The hardness of water sample containing 0.002 mole of magnesium sulphate dissolved in a litre of water is expressed as

The hardness of water sample containing 0.002 mole of MgSO₄ dissolved in 1 L of water.
Hardness is measured in terms of ppm of CaCO₃
$$\begin{gathered} {\mathrm{MgSO}}_4\equiv {\mathrm{CaCO}}_3\equiv 0.002 \mathrm{mol} {\mathrm{L}}^{-1} \\ {\mathrm{CaCO}}_3= 0.002 \mathrm{x} 100 {\mathrm{gL}}^{-1} \\ \begin{array}{l}=0.002\times 100\mathrm{g}\text{ in }{10}^3\mathrm{mL}\\ =\frac{0.002\times 100\times {10}^6}{{10}^3}\mathrm{g}\text{ in }{10}^6\mathrm{mL}\left(\mathrm{ppm}\right)\\ =200 \mathrm{ppm}\end{array} \end{gathered}$$