Exercise 6 | Properties of Gases

1) Ideal gas ⇒ Ideal-gas equation:

PV = nRT 

⇒ P = $\frac{\mathrm{nRT}}{\mathrm{V}}$

⇒ P = $\frac{\mathrm{mRT}}{\mathrm{MV}}$

m = mass in g

R = ideal gas constant = 8.314 m³.Pa.K^-1.mol^-1

T = temperature in K ⇒ 220°C = 493 K

M = molar mass ⇒ M = 3 x M_C + 8 x M_H = 44.1 g.mol^-1

V = volume in m³ ⇒ 2.00 L = 2.00 dm³ = 2.00 x 10^-3 m³

P = $\frac{55.0 \times 8.314 \times 493}{44.1 \times 2.0 \times {10}^{-3}}$= 2.56 x 10⁶ Pa = 25.6 bar

2) Non ideal gas ⇒ Van der Waals equation:

(P + a $\frac{{\mathrm{n}}^2}{{\mathrm{V}}^2}$)(V – nb) = nRT

⇒ (P + a $\frac{{\mathrm{n}}^2}{{\mathrm{V}}^2}$) = $\frac{\mathrm{nRT}}{\mathrm{V} - \mathrm{nb}}$

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

n = number of moles = $\frac{55.0}{44.1}$ = 1.25 mol

a = 9.392 L².bar.mol^-2 = 9.392 x 10^-1 m⁶.Pa.mol^-2

b = 0.0905 L.mol^-1 = 9.05 x 10^-5 m³.mol^-1

P = 2.72 x 10⁶ – 3.67 x 10⁵ = 2.35 x 10⁶ Pa = 23.5 bar