A hydrocarbon contains `10.5 g` of carbon per gram of hydrogen. `1 L` of vapour of the hydrocarbon at `127^(@)C` and 1 atm pressure weighs `2.8 g`. Find the molecular formula of the hydrocarbon.

Explanation

Using the general gas equation : `PV = nRT`, we have
`1 xx 1 = (2.8)/(m) xx 0.0821 xx 400`
Hence, molar mass `= 91.95`
Atomic ratio : `H = (1)/(1), C = (10.5)/(2) = 0.875`
Least whole numbe ratios:
`H = 8` and `C = 7` (0.875 multipled by 8 gives 7 as whole figure).
Hence, empirical formula `= C_(7) H_(8)`
Empirical formula weight = 92
Molar mass and empirical formula mass being the same, the molar formula is `C_(7) H_(8)`.