Asolution of methanol and water has a mole fraction of water of 0.312 and a total vapor pressure of 211 torr at 39.9 ºc. the vapor pressures of pure methanol and pure water at this temperature are 256 torr and 55.3 torr, respectively. is the solution ideal? if not, what can you say about the relative strengths of the solute-solvent interactions compared to the solute-solute and solvent-solvent interactions?

The solution is not ideal.

The relative strengths of the solute-solvent interactions are greater  compared to the solute-solute and solvent-solvent interactions

Explanation:

The total vapor pressure is the sum of the partial pressures of  water and methanol, and they are calculated by the Raoult´s law equation:

Pₐ = Xₐ Pºₐ, where  Pₐ is the partial pressure of component A

                              Xₐ is the molar fraction of A

                              P⁰ₐ is the pressure of pure A

So lets calculate the partial pressures of methanol and water and compare them with the given total vapor pressure of solution:

X H2O = 0.312 ⇒ X CH3OH = 1 - 0.312 = 0.688

PH2O = 0.312 x 55.3 torr =  17.3 torr

PCH3OH = 0.688 x 256 torr = 176.1 torr

Ptotal = PH2O  + PCH3OH  = 17.3 torr + 176.1 torr = 193.4 torr

This pressure is less than the experimental value of 211 torr. So the solution is not ideal. The relative strength of the solute-solvent interactions are greater than the solute-solute and solvent-solvent interactions.

The reason for this is the presence of hydrogen bonding between methanol and water.

i believe you are right for all except the 3rd ( look at sqdancefan his answer is much better)