A hydrocarbon contains $10.5 \mathrm{~g}$ carbon and $1 \mathrm{~g}$ hydrogen. Its $2.8 \mathrm{~g}$ has $1 \mathrm{~L}$ volume at $1 \mathrm{~atm}$ and $127^{\circ} \mathrm{C}$, what is the number of carbon in the molecular formula of given hydrocarbon?

Question

Aicharya · Accepted Answer

Sum of masses of $\mathrm{C}$ and $\mathrm{H}=10.5+1.0=11.5$
$\%$ of $\mathrm{C}=\frac{10.5}{11.5} \times 100=91.3 \%$
$\%$ of $\mathrm{H}=\frac{1.0}{11.5} \times 100=8.7 \%$
Element $\% \quad$ Ratio of atoms $\quad$ Simplest ratio
$\begin{array}{llll}\text { C } & 91.3 & 91.3 / 12=7.61 & 7.61 / 7.61=1 \times 7=7\end{array}$
$\mathrm{H}$
$\begin{array}{lll}8.7 & 8.7 / 1=8.7 & 8.7 / 7.61=1.14 \times 7=8\end{array}$
$\therefore$ Empirical formula $=\mathrm{C}_{7} \mathrm{H}_{8}$
We know that $n=\frac{P V}{R T}$ $\frac{\text { mass }}{\text { molar mass }}=\frac{P V}{R T}$
$\frac{2.81}{\mathrm{M}}=\frac{1 \times 1}{0.082 \times 400} ; \mathrm{M}=92.168 \approx 92$
$\therefore n=\frac{84+8}{92}=1$
$\therefore$ Molecular formula $=\left(\mathrm{C}_{7} \mathrm{H}_{8}ight) \times 1=\mathrm{C}_{7} \mathrm{H}_{8}$ ~

A hydrocarbon contains $10.5 \mathrm{~g}$ carbon and $1 \mathrm{~g}$ hydrogen. Its $2.8 \mathrm{~g}$ has $1…

Solution