Question

The degree of hardness of a sample (in ppm) containing 6 mg of $MgS{O}_4$ per kg of water is:

Answer 1

Hardness is measured in terms of ppm of calcium carbonate.
1 mol of $MgS{O}_4\equiv$ 1 mol of $CaC{O}_3$
$120g$ of $MgS{O}_4\equiv 100g$ of $CaC{O}_3$
$6\times {10}^{-3}g$ of $MgS{O}_4\equiv 5\times {10}^{-3}g$ of $CaC{O}_3$
${10}^{3}g$ of $H_{2}O$ contains $5\times {10}^{-3}g$ of $CaC{O}_3$
So,
${10}^{6}g$ of $H_{2}O$ will contain $\frac{5\times {10}^{-3}\times {10}^6}{{10}^3}g$
So, the answer is 5 ppm.