Question

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

Answer 1

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

Explanation:

We can use the dilution formulas for these calculations:

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

We can rearrange this formula to get

`V_2 = V_1 × c_1/c_2`

15 % concentration

`V_2 = "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 = "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 = "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.