What is the molecular formula of this compound?

Question

At STP, 762 ML of a gas has a mass of 1.02g. If the gas has an emphirical formula of CH3, what is the molecular formula of the compound.

Answer 1

From the emphirical formula of CH3, we have to conclude that the molecular formula is C2H6. The reasons are: CH3 is not a molecule but a radical. Since CH3 provide a single electron for bonding, C2H6 is a molecule. For any n > 2, n(CH3) simply can not bond together. The only solution is C2H6.

Now, we know that one mole of gas occupies 22.4L at STP. From the data given, we know the molar mass of this molecule is:
(22.4/0.762)*1.02g = 30.0g/mol
Therefore the molecule is confirmed ABSOLUTELY C2H6.

Answer 2

PV = nRT

Find n

n (the number of moles) x molar mass (g per mole) = total mass (1.02 g in this case)

The molecular formula must be a multiple of CH3 and the molar mass must be that same multiple of the mass of a CH3 group.