A solution contains 75 mg NaCl per mL. To what extent must it be diluted to give a solution of concentration 15 mg NaCl per mL of solution.

There is 75 mg of NaCl present per mL of solution and the solution is diluted with water till the mass of NaCl in per mL of solution reaches to 15 mg. During dilution, moles of NaCl remains the same.

$\begin{array}{ccc}\mathrm{Moles} \mathrm{of} \mathrm{NaCl} \mathrm{before} \mathrm{dilution}& =& \mathrm{Moles} \mathrm{of} \mathrm{NaCl} \mathrm{after} \mathrm{dilution}\\ \mathrm{Concentration}\times \mathrm{Volume}& =& \mathrm{Concentration}\times \mathrm{Volume}\end{array}$

Concentration of 75 mg of NaCl per mL is 75 mg/mL and the concentration of 15 mg of NaCl per mL is 15 mg/mL. Assume that volume of NaCl before dilution is “V”, determine the fraction of volume added to make the concentration of solution up to 15 mg/mL.

$\begin{array}{ccc}75 \mathrm{mg}/\mathrm{mL}\times \mathrm{V}& =& 15 \mathrm{mg}/\mathrm{mL}\times \mathrm{Volume}\\ \mathrm{Volume}& =& 5\mathrm{V}\end{array}$

Hence, the volume must increase up to five folds.