Question

What mass of nitrogen, N₂, will contain the same number of molecules as 1.8 g of water, H₂O? (Atomic masses: N = 14 u; H = 1 u; O = 16 u)

Answer 1

$$\begin{gathered} \mathrm{Molecular}\mathrm{mass}\mathrm{of}\mathrm{water}=2\times \mathrm{H}+\mathrm{O} \\ \mathrm{Molecular}\mathrm{mass}\mathrm{of}\mathrm{water}=2\times 1+16 \\ \mathrm{Molecular}\mathrm{mass}\mathrm{of}\mathrm{water}=18 \end{gathered}$$
Now,
$$\begin{gathered} \mathrm{Number}\mathrm{of}\mathrm{moles}\mathrm{of}\mathrm{water}=\frac{\mathrm{mass}\mathrm{of}\mathrm{water}}{\mathrm{molar}\mathrm{mass}\mathrm{of}\mathrm{water}} \\ =\frac{1.8}{18} \\ =0.1\mathrm{mol} \end{gathered}$$

Mass of 1 mole of nitrogen = Molar mass of nitrogen = 14 g
Mass of 0.1 mole of nitrogen = 14 $\times$ 0.1
Mass of 0.1 mole of nitrogen = 1.4 g

So, 1.4 g of nitrogen contains an equal number of molecules as present in 1.8 g of water.