The Phase Rule (Gibbs' Phase Rule) correlates the least number of independent variables required to describe a system at equilibrium (F) with its number of components (C) and its number of phases (P). The equation is written as the following:
F is also known as the number of degrees of freedom in the system. The independent variables include temperature, pressure, concentration, viscosity, refractive index, density...etc. The following examples further explains the rule.
Example 1. Pure liquid water at equilibrium with ice. Accordingly, the number of components (C) = 1, the number of phases (P) at equilibrium = 2, and F = 1 - 2 + 2 = 1. Therefore, to fully describe this system we need to mention 1 variable. This can be either temperature or pressure. Thus, to make a full description of the above example we can write it as the following:
Pure liquid water at equilibrium with ice at 0 ˚C or at 1 atmospheric pressure. In other words, Liquid and ice are at equilibrium at 0 ˚C only if the pressure is 1 atmosphere and vise versa. Moreover, liquid and ice water can be at equilibrium at different sets of temperature - pressure values.
Example 2. Pure liquid water. This system contains only 1 component and 1 phase. Therefore, F = 1-1 + 2 = 2. Thus, two variables are needed to fully describe the system; temperature and pressure. To fully describe the state (energy state) of this pure water we need to mention that it is, for example, at 20 ˚C and 1 atmospheric pressure. The state becomes different if either temperature or pressure changes.
Example 3. Sucrose dissolved in pure water.
Accordingly, three variables need to be mentioned; temperature, pressure, and concentration. Assuming that the pressure is constant at 1 atmosphere then a condensed number of degrees of freedom is equal to 2 ; temperature and concentration.
Example 4. Saturated solution of a given solute.
The condensed number of degrees of freedom = 1 (assuming pressure is constant at 1 atmosphere). In this example 2 phases are at equilibrium. Only one variable needs to be mentioned that is either temperature or concentration. The concentration here represents solubility of the solute which is dependent on temperature. For example, solubility of phenol in water is equal to 11% (w/w) only at 50 ˚C. Therefore, to fully describe a saturated phenol - water mixture we either mention that we have a saturated solution of phenol in water at 50 ˚C or that we have a saturated solution of phenol in water with a concentration of 11 % (w/w).
F = C - P + 2
Example 1. Pure liquid water at equilibrium with ice. Accordingly, the number of components (C) = 1, the number of phases (P) at equilibrium = 2, and F = 1 - 2 + 2 = 1. Therefore, to fully describe this system we need to mention 1 variable. This can be either temperature or pressure. Thus, to make a full description of the above example we can write it as the following:
Pure liquid water at equilibrium with ice at 0 ˚C or at 1 atmospheric pressure. In other words, Liquid and ice are at equilibrium at 0 ˚C only if the pressure is 1 atmosphere and vise versa. Moreover, liquid and ice water can be at equilibrium at different sets of temperature - pressure values.
Example 2. Pure liquid water. This system contains only 1 component and 1 phase. Therefore, F = 1-1 + 2 = 2. Thus, two variables are needed to fully describe the system; temperature and pressure. To fully describe the state (energy state) of this pure water we need to mention that it is, for example, at 20 ˚C and 1 atmospheric pressure. The state becomes different if either temperature or pressure changes.
Example 3. Sucrose dissolved in pure water.
C = 2
P = 1
F = 2 - 1 + 2 = 3
Accordingly, three variables need to be mentioned; temperature, pressure, and concentration. Assuming that the pressure is constant at 1 atmosphere then a condensed number of degrees of freedom is equal to 2 ; temperature and concentration.
Example 4. Saturated solution of a given solute.
C = 2
P = 2
F = 2 - 2 + 2 = 2
The condensed number of degrees of freedom = 1 (assuming pressure is constant at 1 atmosphere). In this example 2 phases are at equilibrium. Only one variable needs to be mentioned that is either temperature or concentration. The concentration here represents solubility of the solute which is dependent on temperature. For example, solubility of phenol in water is equal to 11% (w/w) only at 50 ˚C. Therefore, to fully describe a saturated phenol - water mixture we either mention that we have a saturated solution of phenol in water at 50 ˚C or that we have a saturated solution of phenol in water with a concentration of 11 % (w/w).
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