Mixing Volatile Liquids
The standard Vapor Pressure lowering equation assumes that you dissolved a solid powder (like salt) into a liquid. The powder never evaporates.
But what happens if you mix two liquids together that both want to evaporate, like mixing Water and Ethanol (Alcohol)? Both liquids will fight to escape into the air, creating a combined, mixed vapor pressure.
Raoult's Law for Ideal Solutions
The French chemist François-Marie Raoult discovered that if the two liquids mix perfectly (an "Ideal Solution" where they don't chemically react or repel each other), their partial pressures are entirely predictable.
The vapor pressure that Liquid A contributes is simply its pure vapor pressure multiplied by its mole fraction in the mixture. You do the exact same thing for Liquid B, and then add them together to get the total pressure.
The Equation
The Vapor Phase is Always Richer
An incredibly important rule of Raoult's Law: The gas floating above the liquid mixture will always contain a higher percentage of the more volatile liquid. If you mix 50% Water and 50% Alcohol, the gas floating above it might be 80% Alcohol because it evaporates faster. This is the entire scientific basis for Distillation.