9 Liquid and Solid Solutions Phase Change questions

1. At 75ºC, the vapour pressure of water is 38.6 kPa and that of methanol is 151 kPa.  sketch the pressure-composition diagram  for mixtures of methanol and water, assuming they form ideal solutions.
2. n-pentane boils at 36.1 ºC and n-hexane at 68.6 ºC at standard pressure.  Sketch the temperature-composition diagram for mixtures of n-pentane and n-hexane, assuming they form ideal solutions.
3. Use Raoult’s law to calculate the partial pressures (at 30ºC) of hexane and heptane and the mole fraction of hexane in the vapour phase, in equilibrium a liquid mixture in which the mole fraction of hexane is 0.20. At 30ºC, the vapour pressures are 24.9 kPa for hexane and 7.75 kPa for heptane.
4. Use information from Table 1 to sketch the temperature-concentration phase diagram for ethanol-water and for chloroform-acetone systems.  Explain for both systems, the relative strength of the different intermolecular forces, A-A, B-B and A-B.
5. In a eutectic phase diagram for a two-component system of compounds A and B, the eutectic point is 25ºC and is located at 0.8 on the horizontal line where 0 is pure A and 1 is pure B.  The melting point of pure A is 75ºC and of pure B is 50ºC.  Sketch the phase diagram for this system.  Does A and B form a new compound with formula B₄A₁?
6. A liquid mixture of benzene and ethanol is distilled in a fractional distillation apparatus that can achieve near infinite number of steps.  if the mole fraction of ethanol in the liquid is initially 0.10, what will be final composition and boiling point of the distillate be?
7. An aqueous solution of hydrochloric acid, with mole fraction 0.05 is boiled gently in a beaker.  The temperature gradually increases as the boiling progresses and reaches almost 108ºC.  explain this observation, using information from table 1.  what will be the composition of the mixture at that late boiling state.
8. Calculate the mole fraction and molar concentration of oxygen from the air in water at 35ºC, using information from table 2.  The partial pressure of oxygen in air is 21 kPa.

Answers.

1. A Pressure-composition phase diagram for an ideal solution will have the liquid-pressure vs. composition phase linear.  The gas pressure vs composition will be a curve pulled towards the lower pressure pure component.  According question, the vapour pressure of methanol is 151 kPa and that of water is 38.6 kPa, at 75 C, so the diagram will have a straight line joining those two points and a curved line pulled towards the methanol side.
   
2. A temperature-composition phase diagram for an ideal solution will have no lines that are straight but there will not be a minimum or a maximum. Both curves will smoothly go up from the lower BP to the higher BP. The T vs. Liquid composition line will have a slight curve down and the T vs Vapour composition will be pulled towards the lower BP.
3. Raoult’s law for component A is . same for component B.
   Partial pressure of hexane is kPa = kPa
   Partial pressure of heptane is kPa = kPa
   Mole fraction of hexane in vapour is y(hexane)
4. According to table 1, the boiling point of the azeotrope for the ethanol-water system (78.18) is lower than the boiling point of both ethanol and of water. So it is a minimum boiling azeotrope. Let A = ethanol, B = water. These happen when the AB forces are weaker than either the AA and the BB forces. I would rank the strength of the forces from weakest to strongest as AB<BB<AA.
   b.   According to table 1, the boiling point of the azeotrope for the chloroform-acetone system (64.4) is higher than the boiling point of both chloroform (61.2) and of acetone (56.1). So it is a maximum boiling azeotrope.
   Let A = chloroform, B = acetone. These happen when the AB forces are Stronger than either the AA and the BB forces. I would rank the forces from weakest to strongest as BB<AA<AB.

   

5. The eutectic phase diagram has a eutectic point at 25ºC and a composition of (B) = 0.8.  There is no indication of anything other than this simple eutectic point in the diagram so we will draw a simple melting phase diagram.  There is no compound formed.
6. According to table 1, Benzene and ethanol form a system with a maximum boiling azeotrope. In a maximum boiling system, the vapour separated off will be richer in either benzene, or ethanol, depending on which side of the azeotrope the solution starts out.  The question says the starting liquid composition is .1 in ethanol (so, .9 in benzene) and the table puts the azeotrope at .440 benzene.  The starting point is on the ethanol side of the azeotrope, so vapour will be pure ethanol.
7. An aqueous solution of hydrochloric acid, hydrogen chloride in water, has a mole fraction of 0.05 HCl.  According to the information in Table 1, this will be a maximum boiling azeotrope at a composition of 0.111 HCl.  So the starting point is on the HCl side of the azeotrope. That means the distillate will be pure HCl after infinite boiling steps and the liquid left behind will be the azeotrope, with a boiling point of 108.6.  This is what our observations show.  The liquid boiling point slowly increases as HCl is boiled off until what’s left is the azeotropic mixture.  At that point, it boils at 108.8 and the vapour and liquid will have the same composition so no further change is possible.
8. Henry’s law tells us the relationship between the concentration of a component in a liquid and the pressure of that component in equilibrium above the solution.  According to the table, the Henry’s law constant for oxygen in water at 35C is 5.11 and the partial pressure of oxygen is 21 kPa.