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identifying a gas (check partial work)

A cylinder was found in a storeroom of a manufacturing company. The cylinder was so old that the label had fallen off, and no one remembered what the cylinder held. A 5 mg sample was found to occupy 4.13 mL at 23 Celsius and 745 torr. The sample was also found to be composed of only carbon and hydrogen. Identify the gas.

n = PV/RT 5mg = 0.005g

0.98 atm * 0.00413/0.0821*296K = 1.665E-4 mol(what? since comp.not known

M.W.= 0.005/1.665E-4 = 30.03 g/mol

Molecular formula: C2H6 by manipulating the numbers of hydrogen. What is the right logical way to proceed though. Don't I have to follow pattern to find molecular formula?

No, I think this is logical enough. CH4 would be 16, CH3- would be 15 and 30/15 = 2 so two units of CH3 would do it and CH3CH3 (or C2H6) does the trick. You know anything above C3 won't work because 3 x 12 = 36 and that leaves no rooom for H atoms. Thus, C1 and C2 are the only possibilties.

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