdt+Nidi

To simplify the equation, the composition of each phase is expressed as P(C-1), and the number of variances is expressed as P(C-1)+2. Thus, the number of equilibria is expressed as E=C(P-1). The Gibbs Phase rule derivation is determined as:

F={P(C-)+2}-{C(P-1)}

F={CP-P+2-CP+C}

F=C-P+2

Whereas, The Gibbs Phase rule for General System is written as,

P+F=C+2

CONCLUSION:

Gibbs Phase rule is an important aspect of the geological and scientific field. It represents a relationship between the number of the chemical components that are present in the respective phase, under the influence of the variables, that is, temperature and pressure, to determine the equilibrium of the system. Gibbs Phase rule has been used in geothermal barometry to estimate the pressure and temperature, and in Physicochemical conditions, i.e., determining the acidity and the oxidation state of the chemical reactions, etc. Gibbs Phase Rule derivation is determined from the relationship of thermodynamics, so to understand the concept of the Gibbs phase rule formula, it is required to have a basic knowledge of thermodynamics.