Question

A compound having molecular mass 30 ${g}/{mol}\;$ is found to contain 80% of carbon and 20% of hydrogen, then the molecular formula of the compound is:
(A) ${{C}_{6}}{{H}_{6}}$
(B) ${{C}_{2}}{{H}_{5}}OH$
(C) ${{C}_{2}}{{H}_{6}}$
(D) ${{C}_{2}}{{H}_{4}}$

Answer 1

Hint: We can find the percentage composition of given compound from the given details and from this we can find the molar ratio of carbon and oxygen. This will allow us to formulate the empirical formula and from this we could easily find the molecular formula of the unknown compound.

Complete step by step answer:
 -For doing this type of problem we usually assume that the mass of the unknown compound is 100 g. It’s given that the unknown compound contains 80% of carbon and 20% of hydrogen.
-Therefore the weight of hydrogen in the unknown compound is 20 g and the weight of carbon in unknown compound is 80 g.
 - Now we need to work out the molar quantities. For calculating the number of moles we must divide the given mass by molar mass of the element. As we know the molecular weight of hydrogen is 1 g and the molecular weight of carbon is 12. Thus the number of moles of carbon and hydrogen in the unknown compound can be found as follows
\[moles\text{ }of\text{ }carbon=\dfrac{80}{12}=6.67\]
\[moles\text{ }of\text{ }hydrogen=\dfrac{20}{1}=20\]
The ratio of number of moles of carbon to number of moles of hydrogen is shown below,
\[number\text{ }of\text{ }moles\text{ }of\text{ }carbon:number\text{ }of\text{ }moles\text{ }of\text{ }hydrogen=6.67:20\approx 1:3\]

Thus for one mole of carbon, three moles of hydrogen is present in the unknown compound. Hence the empirical formula of the compound is $C{{H}_{3}}$ and the empirical mass is 15${g}/{mol}\;$(12 from one carbon atom and 3 free from three hydrogen atoms).
The molecular formula will be a multiple of empirical formula and it’s shown below
\[molecular\text{ }formula=n\times empirical\text{ }formula\]\[\]
 Where $n=\dfrac{molecular\text{ }mass}{empirical\text{ }mass}$
It’s given in the question that the molecular mass of compound as 30 ${g}/{mol}\;$ and empirical mass is 15${g}/{mol}\;$.
 \[n=\dfrac{30}{15}=2\]
Thus the molecular formula will be ${{\left( C{{H}_{3}} \right)}_{2}}$.That is the molecular formula of unknown compound will be ${{C}_{2}}{{H}_{6}}$.
So, the correct answer is “Option C”.

Note: Keep in mind that there are three major sorts of chemical formulas such as empirical, molecular and structural formula. The empirical formula shows the simplest whole-number ratio of atoms in a compound, structural formulas show how the atoms in a molecule are bonded to each other and molecular formulas show the number of each type of atom in a molecule.