Question

The percentage composition of carbon by mole in methane is:
(A) 80 %
(B) 25 %
(C) 75 %
(D) 20 %

Answer 1

Hint: The number of moles in a given sample of an element or a compound can be calculated by dividing the total mass of the sample by the molar mass of the element or compound, as described by the following formula.
$\text{Moles=}\dfrac{\text{Weight}}{\text{Molecular}\,\text{Weight}}$

Complete step by step answer:
-In the field of chemistry, a mole is defined as the amount of a substance that contains exactly $6.02214076\text{ }\times \text{ }{{10}^{23}}~$ ‘elementary entities’ of the given substance.
-The number $6.02214076\text{ }\times \text{ }{{10}^{23}}~$ is popularly known as the Avogadro number which is the value of the Avogadro constant and is often denoted by the symbol ‘${{N}_{A}}$ ’. The elementary entities that can be represented in moles can be atoms, molecules, monatomic or polyatomic ions, and other particles (such as electrons).
-Methane is a hydrocarbon having the chemical formula $C{{H}_{4}}$.
-In methane there is one atom of carbon and four atoms of hydrogen. It is a hydride of group-14 and the simplest alkane, and is the main constituent of natural gas.
-One mole of methane has a molecular mass of 16 g/mol.
-In one mole of methane, we have one mole of carbon atoms and 4 moles of hydrogen atom, therefore, the percentage composition of C by mole in methane will be,
The percentage of C atom in methane is = $\dfrac{12}{16}\times 100 %$
Hence, percentage of C = 75 %
Therefore, one mole of methane has 75 % of carbon, The correct option is option “C” .

Note: The atomic mass of a carbon-12 atom is 12 atomic mass units, but that of a carbon-13 atom is 13 amu. The atomic mass of an element given will be roughly equal to the sum of all the protons and neutrons present in the nucleus of an atom.
If the percentage composition of hydrogen by mass was asked then, we will give the value 4 as the numerator in the formulae, since there are four moles of hydrogen present in methane.
- The percentage of H atom in methane is = $\dfrac{4}{16}\times 100%$
Therefore, percentage of H in methane = 25 %