Question

A cylinder 1.00m tall with inside diameter 0.120 m is used to hold propane gas(molar mass 44.1 g/mol) for use in a barbecue. It is initially filled in with gas until the gauge pressure is 1.30 x 10^6 Pa and the temperature is 22 degree Celsius. The temperature of the gas remains constant as it is partially emptied out of the tank, until the gauge pressure is 2.50 x 10^5 Pa. Calculate the mass of propane that has been used?

Answer 1

Volume of cylinder V = π x (diameter/2)² x height

= 3.142 x (0.120/2)² x 1.00 = 0.01131 m³

Temperature = 22 deg C = 295 K

Initial pressure P₁ = 1.30 x 10⁶ Pa

Final pressure P₂ = 2.50 x 10⁵ Pa

Using the ideal gas equation PV = nRT:

Initial moles of propane n₁ = P₁V/RT

= 1.30 x 10⁶ x 0.01131/(8.314 x 295) = 5.995 mol

Final moles of propane n₂ = P₂V/RT

= 2.50 x 10⁵ x 0.01131/(8.314 x 295) = 1.153 mol

Moles of propane used = n₁ - n₂

= 5.995 - 1.153 = 4.842 mol

Mass of propane used = moles of propane used x molar mass of propane

= 4.842 x 44.1 = 213.5 ≈ 214 g