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

1 Answer
May 2, 2017

Answer:

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.