6.8. Liquid methyl ethyl ketone (MEK) is introduced into a vessel containing air. The system temperature is increased to 55°C, and the vessel contents reach equilibrium with some MEK remaining in the liquid state. The equilibrium pressure is 1200 mm Hg. (a) Use the Gibbs phase rule to determine how many degrees of freedom exist for the system at equilibrium. State the meaning of your result in your own words. (b) Mixtures of MEK vapor and air that contain between 1.8 mole% MEK and 11.5 mole% MEK can ignite and burn explosively if exposed to a flame or spark. Determine whether or not the given vessel constitutes an explosion hazard.

A) Degree of Freedom (DF) = 2 and this means that 2 variables are required to determine the state of the system

B) The vessel doesn't constitute an explosion hazard.

Explanation:

A) Degree of Freedom(DF)=2 + C - π

Where;

π = 2 (liquid and gas phase equilibrium)

C = 2 (air and MEK)

Thus, DF = 2 + 2 - 2 = 2

DF of 2 means that 2 variables are required to determine the state of the system

B) Using Antoine Equation;

Log(Pmek) = 6.97421 - (1209.6/(55 + 216)) = 2.51

Log(Pmek) = 2.51

Thus,Pmek = 10^(2.51) = 323.59mm of Hg or approximately 324mm of Hg.

So, fraction of mek in vapour phase = 324/1200 = 0.27 or 27%

Now this fraction is more than 11.5% in the question.

Therefore, the vessel contains no explosion hazard.

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