How is the sign of enthalpy of mixing related to positive or negative deviation from raoult's law?

 For positive deviations from Raoult's law, the enthalpy of mixing dH is positive. This means the process is endothermic, as energy is absorbed. Because the forces between unlike molecules (e.g., A-B) are weaker than those between like molecules (e.g., A-A and B-B), more energy is required to break the original bonds than is released when the new ones form. 

Similarly, 

The sign of the enthalpy of mixing dH is negative for solutions exhibiting a negative deviation from Raoult's law. This indicates an exothermic process, meaning energy is released because the attractive forces between unlike molecules (A-B) are stronger than the average of those between like molecules (A-A and B-B). Because the newly formed A-B bonds are stronger, more energy is released upon their formation than is required to break the original A-A and B-B bonds. This net release of energy results in a negative.

Steps of the Mixing Process

To understand why it turns negative, the process can be broken down into three steps:

Breaking A-A bonds: Requires energy (endothermic).
Breaking B-B bonds: Requires energy (endothermic).

     3. Forming A-B bonds: Releases energy (exothermic).     

If step 3 releases more energy than steps 1 and 2 require combined, the overall enthalpy of mixing will be a negative value.