A solution of methanol and water has a mole fraction of water of 0.312 and a total vapor pressure of 211 torr at 39.9 ∘C. The vapor pressures of pure methan ol and pure water at this temperature are 256 torr and 55.3 torr, respectively. ls 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 strategy here is to use Raoult´s law to calculate the theoretical vapor pressure for the concentrations given and compare it with the experimental value of 211 torr.

Raoult´s law tell us that for a binary solution

P total = partial pressure A + partial pressure B = Xa PºA + Xb PºB

where Xa and Xb are the mol fractions, and PºA and PºB are the vapor pressures of pure A and pure B, respectively

For the solution in question we have

Ptotal = 0.312 x 55.3 torr + ( 1- 0.312 ) x 256 torr ( XA + XB = 1 )

Ptotal = 193 torr

Since experimentally, the total vapor pressure is 211 and our theoretical value is smaller ( 193 torr ), we can conclude the interactions solute-solvent are weaker compared to the solute-solute and solvent-solvent interactions.