$(2)$ A concentrated binary solution containing mostly species $2($but $x_{2}1)$ is in equilibrium with a vapor phase containing both species $1$ and $2.$ The pressure of this two$-$phase system is $1$ bar; the temperature is $25C.$ At this temperature, $H_1=200$ bar and $P_2^{\text{s}\text{a}\text{t}}=\frac{0\mathrm{.}10}{b}ar.$ Determine good estimates of $x_1$ and $y_1.$ State and justify all assumptions.

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