where m denotes molar, i.e., change in Gibbs free energy per mole of solution, and x i is the mole fraction of component i . Note that this free energy of mixing is always negative (since each x i ∈ ∈ [ 0 , 1 ] , each ln ⁡ ⁡ x i or its limit for x i → → 0 must be negative (infinite)), i.e., ideal solutions are miscible at any composition and no phase separation will occur.