One litre (taken as 1 kg) of a hard water sample contains 55.5 mg of CaCl2 (111 g/mol) and 95 mg of MgCl2 (95 g/mol). Hardness is expressed as ppm of CaCO3 (100 g/mol) having the same total moles of cations. The hardness is

JEE Advanced levelSingle correct optionDifficulty 3 of 3mc087

One litre (taken as $1 kg$ ) of a hard water sample contains $55.5 mg$ of $CaCl X_{2}$ ( $111 g/mol$ ) and $95 mg$ of $MgCl X_{2}$ ( $95 g/mol$ ). Hardness is expressed as ppm of $CaCO X_{3}$ ( $100 g/mol$ ) having the same total moles of cations. The hardness is

Moles of

Ca X^{2 +}

= 55.5/111 = 0.5 mmol; of

Mg X^{2 +}

= 95/95 = 1.0 mmol; total 1.5 mmol. Equivalent

CaCO X_{3}

= 1.5 mmol x 100 = 150 mg per kg = 150 ppm.