(i) We know that,

1 mole of atoms contain = 6.022 x 10^23 atoms.

Therefore,

1 mole of carbon atoms

= 6.022 x 10^23 carbon atoms.

and, 0.02 moles of carbon

= 6.022 x 10^23 x 0.02 atoms.

= 1.2 x 10^22 atoms.

(ii) We know that, gram atomic mass = 1 mole

Therefore,

12 grams of carbon = 1 mole

and, 1 gram of carbon = 1/12 mole

So, 30 grams of carbon = 1/12 x30 = 2.5 moles

Now, 1 mole of atoms contain 6.022 x 10^23 atoms

Therefore,

1 mole of carbon atoms

= 6.022 xio23 carbon atoms,

and 2.5 moles of carbon

= 6.022 x 10^23 x 2.5 carbon atoms.

= 1.50 x 10^24 carbon atoms.

(iii) 1 mole of Al3+ ions contain = 6.022 x 10^23 atoms

Therefore,

6 moles of Al3+ ions contain

= 6 x 6.022 x 10^23 atoms

= 3.61 x 10^24 atoms