What is Gibbs Phase Rule?
Mathematical physicist Josiah Gibbs is responsible for laying down the theoretical groundwork for chemical thermodynamics. His phase rule equation paved the way for many subsequent discoveries and breakthroughs.
Gibbs Phase Rule is a look at the degrees of freedom for a compound in a closed physical system. The rule states that the freedom degree is always equal to the number of components minus the exact number of phases, plus 2.
While you state Gibbs Phase Rule, also remember that such a system in equilibrium is free from the effects of magnetic, electric and gravitational forces.
The equation is as follows –
F = C – P + 2
Here, F represents the degree of freedom, while C is the chemical component numbers. ‘P’ denotes the types of phases in a particular system. Another way to look at Gibbs Phase Rule definition is that it is an equation to determine the stability of phases present in any material. Keep in mind that equilibrium conditions are the key for this rule to apply.
Before proceeding to Gibbs Phase Rule derivation, here is what you must know about the variables.
Variables of Phase Rule Equation
1. Phase (P)
Any material that you can physically separate in a system is a phase. Therefore, igneous melts, liquids and vapour are considered phases in such a system. Two or more phases can occur in the same state of matter.
A phase can either be pure or a mixture of two or more elements. Nevertheless, each element in a phase must share physical and chemical properties.
2. Chemical Components (C)
C defines the minimum number of components necessary to define all the phases in a particular system.
3. Number of Degrees of Freedom (F)
This signifies the number of variables that you can change without altering the system’s state. Variables can include temperature, pressure and other factors too.
Thermodynamic Derivation of Phase Rule
Gibbs rule relies greatly on the Gibbs-Duhem equation, which is a fundamental basis for thermodynamics. The Gibbs-Duhem equation clarifies the relationship between pressure (P), temperature (T) and potential for chemical components (μ). This equation is as follows -
dG = Vdp – Sdt + ΣNidμi
However, a simpler way to derive the Phase rule is to understand that the composition of each phase is defined as P (C-1). Thus, the total number of variables is equal to
P (C-1) + 2 (Let us consider this as equation 1)
Number of equilibrium for each component’s each phase is P-1
Now for C number of components, the number of equilibrium = P (C-1)
Therefore, total number of equilibria E = C (P-1) (Let us consider this as equation 2)
Now, considering equation 1 and 2, we arrive at the following –
F = {P (C-1) + 2} – {C (P-1)}
F = {CP - P + 2 – CP + C}
F = C – P + 2
Therefore, using this technique, one can arrive at Gibbs Phase Rule easily.
Multiple Choice Question
1. What Does ‘P’ Stand for in the Phase Rule?
a. Pressure
b. Pascal
c. Momentum
d. Phase
Ans: (d) Phase
Example of Phase Rule on Water
Example 1
Consider water (H2O) as the system. At the triple point, i.e. P = 3 (steam, ice and liquid), the C = 1. Therefore, determining its degree of freedom is simple
F = C - P + 2
F = 1 – 3 + 2
F = 0
Example 2
Now, consider water as the system with a liquid-solid curve. In such a case, P = 2, while C is still 1. With derivation of phase rule, we can determine that
F = 1 – 2 + 2
F= 1
Thus, for a liquid-solid curve system, only one variable (pressure or temperature) can be changed, while maintaining equilibrium.
Phase rule derivation is vital to understand and apply the equation. Vedantu’s online teaching platform can help you learn and assess such complex topics in detail. We employ the finest teaching staff to assist students from across India and now you can access us even through our Vedantu app!
FAQs on Derivation of Phase Rule
1. What is the phase rule?
The phase rule is a broad principle in thermodynamics that governs "pVT" systems in thermodynamic equilibrium (systems whose states are completely characterized by the variables pressure (p), volume (V), and temperature (T)). If F represents the number of degrees of freedom, C represents the number of components, and P represents the number of phases,
F = C - P + 2
Josiah Willard Gibbs, an American physicist, derived it in his seminal paper On the Equilibrium of Heterogeneous Substances, which was published in sections between 1875 and 1878. The rule assumes that the components do not interact.
The number of degrees of freedom refers to the highest number of independent intensive variables, or thermodynamic factors like temperature or pressure, that may be changed simultaneously and arbitrarily without affecting one another. A system with one pure chemical is an example of a one-component system, whereas two-component systems, such as combinations of water and ethanol, have two chemically distinct components, and so on. Solids, liquids, and gasses are the most common phrases.
