Question

A sample of 1.000 mol of CO2(g) is confined to a 3.000-L container at 0.000°C. Calculate the pressure of the gas using (a) the ideal-gas equation and (b) the van der Waals equation.

Answer 1

(a) Ideal Gas Law

pV = nRT

R = 0.082058 L atm/K mol

n = 1.0 mol

V = 3 L

T = 273.15 K

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

$p = \frac{1 \times 0.082058 \times 273.15}{3} = 7.47 \; atm$

(b) van der Waals equation

$P + \frac{n^2a}{V^2}(V – nb) = nRT$

$P = \frac{nRT}{V – nb} - \frac{n^2a}{V^2}$

$a = 3.59 \;L^2\;atm/mol^2$

$b = 0.0427 \;L/mol$

$P = \frac{1 \times 0.082058 \times 273.15}{3 – (1 \times 0.0427)} - \frac{1^2 \times 3.59}{3^2} = 7.579 – 0.399 = 7.18 \;atm$