Raoult's and Dalton's law

These are two important basic concepts in distillation. According to Raoult's law, in an ideal solution of two (example) volatile solvents, the partial pressure of each component equals its mole fraction in the liquid multiplied by its vapor pressure.

Raoult's law

According to Raoult's law, the following will apply.

If A is one such solvent in a solution with another volatile solvent B, the partial vapor pressure of A = Mole fraction of A in A's liquid x Vapor pressure. Let's say it is Pa.

Similarly, let's say the partial vapor pressure of B is Pb

By using Raoults law one can find out the partial pressure of each component in an ideal solution of volatile solvents.

Dalton's law

According to Dalton's law, the total pressure is the sum of partial pressures.

Combination of Raoult's and Dalton's law

If you apply the two laws in the above case then you get the total pressure, let's call it P = Pa + Pb.

Let's take an example

" Let's take a non-ideal. solution of water and ethanol at a 1:1 mole ratio. The vapor pressure of water is 760 mm and the vapor pressure of ethanol is 45 mm Hg. The question is: predict total pressure and how it will deviate from Raoult's law interms of positive or negative deviation"

Had this been the ideal solution following would have applied.

In an ideal solution, the total vapor pressure of the solution would be the sum of the partial pressures of each component, as calculated using Raoult's Law.

Using Raoult's law, the partial pressure of water in the solution would be 0.5 760 mm Hg = 380 mm Hg, and the partial pressure of ethanol would be 0.5 45 mm Hg = 22.5 mm Hg. Therefore, the total vapor pressure of the solution according to Raoult's Law would be 380 mm Hg + 22.5 mm Hg = 402.5 mm Hg.

However. it's a non-ideal solution as water and ethanol have structural dissimilarities. Their polarities are different with water being more polar than ethanol.

Here, the total vapor pressure may deviate from Raoult's Law due to interactions between the molecules of water. Remember in a solution if you reduce moles of water you reduce H bonds and increase vapor pressure.

P = Mole fraction x Pa as explained above does not apply. Pa does not remain vapor ptrssure of pure solvent anymore. As explained, the following happens:

As a result, in this non-ideal solution of water and ethanol at a 1:1 mole ratio, the interactions between molecules in the mixture are weaker than what would be expected based on Raoult's law for ideal solutions.

This suggests that the total pressure in the system would deviate positively from Raoult's law.

How and why?

Due to the lesser polarity of the water and ethanol mixture, there will be fewer H bonds in the solution. This will increase the vapor pressure. because there are fewer H bonds to break.

What is a positive deviation from Raoult's law?

Positive deviation from Raoult's law occurs when the observed vapor pressure of a solution is higher than what is expected based on Raoult's law. This happens when the A-B molecular interaction forces are weaker than the average of the attraction in the pure component of the mixture.