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.

Options

A. `C_(6)H_(14)`
B. `C_(5)H_(10)`
C. `C_(6)H_(12)`
D. `C_(7)H_(8)`

Answer

D

Explanation

Using the general gas equation `: pV = nRT`, we have
`1xx 1 = (2.8)/m xx 0.0821 xx 400 `
Hence, molar mmass `= 91.95`
Atomic ratio `H = 1/1, C= 10.5/12 = 0.875 `
Lest whole number ratios:
H = 8 and C = 7 (`0. 875` multiplied 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 molecular formula is `C_(7) H_(8)