More use of phase diagram $(0\mathrm{.}8pt)$

a$)$ For an ideal mixture of two liquids A and $B,$ show that the pressure $p!$ at which the mole

fractions of $A$ in the gas and liquid phases are most different from one another is given by the

geometric mean of the partial pressures of pure A and $B.$

b$)$ Using the result from part $($a$),$ calculate the mole fraction of benzene in the vapor above a

mixture of benzene and toluene at $60C$ for which $x($benzene$)$ differs maximally from

$y($benzene$).$ The vapor pressures of pure benzene and toluene are provided in previous

problem sets.