# Hydrocarbon contains 18.18% hydrogen and 81.82% carbon. One litre of this gas has the same mass as carbon dioxide. What is the molecular formula of this hydrocarbon?

Sep 25, 2016

Given the percentage composition of HC as C->81.82% and H->18.18%

So the ratio of number if atoms of C and H in its molecule can will be

$C : H = \frac{81.82}{12} : \frac{18.18}{1}$

$C : H = 6.82 : 18.18$
$= \frac{6.82}{6.82} : \frac{18.18}{6.82} = 1 : 2.66 \approx 3 : 8$

So the Empirical Formula of hydrocarbon is ${C}_{3} {H}_{8}$

As the mass of one litre of hydrocarbon is same as that of $C {O}_{2}$ The molar mass of the HC will be same as that of $C {O}_{2}$ i.e $44 \frac{g}{\text{mol}}$

Now let Molecular firmula of the HC be ${\left({C}_{3} {H}_{8}\right)}_{n}$

Using molar mass of C and H the molar mass of the HC from its molecular formula is
$\left(3 \times 12 + 8 \times 1\right) n = 44 n$

So

$44 n = 44 \implies n = 1$

Hence the molecular formula of HC is ${C}_{3} {H}_{8}$