Consider a binary system containing components a and $b,$ wherein a rich $$ liquid phase coexists

with $b$ rich $$ liquid phase. Both these coexisting phases are in equilibrium with vapor containing

a and $b.$ Consider vapor phase mixture to be in ideal gas state but both liquid phases not to be

the ideal mixtures $({}_i^{}1,{}_i^{}1).$ Write the equilibrium criterion for this case in terms of mole

fractions of a and $b$ in all the three phases and the activity coefficients. Draw a representative

phase diagram in terms of temperature plotted as a function of mole fraction of $a.$ Clearly show

the region at which the three phases coexist. Under what conditions such behavior is observed

$($comment based on favorable$/$unfavorable like$/$unlike interactions$).$

$(15$ points$)$