Question

How much pure acid should be mixed with 2 gallons of a 50% acid solution in order to get an 80% acid solution?

Answer 1

You should add 3 gal of pure acid to 2 gal of 50 % acid.

Explanation:

You have

`"100 % acid + 50% acid → 80 % acid"`

You can use the dilution formulas

`c_1V_1 + c_2V_2 = c_3V_3`

Let the volume of pure acid be `x` gal. Then

`100 color(red)(cancel(color(black)(%))) × x color(red)(cancel(color(black)("gal"))) + 50 color(red)(cancel(color(black)(%))) × 2 color(red)(cancel(color(black)("gal"))) = 80 color(red)(cancel(color(black)(%))) × (x + 2) color(red)(cancel(color(black)("gal")))`

`100x + 100 = 80x + 160`

`20x = 60`

`x = 3`

∴ You add 3 gal of 100 % acid to 2 gal of 50 % acid.