Question

A gaseous compound is composed of $85.7\%$ by mass carbon and $14.3\%$ by mass hydrogen. Its density is $2.5{\text{g L}}^{-1}$ and one mole of the gas occupies $44.8\text{L}$ of space at a particular temperature and pressure. Determine the molecular formula of the compound.

• A. $C_2{H}_4$
• B. $C_2{H}_2$
• C. $C_4{H}_8$
• D. $C_4{H}_{10}$

Answer 1

The correct option is C $C_4{H}_8$

Since, we have the volume of $1\text{mol}$ of gas and the density in ${\text{g L}}^{-1}$, looking at the units, the molecular mass will be given by $d\times V$
$2.5\times 44.8{\text{g mol}}^{-1}=112{\text{g mol}}^{-1}$
Now, Empirical ratio for $C$ and $H$ as per their composition is,
$\frac{85.7}{12}:\frac{14.3}{1}=7.14:14.3=1:2$
$\therefore$ Empirical Formula is $C{H}_2$
So, Molecular formula will be $(C{H}_2{)}_n$, where
$n=\frac{112}{12+2}=8$
Molecular formula is $C_8{H}_{16}$.