For example, if the two components differ only in isotopic content, then Raoult's law is essentially exact. Comparing measured vapor pressures to predicted values from Raoult's law provides information about the true relative strength of intermolecular forces. If the vapor pressure is less than predicted (a negative deviation), fewer molecules of each component than expected have left the solution in the presence of the other component, indicating that the forces between unlike molecules are stronger. The converse is true for positive deviations. For a solution of two liquids A and B, Raoult's law predicts that if no other gases are present, then the total vapor pressure above the solution is equal to the weighted sum of the "pure" vapor pressures and of the two components. Thus the total pressure above the solution of A and B would be Since the sum of the mole fractions is equal to one, This is a linear function of the mole fraction , as shown in the graph. Thermodynamic considerations Raoult's 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 Raoult's 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 and is the mole fraction of component in the pure state. 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: Ideal mixing An ideal solution would follow Raoult's law, but most solutions deviate from ideality. Interactions