A 0.500 g sample of He at STP has a volume that is one-half that of an unknown pure gas also at STP. The unknown pure gas sample has a mass of 36.5 g. What is the molar mass of the unknown gas?

Molar mass of the unknown gas: 146 g / mol

Explanation:

At STP, any "ideal" gas is contained in a volume of 22.4L. This situation, for 1 mol of gas. In this case we have:

0.5 g / 4 g/mol = 0.125 moles of He

These amount of He occupies 0.125 mol. 22.4L / 1 mol = 2.8 L so the double of volume will be occupied by the unkown gas.

22.4 L / 1 mol = (2.8 L. 2) / x moles

22.4L / 1 mol = 5.6 L / x mol

x mol = 5.6L / 22.4L → 0.25 moles

To determine the molar mass of the unknown gas → 36.5 g / 0.25 mol = 146 g / mol