Answer to Question #188639 in General Chemistry for nana

Question

calculate the molar volume of argon at 100'C and 100 atm on the assumption that it is a van der waals gas

Answer 1

So molar volume is the volume of 1 mole. here's the Van der Waals equation

(P + an²/V²) x (V - nb) = nRT

V - Pnb + an²/V - an³b/V² = nRT

PV - Pnb + an²/V - an³b/V² - nRT = 0

multiply through by V²

(P)V³ + (-Pnb - nRT)V² + (an²)V - an³b = 0

P = 100 atm

T = 373.15 K

n = 1 mole

a = 1.355 L²bar/mol² x (1atm / 1.01325bar) = 1.337 L²atm/mol²

b = 0.03201 L/mol

(100 atm) * V³ + (-33.82 Latm) * V² + (1.337 L²atm) * V - (0.04280 L³atm) = 0

100V³ - 33.82V² + 1.337V - 0.04280 = 0

V/n = 0.299 L/mol