$13\mathrm{.}67.$ A system formed of methane$(1)$ and a light oil$(2)$ at $200K$ and $30$ bar consists of a vapor phase containing $95$mol$-\%$ methane and a liquid phase containing oil and dissolved methane. The fugacity of the methane is given by Henry's law, and at the temperature of interest Henry's constant is $H_1=200$ bar. Stating any assumptions, estimate the equilibrium mole fraction of methane in the liquid phase. The second virial coefficient of pure methane at $200K$ is $-105c{m}^3*mo{l}^{-1}.$