How many phase rule variables must be specified to fix the thermodynamic state of each of the following systems? show how you determine these.

(i) a sealed flask containing a liquid ethanol-water mixture in equilibrium with its vapor.

(ii) a sealed flask containing a liquid ethanol-water mixture in equilibrium with its vapor and nitrogen.

(iii) a sealed flask containing ethanol, toluene, and water as two liquid phases plus vapor.

(i) F = 2

(ii) F = 3

(iii) F = 2

Explanation:

We would be applying the famous Gibbs Phase Rule to explaining this problem;

By applying the formula;

F+P = C +2

Where P = this represent the phase

F = this is called the degree of freedom

C = this represent the component in the system

Ok let us begin;

(i). from this we can see that there are 2 components i.e. (water + ethanol) and the phase in question is a vapor phase + liquid phase.

So from the formula;

F = C-P+2

F = 2 – 2 + 2 = 2

Therefore, F = 2.

(ii). Also, from the statement, we can figure there are 3 components, while the phases are two like the previous one above, i.e. liquid + vapor

F = 3 – 2 + 2 = 5 – 2 = 3

F = 3

(iii). From this statement, we can figure there are 3 components, and the phases are 3 i.e. (2 liquid phases + 1 vapor phase)

From the formula;

F = 3 – 3 + 2 = 0 + 2

F = 2

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