Why two immiscible liquids will boil at at a lower temperature than the boiling points of either pure component

Not quiet the right statement: I assume you meant the AGITATED mixture of immiscible liquids.

http://chemwiki.ucdavis.edu/Physical_Chemistry/Equilibria/Phase_Equilibria/9._Immiscible_Liquids_and_Steam_Distillation

The phenomenon of two immiscible liquids boiling at a lower temperature than their individual boiling points is known as azeotropy. Azeotropes are mixtures of liquids that have a constant boiling point and composition, which is different from the boiling points of their pure components.

Now, to understand why this happens, we need to consider the concept of vapor pressure. The vapor pressure of a liquid is the pressure exerted by its vapor when it is in equilibrium with its condensed phase (liquid).

When two immiscible liquids are mixed together, the vapor pressure of the resulting mixture can be different from the vapor pressures of the individual components. This is due to the interactions between the molecules of the two liquids.

In some cases, when two immiscible liquids are mixed, their molecules may have a stronger attraction to each other compared to the attraction between the molecules of the same liquid. As a result, the vapor pressure of the mixture can be lower than the vapor pressures of the individual components.

Now, let's talk about boiling. Boiling occurs when the vapor pressure of a liquid equals the atmospheric pressure. When two immiscible liquids are mixed and their vapor pressure is lower than the atmospheric pressure at a particular temperature, the mixture will boil at a lower temperature.

Basically, the presence of the second liquid lowers the vapor pressure of the mixture, which means that the mixture needs less energy (lower temperature) to reach a vapor pressure equal to the atmospheric pressure and boil.

To find the exact boiling temperature of such mixtures, you would need to refer to phase diagrams or tables that provide information on azeotropic mixtures. These resources contain experimental data that can help determine the boiling points of these mixtures at different compositions.