Question

How much water should be added to a 15 gallon solution of 35% hydrogen peroxide to create an 8% solution? how many gallons would there be of the 8% solution?

Answer 1

15 gallons of 35% peroxide solution contains 0.35 × 15 = 5.25 gallons of hydrogen peroxide. The rest of the volume is made up of 15 - 5.25 = 9.75 gallons of water.

If we add $x$ gallons of water to the solution, the amount of hyrdrogen peroxide in the solution stays the same, but the volume of water increases to $9.75+x$ gallons, and the total volume increases to $15+x$ gallons.

To get a concentration of 8% in this diluted solution, we add $x$ gallons of water such that

$\dfrac{5.25}{15+x} = 0.08$

Solve for $x$.

$5.25 = 0.08 (15 + x)$

$5.25 = 1.2 + 0.08x$

$0.08x = 4.05$

$x = 50.625$

To get the desired concentration, one must add 50.625 gallons of water, and one will end up with a total volume of 65.625 gallons of solution.