Problem $1$ a$.$ Using the virial equation of state $($with one correction term$),$ b$.$ Given the equation of state of a gas, where B$(400$ K$)=0\mathrm{.}00001$ m$^3/$mol and C$(400$ K$)0\mathrm{.}005$ m$^6/$mol$^2,$ calculate the pure$-$state fugacity at P $=0\mathrm{.}01$ MPa and T $=600$ K$.$ c$.$ Calculate the fugacity of pure liquid water at $70$ degreeC at both $100$ bar and $400$ bar. Hint: You will need to determine the vapor pressure of water at this temperature. d$.$ Using corresponding states, calculate the fugacity coefficient of a pure liquid at T $300$ K and P $=3$MPa. You know that TC $=400$K and PC $=10$MPa.