The hardness of a water sample containing 10 ^ - 3 M MgSO _ 4...

${10}^{- 3}$ mole ${\text{MgSO}}_{4} = {10}^{- 3}$ mole of ${\text{MgSO}}_{4}$ present in $\text{1L}$ solutions.

${nCaCO}_{3} = {nMgSO}_{4}$

${ppm}_{\left(\text{In}\text{term}\text{of}{\text{CacO}}_{3}\right)} = \dfrac{{10}^{- 3} \times 100}{1000} \times {10}^{6}$

${ppm}_{\left(\text{In}\text{term}\text{of}{\text{CaCO}}_{3}\right)} = 100\text{ppm}$

Hard water is water that has high mineral content. Hard water is formed when water percolates through deposits of limestone, chalk or gypsum which are largely made up of calcium and magnesium carbonates, bicarbonates and sulfates.&