# What volume of distilled water must we add to 50 mL of a 20 % solution to get concentrations of 15 %, 10 % and 5 %?

May 5, 2017

Add 17 mL, 50 mL, and 150 mL of water, respectively.

#### Explanation:

We can use the dilution formulas for these calculations:

$\textcolor{b l u e}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} {c}_{1} {V}_{1} = {c}_{2} {V}_{2} \textcolor{w h i t e}{\frac{a}{a}} |}}} \text{ }$

We can rearrange this formula to get

V_2 = V_1 × c_1/c_2

15 % concentration

${V}_{2} = \text{50 mL" × (20 color(red)(cancel(color(black)(%))))/(15 color(red)(cancel(color(black)(%)))) = "67 mL}$

The final volume must be 67 mL, so you must add 17 mL of distilled water to get a 15 % solution.

10 %concentration

${V}_{2} = \text{50 mL" × (20 color(red)(cancel(color(black)(%))))/(10 color(red)(cancel(color(black)(%)))) = "100 mL}$

The final volume must be 100 mL, so you must add 50 mL of distilled water to get a 10 % solution.

5% concentration

${V}_{2} = \text{50 mL" × (20 color(red)(cancel(color(black)(%))))/(5 color(red)(cancel(color(black)(%)))) = "200 mL}$

The final volume must be 200 mL, so you must add 150 mL of distilled water to get a 5 % solution.