Question

A hydrocarbon contains $75%$ of carbon. Then its molecular formula is:
A.$C{{H}_{4}}$
B.${{C}_{2}}{{H}_{4}}$
C.${{C}_{2}}{{H}_{6}}$
D.${{C}_{2}}{{H}_{2}}$

Answer 1

Hint:Before talking about the answer, you should know about hydrocarbons. Hydrocarbons is an organic compound that consists of hydrogen and carbons. You should also know about the formula to calculate the number of moles. Moles are defined as a unit which can be calculated by weight per molar mass. Molar mass is defined as the addition of atomic masses of each element.
Formula used: $n=\dfrac{w}{M}$
Where, $n$ is the number of moles in a compound
$w$ is defined as the weight of the compound
$M$ is the molar mass of the compound.

Complete answer:
Let us assume that the weight of the unknown sample is $100g$ where it is given that , the carbon $75%$ and the hydrogen is $25%$ which is equal to $100%$
Hence, the weight of carbon is $75g$
And weight of hydrogen is $25g$
Since, the chemical formula deals with the number of moles not with weight in grams. Therefore, you have to convert each element by multiplying with element of their respective atomic masses.
The atomic mass of carbon is $12g$
The atomic mass of hydrogen is $1g$
Now, you have to calculate the moles of carbon and hydrogen
$n=\dfrac{w}{M}$
Where, $n$ is the number of moles in a compound
$w$ is the weight of the compound
$M$ is the molar mass of the compound
Now, on substituting the values in the above formula we get
Moles of carbon $=\dfrac{75}{12}=6.25mol$
Moles of hydrogen $=\dfrac{25}{1}=25mol$
Now, you can see that every $6.25molC=25molH$
Now, let us divide both the sides with the smallest number of moles which is carbon having $6.25g$
$C=\dfrac{6.25}{6.25}=1$
$H=\dfrac{25}{6.25}=4$
Therefore, the molecular formula is ${{C}_{1}}{{H}_{4}}$ that is $C{{H}_{4}}$
So, the correct option is $\left( A \right)$.

Additional information
Methane is defined as the main constituent of the natural gas, and it is the simplest alkane. Methane is used as fuels for automobiles, homes.

Note:
The unit of molar mass and weight is taken in grams.
To calculate the number of moles, you should know the atomic masses of carbon and hydrogen.
Molecular formula is defined as the kind of atoms and number of each atom present in a molecule.