Exercise 5 | Properties of Gases

ρ = m / V

Ideal-gas equation:

PV = nRT

⇒ PV = $\frac{\mathrm{mRT}}{\mathrm{M}}$

⇒ $\frac{\mathrm{m}}{\mathrm{V}}$ = $\frac{\mathrm{PM}}{\mathrm{RT}}$

⇒ ρ = $\frac{\mathrm{PM}}{\mathrm{RT}}$

P = pressure in Pa ⇒ 1.00 atm = 1.013 x 10⁵ Pa

M = molar mass ⇒ M = M_C + 4 x M_H = 16.4 g.mol^-1

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

T = temperature in K ⇒ 10.0°C = 288 K

ρ = $\frac{1.013 \times {10}^5 \times 16.4}{8.314 \times 288}$ = 6.94 x 10² g.m^-3 = 6.94 x 10^-1 g.L^-1