The hardness of water (hardness count) is usually expressed in parts per million (by mass) of CaCO₃, which is equivalent to milligrams of CaCO₃ per liter of water. What is the molar concentration of Ca²⁺ ions in a water sample with a hardness count of 175 mg CaCO₃/ L?

\({\rm{Molarity = }}\frac{{{\rm{No}}{\rm{.}}\,{\rm{of}}\,{\rm{moles}}}}{{{\rm{Liter}}\,{\rm{of}}\,{\rm{solution}}}}\)

Given

Mass concentration CaCO₃= 175 mg /L

1 mol Ca= 40.078 g

1 mol C= 12.011 g

1 mol O= 15.999 g

\(\begin{align}{\rm{Molar mass}}\,{\rm{of}}\,{\rm{CaC}}{{\rm{O}}_{\rm{3}}}{\rm{ = 40}}{\rm{.078 + 12}}{\rm{.011 + 3 \times 15}}{\rm{.999}}\\{\rm{ = 100}}{\rm{.086}}\,{\rm{g}}\,{\rm{mo}}{{\rm{l}}^{{\rm{ - 1}}}}\end{align}\)

\(\begin{align}Molarity{\rm{ }} &= 175\frac{{mg}}{L}\left( {\frac{{1\,g}}{{1000mg}}} \right)\left( {\frac{{1\,mol\,CaC{O_3}}}{{100.086g}}} \right)\left( {\frac{{1\,mol\,C{a^{2 + }}}}{{1\,mol\,CaC{O_3}}}} \right)\\ &= 1.75 \times {10^{ - 3}}M\end{align}\)

The molar concentration is \({\rm{1}}{\rm{.75 \times 1}}{{\rm{0}}^{{\rm{ - 3}}}}{\rm{M}}\).