Question

In addition to carbon monoxide $(CO)$ and carbon dioxide $(C{O_2})$ , there is a third compound of carbon called carbon suboxide. If a $2.5g$ sample of carbon sub-oxide contains $1.32g$ of $C$ and $1.18g$ of $O$ , using the law of multiple proportions, a possible formula of carbon suboxide can be deduced. What is the number of carbon atoms in such a formula?

Answer 1

Hint: We have studied chemistry in multiple proportions. It states that if two elements form more than one compound between then then the ratios of the masses of the second element which combines in a fixed mass proportion of the first element will always be ratios of small whole numbers. This law is also called Dalton’s law.

Complete step by step answer:
We know that carbon has another compound called carbon suboxide. It is also called tricarbon dioxide as it contains three carbon atoms bonded to two oxygen atoms.
As per given in the question, we have
Carbon suboxide = $2.5g$
Carbon proportion = $1.32g$
Oxygen proportion = $1.18g$
We know the atomic mass of carbon is $12$ and that of oxygen is $16$ .
In carbon monoxide the ratio of carbon to oxygen is given by
$ = \dfrac{{12}}{{16}} = \dfrac{1}{{1.33}}$
On simplification we get,
$ = 0.75$
In carbon dioxide the ratio is given by,
$ = \dfrac{{12}}{{32}} = \dfrac{1}{{2.66}}$
On simplification we get,
$ = 0.375$
For carbon suboxide, the ratios is given by,
$ = \dfrac{{1.32}}{{1.18}}$
On simplification we get,
$ = 1.12$
The ratio of carbon monoxide to carbon dioxide to carbon suboxide is observed as $2:1:3$ .
Likewise, we will determine the ratio of the given mass of carbon atom to its molecular mass with the ratio of mass of oxygen given to its molecular mass.
$\dfrac{{1.32}}{{12}}:\dfrac{{1.18}}{{16}} = 3:2$
We can clearly observe that the ratio between mass proportion of carbon to oxygen is $3:2$.
Hence, the derived chemical formula is ${C_3}{O_2}$ .
Hence, the correct answer is option A.

Note:
We need to remember that the law of multiple proportions fails in case of non-stoichiometric compounds and polymers and oligomers. As obtaining a small whole number is difficult for these compounds which contain long chains of hydrocarbons. Carbon suboxide is also called cumulene as it has four double bonds. Physically it is an oily gas at room temperature and has an obnoxious odour. It is used in the preparation of malonates. It can polymerize spontaneously under certain conditions to form a red, yellow or black solids.