Calculate the number of atoms in:
$(i)$ $0.02$ moles of carbon
$(ii)$ $30$ grams of carbon
$(iii)$ $6$ moles of aluminium ions.

(N/A) $(i)$ We know that $1$ mole of atoms contains $6.022 \times 10^{23}$ atoms.
Therefore,$0.02$ moles of carbon atoms $= 6.022 \times 10^{23} \times 0.02 = 1.2044 \times 10^{22}$ atoms.
$(ii)$ We know that the molar mass of carbon is $12 \text{ g/mol}$.
Number of moles $= \frac{\text{Given mass}}{\text{Molar mass}} = \frac{30 \text{ g}}{12 \text{ g/mol}} = 2.5$ moles.
Number of atoms $= 2.5 \times 6.022 \times 10^{23} = 1.5055 \times 10^{24}$ atoms.
$(iii)$ We know that $1$ mole of ions contains $6.022 \times 10^{23}$ ions.
Therefore,$6$ moles of aluminium ions $= 6 \times 6.022 \times 10^{23} = 3.6132 \times 10^{24}$ atoms.