A cylinder of compressed gas rolls off a boat and falls to the bottom of a lake.

Question

A cylinder of compressed gas rolls off a boat and falls to the bottom of a lake. Eventually it rusts and the gas bubbles to the surface. A chemist collects a sample of the gas with the idea of trying to identify the gas. The wet gas collected occupies a volume of 277 mL at a pressure of 828 torr and temperature of 28.0oC. The vapor pressure of water at 28.0oC is 0.0372 atm.

1. Calculate the volume (L) that the gas occupies after it is dried (the water vapor removed) and stored at STP.

The mass of the dry gas is 1549 mg. A fragment of the tank indicates that the gas is a monoatomic element.
2. Write out the full name of the gas.

Explanation / Answer

(1) P(gas) = P(total) - P(H2O)

= 828/760 - 0.0372 = 1.0523 atm


Ideal gas equation: PV = nRT

Moles of gas n = PV/RT

= 1.0523 x 0.277/(0.08206 x (273.15 + 28.0))

= 0.011795 mol


Volume of gas at STP = moles x molar volume at STP

= 0.011795 x 22.4

= 0.264 L


(2) Molar mass of gas = mass/moles of gas

= 1.549/0.011795

= 131 g/mol


Thus the gas is Xenon (Xe) which has an molar mass of 131 g/mol

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