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# 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.

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The number of variables to be specified to fix the thermodynamics state of each of the following system is calculating by using the Gibbs phase rule for the multi-phase system at equilibrium is

$F=2-\pi +N$

Where $\pi$ is the number of phases and $N$ is the number of chemical species and $F$ is called the degree of freedom or number of intensive variable to fixed for defining the thermodynamic state

Here the number of Phases $\pi=2$ liquid and vapor \ The number of components are $N=2$ ethanol and water. Now the Degree of freedom $(F)$

$F=2-2+2=2$

Hence for defining the thermodynamic state, we have to fix two-variable. Temperature and Pressure may be specified for a system comprised of ethanol-water in equilibrium with its vapor

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