Question

How many atoms are present in 0.1 mole of a tetra atomic gas? (Given ${{\text{N}}_{\text{A}}} = 6.02 \times {10^{23}}{\text{ mo}}{{\text{l}}^{ - 1}}$)
$
  {\text{A}}{\text{. 2}}{\text{.4}} \times {\text{1}}{{\text{0}}^{22}} \\
  {\text{B}}{\text{. 6}}{\text{.026}} \times {\text{1}}{{\text{0}}^{22}} \\
  {\text{C}}{\text{. 2}}{\text{.4}} \times {\text{1}}{{\text{0}}^{23}} \\
  {\text{D}}{\text{. 3}}{\text{.600}} \times {\text{1}}{{\text{0}}^{23}} \\
 $

Answer 1

Hint- Here, we will proceed by obtaining the number of molecules in 0.1 mole of the gas and then, we will find the number of atoms in 0.1 mole of the gas by multiplying the number of molecules in 0.1 mole of the gas with 4.

Complete answer:
As we know that the number of molecules in 1 mole of a gas is given by Avogadro’s number which is given by
Number of molecules in 1 mole of a gas = $6.02 \times {10^{23}}{\text{ }}$molecules
In order to find the number of molecules in 0.1 mole of a gas, we will multiply 0.1 with the number of molecules in 1 mole of a gas (i.e., Avogadro’s number)
i.e., Number of molecules in 0.1 mole of a gas = 0.1$ \times $( Number of molecules in 1 mole of a gas)
$ \Rightarrow $ Number of molecules in 0.1 mole of a gas = $0.1 \times 6.02 \times {10^{23}} = 6.02 \times {10^{22}}$ molecules
For any tetra atomic gas, in one molecule of the gas there will be four atoms.
In order to find the total number of atoms in 0.1 mole of a tetra atomic gas, we will multiply 4 with the number of molecules in 0.1 mole of the gas.
i.e., Number of atoms in 0.1 mole of a tetra atomic gas = 4$ \times $( Number of molecules in 0.1 mole of a gas)
$ \Rightarrow $ Number of atoms in 0.1 mole of a tetra atomic gas = $4 \times 6.02 \times {10^{22}} = 24.08 \times {10^{22}} = 2.4 \times {10^{23}}$ atoms
Therefore, there are $2.4 \times {10^{23}}$ atoms in 0.1 mole of a tetra atomic gas.

Hence, option C is correct.

Note- Avogadro's number is the number of units in one mole of any substance (defined as its molecular weight in grams) given by ${{\text{N}}_{\text{A}}} = 6.02 \times {10^{23}}{\text{ mo}}{{\text{l}}^{ - 1}}$. The units may be electrons, atoms, ions, or molecules, depending on the nature of the substance and the character of the reaction.