(i)What is the free energy of mixing I g of polystyrene of molar mass M = lif gmol- 1• with I mol of cyclohexane at 34 °C?Note that 34 °C is the 0-temperature for a polystyrene solution in cyclohexane (Flory inter­action parameter x = 1/2). The molar volume of polystyrene is vp, = 9.5 x 104 cm3 mo1- 1, the molar volume of cyclohexane is Vcyc= 108cm3 mol - 1• Assume no volume change upon mixing and assume that the volume of one solvent molecule is the lattice site volume v0.(ii)What does the sign of the free energy of mixing imply about the stability of a homogeneous solution?(iii)Under what conditions does the homogeneous solution spontaneously phase separate by spinodal decomposition?(iv)When is the homogeneous solution metastable?