Calculate $Z$ and $V$ for ethylene at $25C$ and $12$ bar by the following equations:

$($a$)$ The three item truncated virial equation with the following experimental values of

virial coefficients:

$B=-140c{m}^{3}mo{l}^{-1},C=7200c{m}^{6}mo{l}^{-2}$

$($b$)$ The two$-$item truncated virial equation, with a value of $B$ from the generalized Pitzer

correlation.

$($c$)$ The Peng$/$Robinson equation.

Answer

$($a$)Z=0\mathrm{.}929$ and $V=1919c\frac{m^3}{m}ol($Iteration required$)$

$($b$)Z=0\mathrm{.}932,V=1925c\frac{m^3}{m}ol$

$($c$)Z=0\mathrm{.}92,V=1900\mathrm{.}6c\frac{m^3}{m}ol$

A $30-m^3$ tank contains $14m^3$ of liquid $n-$butane in equilibrium with its vapor at $25C.$

Estimate the mass of n$-$butane in the tank. The vapor pressure of $n-$butane at the given

temperature is $2\mathrm{.}43$ bar. Use Pitzer's and Rackett's equations when applicable.

Calculate the mass of n$-$butane vapour: $m_{\text{v}\text{a}\text{p}}=98kg$

Calculate the mass of n$-$butane liquid: $m_{\text{l}\text{i}\text{q}}=7983kg$

The total mass of n$-$butane in the tank: $m=8081kg$

A rigid closed vessel with a volume of $200$ liters contains $2kg$ of $n-$hexane in gas

state at $T=100C.$ This vessel is heated to a temperature of $500C.$ The PVT behavior

of n$-$hexane can be well predicted by the virial equation of state if Pitzer's generalized

correlations are used, but we intend to estimate the pressure of the vessel over the

temperature range of $100$ to $500C$ using the ideal gas equation of state. Calculate the

errors of this estimation over the mentioned temperature range at $100C$ and $500C,$

respectively.

At $100C,$ error $\%=4\mathrm{.}7\%$

At $500C,$ error $\%=0\mathrm{.}625\%$