Question

A gaseous compound is composed of $85.7\%$ by mass carbon and $14.3\%$ by mass hydrogen. Its density is $2.28\text{g/L}$ at $300\text{K}$ and $1\text{atm}$. Determine the molecular formula of the compound.

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

Answer 1

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

$\because d=\frac{PM}{RT}\Rightarrow M=\frac{dRT}{P}=\frac{2.28\times 0.0821\times 300}{1}=56.15\text{g/mol}$

Empirical formula $=\frac{85.7}{12}:\frac{14.3}{1}=7.14:14.3=1:2$
Empirical formula is $C{H}_2$.
Molecular formula is $(C{H}_2{)}_n$ where $n=\frac{56.15}{12+2}\approx 4$.
Therefore molecular formula is $C_4{H}_8$.