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) From Gibbs phase rule F = C - P + 2

C = number of components = 2 (MEK & air) P = number of phases = 2 (liquid and vapor) F = 2 - 2 + 2 = 2 Two variables need to be specified to fixed the system as this implies that the DOF = 2 Where DOF = Degrees of freedom

b) Applying the Antoine equation

log P x MEK = 6.97421 - 1209.6 / (T + 216) Temperature T = 55 °C Plugging the values into the equation; log P x MEK = 6.97421 - 1209.6 / (55 + 216) = 2.51 P*MEK = 323.59 mmHg Hence, Liquid and vapor phase are in equilibrium

Partial pressure of MEK = P*MEK = 323.59 mmHg

Mol fraction of MEK in vapor phase

y = Partial pressure / equilibrium pressure = 323.59 / 1200 = 0.269 which is greater than 0.115

Therefore, the value gotten is indicative that the given vessel won't constitute an explosion hazard.