Question 3.1: How many phase-rule variables must be specified to fix the t...
How many phase-rule variables must be specified to fix the thermodynamic state of each of the following systems?
(a) Liquid water in equilibrium with its vapor.
(b) Liquid water in equilibrium with a mixture of water vapor and nitrogen.
(c) A three-phase system of a saturated aqueous salt solution at its boiling point with excess salt crystals present.
(a) The system contains a single chemical species existing as two phases (one liquid and one vapor), and
F = 2 − π + N = 2 − 2 + 1 = 1
This result is in agreement with the fact that for a given pressure water has but one boiling point. Temperature or pressure, but not both, can be specified for a system comprised of water in equilibrium with its vapor.
(b) Two chemical species are present. Again there are two phases, and
F = 2 − π + N = 2 − 2 + 2 = 2
The addition of an inert gas to a system of water in equilibrium with its vapor changes the characteristics of the system. Now temperature and pressure may be independently varied, but once they are fixed the system described can exist in equilibrium only at a particular composition of the vapor phase. (If nitrogen is considered negligibly soluble in water, the liquid phase is pure water.)
(c) The three phases (π = 3) are crystalline salt, the saturated aqueous solution, and vapor generated at the boiling point. The two chemical species (N = 2) are water and salt. For this system,
F = 2 − 3 + 2 = 1