Question

A compound having molecular mass 30 g/mol is found to contain $80\%$ of carbon and $20\%$ of hydrogen, then the molecular formula of the compound is:

• A. $C_6{H}_6$
• B. $C_2{H}_{5}OH$
• C. $C_2{H}_6$
• D. $C_2{H}_4$

Answer 1

The correct option is C $C_2{H}_6$

Let the mass of unknown compound be 100 g.

Given that the compound contains $80\%$ of carbon and $20\%$ of hydrogen.

Therefore, weight of carbon in the compound $=80g$

weight of hydrogen in the compound $=20g$

Molecular weight of carbon $=12g$

Molecular weight of hydrogen $=1g$

$\therefore$ moles of carbon in the compound $=\frac{80}{12}=6.67$

Moles of hydrogen in the compound $=\frac{20}{1}=20$

Ratio of no. of moles of carbon to no. of moles of hydrogen-

No. of moles of carbon : no. of moles of hydrogen $=6.67:20\approx 1:3$

$\therefore$ 3 moles of hydrogen are present in the compound for 1 mole of carbon.

Hence, the empirical formula of the compound is $C{H}_3$.

empirical mass$=15$ g/mol

Molecular formula $={\left(C{H}_3\right)}_n$

whereas,

$n=\frac{\text{molecular mass}}{\text{empirical mass}}=\frac{30}{15}=2$

Thus, the molecular formula of the compoud is $C_2{H}_6$