Question

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 methanol and pure water at this temperature are 256 torr and 55.3 torr, respectively.Is the solution Ideal?

Answer 1

Answer : This is not an ideal mixture.

Explanation :

Using Raoult's law :

$P_{Mixture}=p_{CH_3OH}+p_{H_2O}\\\\P_{Mixture}=x_{CH_3OH}\times p^o_{CH_3OH}+x_{H_2O}\times p^o_{H_2O}$

where,

$P_{Mixture}$ = total vapor pressure of mixture

$p^o_{CH_3OH}$ = vapor pressure of pure methanol = 256 torr

$p^o_{H_2O}$ = vapor pressure of pure water = 55.3 torr

$x_{H_2O}$ = mole fraction of water = 0.312  

$x_{CH_3OH}$ = mole fraction of methanol = 1 - 0.312 = 0.688

Now put all the given values in the above formula, we get:

$P_{Mixture}=x_{CH_3OH}\times p^o_{CH_3OH}+x_{H_2O}\times p^o_{H_2O}$

$P_{Mixture}=0.688\times 256torr+0.312\times 55.3torr$

$P_{Mixture}=193.4torr$

From this we conclude that the total vapor pressure of mixture is less than the total given vapor pressure of 211 torr. That means, the interactions between the methanol and water would be weaker than those between the individual substances. So, this is not an ideal mixture.

Hence, this is not an ideal mixture.