A 9.800 mol sample of nitrogen gas is maintained in a 0.8166 L container at 301.8 K. What is the pressure in atm calculated using the van der Waals' equation for N2 gas under these conditions? For N2, a = 1.390 L2atm/mol2 and b = 3.910×10-2 L/mol.

The van der Waals' equation relates the properties of a gas, introducing constants "a" and "b" in order to consider gases as real gases. The equation is:

[tex](P+a.\frac{n^{2} }{V^{2} } ).(V-nb)=n.R.T[/tex]

where,

P: pressure

a: correction factor for intermolecular forces

V: volume

b: correction factor for molecules' volume

n: moles

R: ideal gas constant

T: absolute temperature

[tex](P+\frac{1.390L^{2}atm}{mol^{2}}.\frac{(9.800mol)^{2}}{(0.8166L)^{2}}).(0.8166L-9.800mol.\frac{3.910 \times 10^{-2}L}{mol})=9.800mol \times \frac{0.08206atm.L}{mol.K} \times 301.8K\\(P + 200.2atm).(0.4334L) = 242.7atm.L\\P=359.8 atm[/tex]