Raoults law was first observed empirically and led François-Marie Raoult to postulate that the vapor pressure above an ideal mixture of liquids is equal to the sum of the vapor pressures of each component multiplied by its mole fraction. Taking compliance with Raoults Law as a defining characteristic of ideality in a  solution, it is possible to deduce that the chemical potential of each component of the liquid is given by
where  is the chemical potential in the pure state and  is the mole fraction of component  in the ideal solution.  From this equation, other thermodynamic properties of an ideal solution may be determined.  If the assumption that the vapor follows the ideal gas law is added, Raoult's law may be derived as follows.
If the system is ideal, then, at equilibrium, the chemical potential of each component  must be the same in the liquid and gas states. That is,
Substituting the formula for chemical potential gives
as the gas-phase mole fraction depends on its fugacity, , as a fraction of the pressure in the reference state, .
The corresponding equation when the system consists purely of component  in equilibrium with its vapor is
Subtracting these equations and re-arranging leads to the result
For the ideal gas, pressure and fugacity are equal, so introducing simple pressures to this result yields Raoult's law: