Question

Nitrogen is stored in a 0.425 m² tank at 560 atm, 456 K. Determine the mass of nitrogen in the tank using (a) ideal gas theory, (b) the compressibility factor, (c) van der Waals equation.

Answer 1

Ideal gas equation

$PV=nRT$

$V=\frac{nRT}{P}$

$$V=\frac{1\times8.31\times456}{560\times10^5}=\frac{3707.28}{560\times10^5}=6.760\times10^{-5} m^3$$

$$560\times10^5\times6.76\times10^{-5}=8.31\times456$$

LHS=RHS

Compressibility factor

$Z=\frac{PV}{RT}$

$Z=\frac{560\times10^5\times6.760\times10^{-5}}{8.31\times456}=0.999$

Wander val equation

$(P+\frac{an^2}{V^2})(V-nb)=nRT$

n=1mol

$(P+\frac{a}{V^2})(V-b)=RT$

$$(560\times10^5+\frac{a}{6.76\times10^{-5}})(6.76\times10^{-5}-b)=8.31\times456$$

LHS=RHS