How many phase rule variables must be specified to fix the thermodynamic state of each of the following systems?
(a) A sealed flask containing a liquid ethanol-water mixture in equilibrium with its vapor.
(b) A sealed flask containing a liquid ethanol-water mixture in equilibrium with its vapor and nitrogen.
(c) A sealed flask containing ethanol, toluene, and water as two liquid phases plus vapor.
a. Using the phase rule FF = 2 ? ? + N, where ?? is the number of phases, N is the number of chemical species, and F is the degrees of freedom or the number of variables that must be specified, we can determine that ? = 2 for the liquid and vapor, and N = 2 for the ethanol and water, F = 2 ? 2 + 2 = 2. 2 variables need to be specified.
b. ? = 2 for liquid and vapor, and N = 3 for the ethanol, water, and nitrogen, leaving
F = 2 ? 2 + 3 = 3. 3 variables must be specified
c. ? = 3 for the two liquids and vapor, and N = 3 for the ethanol, water, and toluene, leaving F = 2 ? 3 + 3 = 2. 2 variables must be specified
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