Question

Number of carbon atoms present in 22g $C{O_2}$ is
A.$6.02 \times {10^{23}}$
B.$3.01 \times {10^{^{23}}}$
C.$3.01 \times {10^{^{ - 23}}}$
D.$6.02 \times {10^{ - 23}}$

Answer 1

Hint:An atom is the smallest unit of matter that forms chemical elements. Every solid, liquid, gas is composed of atoms. An atom consists of atomic number and atomic mass. Atoms form molecules. We shall calculate the number of moles in the given weight and multiply it with Avogadro’s number to find the number of molecules in it.
Formula Used: ${\text{Moles of a substance = }}\dfrac{{{\text{Weight of substance}}}}{{{\text{Molecular mass of substance}}}}$

Complete step by step answer:
The mole (symbol: mol) is the unit of measurement for quantity of substance in the International System of Units. The mole is widely used in chemistry as a convenient way to tell the quantity of reactants and products of a chemical reaction. It is used to calculate the amount of a substance.
For 22g of carbon dioxide,
${\text{Moles of carbon dioxide = }}\dfrac{{{\text{Weight of carbon dioxide}}}}{{{\text{Molecular mass of carbon dioxide}}}}$
Molecular mass of carbon dioxide is 44 g.
Hence, ${\text{Moles of carbon dioxide = }}\dfrac{{22}}{{44}}{\text{ = }}\dfrac{1}{2}$
Now, 1 mole of carbon dioxide contains $6.02 \times {10^{23}}$ molecules of carbon dioxide. As a single molecule of carbon dioxide contains 1 atom of carbon, that is why, $6.02 \times {10^{23}}$ molecules of carbon dioxide will contain $6.02 \times {10^{23}}$ atoms of carbon.
As one mole of carbon dioxide contains $6.02 \times {10^{23}}$ atoms of carbon, half mole of carbon dioxide will contain half of the $6.02 \times {10^{23}}$ atoms of carbon and that will be equal to $3.01 \times {10^{^{23}}}$ carbon atoms.

Therefore, 22 g of carbon dioxide will contain $3.01 \times {10^{^{23}}}$ carbon atoms, which is option B.

Note:
$6.02 \times {10^{23}}$ is the Avogadro number. Avogadro's law is an experimental gas law relating the volume of a gas to the amount of substance of gas present. Avogadro's law states at the same temperature and pressure, equal volumes of gases have the same number of molecules. For a given mass of an ideal gas, the moles and volume of the gas are directly proportional if the pressure and temperature are constant.