Answer to Question #96301 in Molecular Physics | Thermodynamics for Jake

Question

Use the van der Waals equation and the ideal gas equation, calculate the volume of 1.000 mol of neon gas at a pressure of 500.0 atm and a temperature of 355.0 K. Explain why the two values are different. (For Ne: a = 0.211 L2 atm/mol2 and b = 0.0171 L/mol)

Answer 1

the Van der Waals equation:

$(p+\frac{a\nu^2}{V^2})(V-b\nu)=\nu RT\\ V^3-(\frac{RT}{p}+b)\nu V^2+\frac{a\nu^2}{p}V-\frac{ab\nu^3}{p}=0\\ V^3-5.9172V^2+0.000422V-7.2162\cdot10^{-6}=0$

If we solve that equation, then we get $V=5.92713 \, L$