Question

If ${10}^5$g of a sample of water contains $16.2$ g of $Ca(HC{O}_3{)}_2$, then the hardness of water is __________ .

• A. $200$ ppm
• B. $300$ ppm
• C. $60$ ppm
• D. $100$ ppm

Answer 1

The correct option is D $100$ ppm

$16.2$ g of calcium hydrogen carbonate are present in ${10}^5$g of water.
Hence, the concentration of calcium hydrogen carbonate in ppm is $\frac{\text{mass of solute}}{\text{total mass of solution}}\times {10}^6=\frac{16.2}{{10}^5}\times {10}^6=162$ ppm.
Also, the hardness is expressed in terms of calcium carbonate.
$1$ gm mole or $162$ g of calcium hydrogen carbonate $\equiv$ $1$ gm mole or $100$ g of calcium carbonate.
$162$ ppm of calcium hydrogen carbonate $\equiv$ $100$ ppm of calcium carbonate.
Hence, the hardness of solution is $100$ ppm.