Calculate the mass of the following : (i) 0.5 mole of N2 gas (ii) 0.5 mole of N atoms (iii) 3.011 x 1023 N atoms (iv) 6.

Solution

(i) 1 mole of N2 = Molar mass of N2 = 28 g

∴ 0.5 mole of N2 = 28 × 0.5 = 14 g

Alternatively, Mass (m) = Number of moles (n) × Molar mass of N2 (M)

      = 0.5 mol × 28 g mol−1 = 14 g.

(ii)      1 mole of N atoms   = Number of moles N = 14 g

∴0.5 mole of N atoms   = 14 0.5 g = 7 g

Alternatively, Mass (m) = Number of moles (n) x Molar mass of N (M)

 = 0.5 mol x 14 g mol−1 = 7 g

(iii) 1 mole of N atoms = 6.022 x 1023 atoms of N = Molar mass of N = 14 g

Thus, 6.022 x 1023 atoms have mass = 14 g

∴    3.011 x 1023 atoms will have mass = x 3.011 x 1023  g = 7 g

Alternatively, applying the formula directly, we have

  0.5 mole of N atoms = 14 g × 0.5 = 7 g

(iv) 1 mole of N2 molecules = 6.022 x 1023 molecules = Molar mass of N2 = 28 g

Thus, 6.022 x 1023 molecules of N2 have mass 28 g

Alternatively,

         m = n × m = 1 mol × 28 g mol−1 = 28 g.