$3\mathrm{.}101($Moran $8^{th}$ edition$)$ A tank contains $0\mathrm{.}5m^3$ of nitrogen $(N_2)$ at $-71C$ and $1356$ kPa $.$

Determine the mass of nitrogen, in kg $,$ using:

a$)$ The ideal gas model

b$)$ Data from the compressibility chart

c$)$ Comment on the applicability of the ideal gas model for nitrogen at this state