Question

Question #a4ff2

Answer 1

`"39 mL"`

Explanation:

Your stock solution is `"32% v/v"` isopropyl alcohol, which is commonly called rubbing alcohol, which means that every `"100 mL"` of this stock solution contain `"32 mL"` of rubbing alcohol.

Your target solution must be `"5% v/v"` rubbing alcohol, which means that every `"100 mL"` of this target solution must contain `"5 mL"` of rubbing alcohol.

Your first goal here will be to determine how many milliliters of rubbing alcohol must be present in this target solution.

You will have

`250 color(red)(cancel(color(black)("mL solution"))) * overbrace("5 mL rubbing alc."/(100color(red)(cancel(color(black)("mL solution")))))^(color(purple)("5% v/v")) = "12.5 mL rubbing alc."`

Now all you have to do is figure out what volume of the stock solution will contain this many milliliters of rubbing alcohol

`12.5 color(red)(cancel(color(black)("mL rubbing alc."))) * overbrace("100 mL solution"/(32color(red)(cancel(color(black)("mL rubbing alc.")))))^(color(blue)("32% v/v")) = "39.06 mL solution"`

I'll leave the answer rounded to two sig figs

`"volume of stock solution needed" = color(green)(|bar(ul(color(white)(a/a)"39 mL"color(white)(a/a)|)))`