Question

0.2 mol of hydrocarbons undergo complete combustion to give 35.2 of carbon dioxide and 14.4g of water as the only product. What is the molecular formula of hydrocarbon

Answer 1

Answer:

$\rm C_4 H_8$.

Explanation:

Look up the relative atomic mass of $\rm C$, $\rm H$, and $\rm O$ on a modern periodic table:

• $\rm C$: $12.011$.
• $\rm H$: $1.008$.
• $\rm O$: $15.999$.

Calculate the molecular mass of $\rm CO_2$ and $\rm H_2O$:

$M(\mathrm{CO_2}) = 12.011 + 2 \times 15.999 = 44.009\; \rm g \cdot mol^{-1}$;

$M(\mathrm{H_2O}) = 2 \times 1.008 + 15.999 = 18.015\; \rm g \cdot mol^{-1}$.

Given the mass $m$ of $\rm CO_2$ and $\rm H_2O$ produced, calculate the number of moles of molecules that were produced:

$\displaystyle n(\mathrm{CO_2}) = \frac{m(\mathrm{CO_2})}{M(\mathrm{CO_2})} \approx 0.80\; \rm mol$;

$\displaystyle n(\mathrm{H_2O}) = \frac{m(\mathrm{H_2O})}{M(\mathrm{H_2O})} \approx 0.80\; \rm mol$.

Calculate the number of moles of $\rm C$ atoms and $\rm H$ atoms in these $\rm CO_2$ and $\rm H_2O$ molecules.

• Each $\rm CO_2$ molecule contains one $\rm C$ atom. Therefore, that $0.80\; \rm mol$ of $\rm CO_2\!$ contains $0.80\; \rm mol\!$ of $\rm C\!$ atoms.
• Each $\rm H_2O$ molecule contains two $\rm H$ atoms. Therefore, that $0.80\; \rm mol$ of $\rm H_2O\!$ contains $2 \times 0.80\; \rm mol = 1.60\; \rm mol$ of $\rm H\!$ atoms.

The combustion reaction here include two reactants: the hydrocarbon and $\rm O_2$.

As the name suggests, hydrocarbons contain only $\rm C$ atoms and $\rm H$ atoms. On the other hand, $\rm O_2$ contains only $\rm O$ atoms.

Therefore, all the $\rm C$ and $\rm H$ atoms in those $\rm CO_2$ and $\rm H_2O$ molecules are from the unknown hydrocarbon. (With a similar logic, all the $\rm O$ atoms in those combustion products are from $\rm O_2$.)

In other words, that $0.20\; \rm mol$ of this unknown hydrocarbon molecules contains:

• $0.80\; \rm mol$ of $\rm C$ atoms, and
• $1.60\; \rm mol$ of $\rm H$ atoms.

Hence, each of these hydrocarbon molecules would contain $(0.80\; \rm mol) / (0.20\; \rm mol) = 4$ carbon atoms and $(1.60\; \rm mol) / (0.20\; \rm mol) = 8$ hydrogen atoms.

The molecular formula of this hydrocarbon would be $\rm C_{4} H_{8}$.