Work on the following problems using the generalized Z$-$charts from the class notes:

a$)$ Calculate the mass of ethane contained in a $0\mathrm{.}5f{t}^3$ vessel at $140F$ and $2000$ psia.

b$)$ If $10$ pounds mass of ethane is contained in a $0\mathrm{.}5f{t}^3$ vessel, at what temperature does it exert a pressure of $3000$ psia?

c$)$ To what pressure does one fill a $0\mathrm{.}1m^3$ vessel at $25C$ in order to store $25kg$ of ethylene in it$?$

d$)$ For each of the previous parts, use the Z$-$charts to determine whether or not the virial equation in the form $Z=1+B\frac{P}{R}T$ is valid.