Question

The number of atoms in 0.1 mol triatomic gas is:
$\left( {{N_A} = 6.02 \times {{10}^{23}}mo{l^{ - 1}}} \right)$

$$A.{\text{ }}6.026 \times {10^{22}} \\\ B.{\text{ 1}}{\text{.806}} \times {10^{23}} \\\ C.{\text{ }}3.6 \times {10^{23}} \\\ D.{\text{ 1}}{\text{.8}} \times {10^{22}} \\\$$

Answer 1

Hint: In order to solve the given problem first we will understand the structure of the triatomic molecule then we will understand the concept behind the number of molecules in one mole of any gas. Finally after finding the number of atoms in a molecule and total number of molecules we will use the value of Avogadro’s number given along the problem to find the number of atoms.

Complete step by step solution: Given that: the gas molecule is triatomic.
Also we have the number of moles of gas is 0.1.
To find the number of atoms present in 0.1 mole of gas.
As we know that the triatomic gas of a triatomic molecule means that the number of atoms present in one molecule of the gas is 3.
As we know that there is Avogadro’s number of molecules in one mole of gas. So we have ${N_A} = 6.02 \times {10^{23}}$ molecules in one mole of gas.
As we have 0.1 mole of gas present, so the number of molecules in 0.1 moles of the gas is:

$$= 0.1 \times {N_A} \\\ = 0.1 \times 6.02 \times {10^{23}} \\\ = 6.02 \times {10^{22}} \\\$$

Now since we have the number of molecules of the gas. And also we know that there are 3 atoms present in one molecule.
So the number of atoms present in 0.1 mole of the gas is:

$$= 3 \times 6.02 \times {10^{22}} \\\ = 18.06 \times {10^{22}} \\\ = 1.806 \times {10^{23}} \\\$$

Hence, the number of atoms in 0.1 mol triatomic gas is $1.806 \times {10^{23}}$

So, the correct answer is option B.

Note: In order to solve such problems students must remember the value of Avogadro’s number and the relationship between the Avogadro’s number and number of molecules and atoms in one mole. The students should also remember that monoatomic molecule means the molecule with one atom, diatomic molecule means the molecule with two atoms, triatomic molecule means the molecule with three atoms and so on.