Question

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

Answer 1

You must add 225 mL of water.

Explanation:

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

`color(blue)(bar(ul(|color(white)(a/a)c_1V_1= c_2V_2color(white)(a/a)|)))" "`

`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.