LPG is a useful fuel in rural locations without natural gas pipelines. A leak during the filling of a tank can be extremely dangerous because the vapor is denser than air and drifts to low elevations before dispersing, creating an explosion hazard. a.) What volume of vapor is created by a leak of 40 L of LPG? Model the liquidbefore leaking as propane with density pL=0.24g/cm^3. b) what is the mass density of pure propane vapor after depressurization to 293K and 1 bar? compare to the mass density of air at the same conditions.

The aanswers to the question are

(a) 5.33 m³

(b) 1.83 kg/m³

Explanation:

Volume of leak = 40 L, density of propane = 0.24g/cm³

Mass of leak = Volume * Density = 40000 cm³*0.24 g/cm³ = 9600 gram

Molar mass of propane = 44.1 g/mol Number of moles = 9600/44.1 = 217.69 moles

at 1 atmosphare and 298.15 K we have

PV = nRT therefore V = nRT/P = (217.69*8.3145*298.15) / ‪101325‬ = 5.33 m³

The volume of the vapour = 5.33 m³

(b) Density = mass/volume

Recalculating the above for T = 293 K we have V = 5.33*293:298.15 = 5.23 m³

Therefore density of propane vapor = 9600/5.23 = 1834.22 g/m³ or 1.83 kg/m³