# How many milliliters of water must be added to 300 ml of 70% alcoholic solution to make a 40% alcoholic solution?

Jan 6, 2017

You must add 225 mL of water.

#### Explanation:

This is a dilution problem, so we can use the dilution formula:

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

c_1 = 70 %; V_1 = "300 mL"
c_2 = 40 %; V_2 = "?"

V_2 = V_1 × c_1/c_2 ="300 mL" × (70 color(red)(cancel(color(black)(%))))/(40 color(red)(cancel(color(black)(%)))) = "525 mL"

Thus, you would add 225 mL of water to 300 mL of 70 % alcohol, and you would get 525 mL of 40 % alcohol.

Check:

300 mL of 70 % alcohol contains 210 mL of alcohol, and 525 mL of 40 % alcohol contains 210 mL of alcohol.