Question

Calculate the second Virial coefficient (B2) of Methane at 300 K from its van der Waals constants: a0.2283 Pa m^6 mol^-2 and b = 0.0428x 10 ^-3 m^3 mol^-1. Calculate the compressibility factor at 300 K and 1 bar.

Answer 1

Given conditions

Temperature T = 300 K

Pressure P = 1 bar

van der Waals constants

a = 0.2283 Pa.m6.mol-2

a = 0.2283 Pa * (1bar/10^5Pa) m6 * (1000L/m3)² mol-2

a = 2.283 bar L2 mol-2

b = 0.0428 * 10^-3 m3.mol-1

b = 0.0428 * 10^-3 m3 * (1000L/m3) mol-1

b = 0.0428 L mol-1

First virial coefficient B1 = b - (a/RT)

= 0.0428 - (2.283/0.08314*300)

= - 0.0487 L/mol

Second virial coefficient B2 = b²

= ( 0.0428)²

= 1.83*10^-3 L2/mol2

Compressibility factor

Z = 1 + B1/V + B2/V²

Molar volume V = RT/P = 0.08314*300/1 = 24.942 L/mol

Z = 1 + (-0.0487/24.942) + (1.83*10^-3/24.942²)

Z = 1 - 0.0019525 + 2.9416*10^-6

Z = 0.99805