Pure liquid species 2 and 3 are for practical purposes immiscible in one another. Liquid species 1 is soluble in both liquid 2 and liquid 3. One mole each of liquids 1, 2, and 3 are shaken together to form an equilibrium mixture of two liquid phases: an α-phase containing species 1 and 2, and a β-phase containing species 1 and 3. What are the mole fractions of species 1 in the α and β phases, if at the temperature of the experiment, the excess Gibbs energies of the phases are given by:

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RT=04x7x2 (GE) RT off =0844 and