What is meant by positive and negative deviations from Raoult’s law and how is the sign of Δ_mix H related to positive and negative deviations Raoult’s law?

Answer:

According to Raoult's law, the partial vapour pressure of each component in any solution is directly proportional to its mole fraction.

The solution which obeys Raoult's law over enitre range  is known as ideal solution.
The solution which do not obeys Raoult's law is known as non- ideal solution.

Non-ideal solution have vapour pressure either higher or lower is  predicted by raoult's law

If the vapour pressure is higher then solution is said to exhibit positive deviation, And if the vapour pressure is lower than the solution than it said to be negtive deviation.

Positive Deviation from Raoult’s law. In those non-ideal solutions, when partial pressure of component ‘A’ in the mixture of ‘A’ and ‘B’ is found to be more than that calculated from Raoult’s law. Similarly, the partial vapour pressure of component ‘B’ can be higher than calculated from Raoult’s law.
This type of deviation from ideal behaviour is called positive deviation from Raoult’s law,
e.g., water and ethanol, chloroform and water, ethanol and CCl₄, methanol and chloroform, benzene and methanol, acetic acid and toluene, acetone and ethanol, methanol and H₂O.
For positive deviation ΔH_mixing > 0. (+ ve)

Negative Deviation from Raoult’s law. When the partial vapour pressure of component ‘A’ is found to be less than calculated from Raoult’s law on adding the second component ‘B’. When A is added to B, the partial vapour pressure of solution is less than that of ideal solution of same composition. Boiling point of such a solution is relatively higher than the boiling point of A and B respectively. This type of deviation from ideal behaviour is known as negative deviation from Raoult’s law e.g., chlorofom and acetone, chloroform and methyl acetate, H₂O and HCl, H₂O and HNO₃ acetic acid and pyridine, chloroform and benzene.
For negative deviation ΔH_mixing < 0.