Question

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

• A. $C_4{H}_4$
• B. $C_4{H}_8$
• C. $C_8{H}_{16}$
• D. $C_8{H}_8$

Answer 1

The correct option is C $C_8{H}_{16}$

Since we have the volume of 1 mol of gas and the density in g/L, looking at the units, the molecular mass will be given by $d\times V$
$M=2.5{\text{g L}}^{-1}\times 44.8\text{L}=112\text{g}$
Empirical formula,
Assuming 100 g of the compound,
Moles of C = $\frac{85.7}{12}$
Moles of H = $\frac{14.3}{1}$
Their mole ratio,
$\frac{85.7}{12}:\frac{14.3}{1}=7.14:14.3=1:2$
$\therefore$ Empirical Formula is $C{H}_2$
So, molecular formula would be $(C{H}_2{)}_n$, where
$n=\frac{112}{12+2}=8$
Molecular formula is $C_8{H}_{16}$.