The number of atoms present in 0.1 moles of a triatomic gas is

The correct option is 1.806 × 10²³.

To find the total number of atoms in the given sample, we can break down the calculation step-by-step:

Step 1: Recall Avogadro's number
One mole of any substance contains Avogadro's number (
$N_A$
) of molecules. Avogadro's number is given by:
$$N_A=6.022\times {10}^{23}\text{molecules/mol}$$

Step 2: Calculate the number of molecules in 0.1 moles of the gas
The number of gas molecules in 0.1 moles is:
$$\text{Number of molecules}=\text{Number of moles}\times N_A$$
Substituting the given value of moles:
$$\text{Number of molecules}=0.1\times 6.022\times {10}^{23}=6.022\times {10}^{22}\text{molecules}$$

Step 3: Calculate the total number of atoms
Since the gas is triatomic, each molecule is made up of 3 atoms. Therefore, the total number of atoms is:
$$\text{Number of atoms}=3\times \text{Number of molecules}$$
Substituting the number of molecules:
$$\text{Number of atoms}=3\times 6.022\times {10}^{22}$$
$$\text{Number of atoms}=18.066\times {10}^{22}$$
Expressing this value in standard scientific notation yields:
$$\text{Number of atoms}=1.806\times {10}^{23}$$
Thus, the total number of atoms present in 0.1 moles of the triatomic gas is 1.806 × 10²³.