Question

Calculate the number of atoms in each of the following :

(i) 23 g of Na atoms [1]

(ii) 14 g of N2 molecule [2]

(iii) 0.2 mole of CH4​

Answer 1

We know,

• No. of atoms = (No. of moles)(Avogadro no.)
• No. of moles = (Given mass)/(Molar mass)

(i) Given mass of $Na$ = 23 g

Molar mass of $Na$ = 23 g

∴ No. of moles = (23 g)/(23 g) = 1 mol

So, no. of atoms = 1 × 6.022 × 10²³ = 6.022 × 10²³ atoms.

(ii) Given mass of $N_2$ molecule = 14 g

Molar mass of $N_2$ molecule = 28 g

∴ No. of moles = (14 g)/(28 g) = 0.5 mol

So, no. of molecules = 0.5 × 6.022 × 10²³ = 3.011 × 10²³ molecules.

1 $N_2$ molecule = 2 atoms of $N$

∴ No. of atoms = 2 × 3.011 × 10²³ = 6.022 × 10²³ atoms.

(iii) No. of moles of $CH_4$ = 0.2 mol

∴ No. of molecules of $CH_4$ = 0.2 × 6.022 × 10²³

⇒ No. of molecules = 1.2044 × 10²³

∵ 1 $CH_4$ molecule contans = 5 atoms,

∴ No. of atoms = 5 × 1.2044 × 10²³ = 6.022 × 10²³.

∴ 23 g of Na atoms, 14 g of N2 molecule and 0.2 mole of CH4, all contain 6.022 × 10²³ number of atoms.