2. How is the phase rule derived?
On the basis of the thermodynamic rule, Gibbs phase rule can be obtained as follows:
Let's start with a heterogeneous system in equilibrium with Pn number of phases and Cn number of components. Assume that a component's transition from one phase to the next does not entail any chemical reactions. When the system is in equilibrium, the following parameters can be used to describe it:
Temperature
Pressure
Each phase's composition.
The total number of variables necessary to express the system's state is:
For all phases, the pressure is the same.
All phases have the same temperature.
Concentration.
With respect to the C components, the independent concentration variables for one phase are C – 1. As a result, P (C – 1) is the independent concentration variable for P phases in relation to C components.
Total number of variables = P (C – 1) + 2 (1)
Number of Equilibria in Total:
The chemical potential of each component in all phases must be the same for the system's distinct phases to remain in equilibrium.
For each P phase of each component, the number of equilibria is P – 1.
The number of equilibria for P phases for C components is P (C – 1).
As a result, E = C (P – 1) is the total number of equilibria involved.
3. What are the foundations of the phase rule?
The foundations of the phase rule are:
A phase is a type of matter with chemical composition and physical condition that are both homogeneous. Solid, liquid, and gas are the most common phrases. Two immiscible liquids (or liquid mixtures with differing compositions) separated by a definite border, just as two immiscible solids, are counted as two different phases.
The number of components (C) is the minimum number of chemically independent constituents required to define the composition of all phases of the system. See component for an example (thermodynamics).
In this context, the number of degrees of freedom (F) refers to the number of intensive variables that are independent of one another.
The rule is based on the fact that the intense variables are constrained by phase equilibrium. More precisely, the chemical potentials of the phases must be equivalent since they are in thermodynamic equilibrium with each other. The number of degrees of freedom is determined by the number of equality relationships. If the chemical potentials of a liquid and its vapour are both affected by temperature (T) and pressure (p), the equality of chemical potentials means that each of those factors is interdependent.
To be more explicit, C 1 intensive factors (such as mole fractions) in each phase define the composition of each phase. (C 1)P + 2 = (C 1)P + 2 = (C 1)P + 2 = (C 1)P + 2 = (C 1)P + 2 = (C 1)P + 2 = (C 1)P + 2 = (C 1)P + 2 = (C 1) Because each component's chemical potential must be identical in all phases, the number of restrictions is C(P 1). The rule holds true if the equilibrium between phases is impacted only by temperature, pressure, and concentration, and not by gravitational, electrical, or magnetic forces, or by surface area.
4. What are the pure substances in the phase rule?
C = 1 for pure substances, resulting in F = 3 P. Two factors (F = 2), such as temperature and pressure, can be chosen separately to be any pair of values consistent with the phase in a single phase (P = 1) condition of a pure component system. F declines from 2 to 1 when the temperature and pressure combination reaches a point where the pure component separates into two phases (P = 2). When the system enters the two-phase zone, temperature and pressure can no longer be controlled independently.
The boundary curve between the liquid and gas areas in the phase diagram to the right depicts the temperature and pressure constraint when the single-component system has separated into liquid and gas phases at equilibrium. On a two-phase circuit, the only way to increase pressure is to raise the temperature. When the temperature of the gas is lowered by cooling, part of it condenses, lowering the pressure.
5. What are the two-component systems in the phase rule?
The two components system in the phase rule are:
C = 2 for binary mixes of two chemically distinct components, resulting in F = 4 P. The composition of each phase, which is frequently stated as a mole fraction or mass fraction of one component, is another degree of freedom in addition to temperature and pressure.
Consider the system of two totally miscible liquids in equilibrium with their vapours, such as toluene and benzene. A boiling-point diagram can be used to explain this system, which depicts the composition (mole fraction) of the two phases in equilibrium as a function of temperature (at a fixed pressure). The Vedantu app and website provides you with free study materials.
6. What does c stand for in the phase rule equation?
C stands for the number of chemical compounds existing in the system.
7. What are the variables in the phase rule?
Temperature and pressure act as variables in such a case. The degree of freedom determines whether a system can alter one or both of these variables.