To reduce 16 ounces of a 25% solution of antiseptic to a 10% solution, how much distilled water should a nurse add?

1 Answer
Jun 15, 2016

Answer:

#"24 ounces"#

Explanation:

Here's a more intuitive approach to use here.

You know that your initial solution has a percent concentration, presumably volume by volume, of #25%#. This means that any volume of this solution contains #1# part solute and #3# parts solvent.

The target solution must have a concentration of #10%#, which means that any volume of this solution will contain #1# part of solute and #9# parts solvent.

Your starting solution has a volume of #16# ounces, or #4# parts, each with a volume of #4# ounces.

In order to get to a solution that has a total of #10# parts, you must add #6# parts of solvent to the initial solution. Since we know that

#"1 part " = " 4 ounces"#

it follows that you must add

#6color(red)(cancel(color(black)("parts"))) * "4 ounces"/(1color(red)(cancel(color(black)("part solvent")))) = "24 ounces"#

of distilled water, which is your solvent, to the initial solution.

The target solution will contain #1# part solute and #9# parts distilled water for a total of #10# parts of solution, and hence have a percent concentration of #10%#.