Question

1. Based on the phase diagram in Figure 1, construct the Gibbs free energy curves for the solid and liquid phases at T1,T2, T3 and T4. Assume that A and 8 components are mutually soluble in any amounts in both solid and liquid phases (unlimited solubility) and form ideal solutions. (30 marks) liquid т, T2=Tmg Jie line solid T. O X х,

Answer 1

1 Angi if the Imolar) gibbs free energy of pure A is gA and That of Pure B is g.B. Then the gibbs free energy for the combination of pure componets is Icprese, combined) - Jn-*+ 38*B. As a function of composition the gibb's free energy for the combination of Pure A and pure. Bis a . straight line Connecting ga and g as shown below. ov a3 Now, Let us remove the imaginary partition and let A and B atoms are mix. here should be some change m e due to this mixing. From that we can easily get the change in gibbs free energy due to mixing . od og A xo B Ag mix to get the total Now we sum g pure, combined) and bbs free energy of the solution, on t alous, combined 02 Daniel9 8

www unit At this point we have the genaral shape of g(x6) curves four phars in a binary system. This overal shape holds for both the solid and liquid phases, so long as both mare ideal solutions Ove compare 9 sol (x3) with Tua (XB) for variouy Temparateus. (IXT. High Temparature i at Temparature above the meeting points of both Pure A and Pue B, The liquid is the Stable phase for all compositions : sollxb) > gcq (XB) gibbs free energy cureres ndon gibassen v Land Composition 1 (2) Yow Temparature i at temparature below the meeting point of pare A and Pure B, the solid is the stable phase for all Compositions.!:. Sau (XB) <dcg(*8) gibb's free energy Curves molar gibbs free enney compofition, XB

13) Intermediate tempaatwe As the temparature is brough down from high to low I sol (XB) starts to move below That of Iliq (XB). The minima in the two curves in genaral donot occurs at the same point. So for some compositions I sol (TB) 9 Liq(XB), while for others isd (+8) < gia (78). molar Flob's free en slid liewed composition .XB