Question

$A$ water sample contains $22.2\, mg$ of $CaCl _{2}$ in $1 \, L$ of sample. The degree of hardness of water in terms of $CaCO _{3}$ equivalent is ____$ppm$.
[Molar mass of $CaCO _{3}=100\, g \, mol ^{-1}$, molar mass of $CaCl _{2}=111 \, g \, mol ^{-1}$ ]

Answer 1

$ppm$ is parts per million $\left(10^{6}\right)$. This is equivalent to $mg$ per litre.
$1 \,L$ of water contains $22.2 \, mg$ of $CaCl _{2}$.
Now, $111 \,g$ of $CaCl _{2} \equiv 100 \,g \,CaCO _{3}$
$22.2 \,mg$ of $CaCl _{2}=\frac{22.2 \times 100}{111}$
$=20 \, mg$ of $CaCO _{3}$ in $1 \, L$ of water
$\therefore $ Hardness of water sample $=20 \,ppm$