Question

What is the molar mass of a pure gaseous compound having a density of 2.95 g/l at 32⁰c and 860 mm hg? (1 atm = 760 mm hg)?

Answer 1

Given:
ρ = 2.95 g/L = 2.95 kg/m³, the density
T = 32°C = 32+273 K = 305 K, the temperature
p = 860 mm Hg = (860/760) atm = 1.1316 atm
= 1.1316*101325 Pa
= 1.14657 x 10⁵ Pa

The ideal gas law is
p = ρ*(R/M)*T
where
R = 8.314 J/(mol-K), the gas constant
M = molar mass, kg/mol

The molar mass is

`M= (\rho R T)/(p) = ((2.95 \, kg/m^(3))*(8.314 \, J/(mol-K)*(305 \, K))/(1.14657 * 10^(5) \, Pa) =0.0652 \, kg/mol`
The molar mass is 0.0652 kg/mol = 65.2 g/mol

Answer: 65.2 g/mol