Question

What volumes of a 2 % solution and a 6 % solution must I mix to get 300 mL of a 5 % solution?

Answer 1

You must mix `"75 cm"^3` of the 2% solution and `"225 cm"^3` of the 6 % solution.

Explanation:

We can use a modification of the dilution formula to solve this problem:

`color(blue)(bar(ul(|color(white)(a/a)V_1c_1 + V_2c_2 = V_3c_3color(white)(a/a)|)))" "`

Let `x` = the volume of 2 %.
Then `300 - x` = the volume of 6 %.

Then

`x × 2color(red)(cancel(color(black)(%))) + (300-x) × 6color(red)(cancel(color(black)(%))) = 300 × 5color(red)(cancel(color(black)(%)))`

`2x + 1800 - 6x = 1500`

`4x = 300`

`x = 300/4 = 75`

∴ You must use `"75 cm"^3` of 2% and `"225 cm"^3` of 6 %.

Check:

`75 × 0.02 + 225 × 0.06 = 300 × 0.05`

`1.5 + 13.5 = 15`

`15 = 15`

It checks!