Question

Question #eb6dd

Answer 1

`"290 mL isopropyl alcohol"`

Explanation:

Rubbing alcohol is simply a solution of isopropyl alcohol of various concentrations by volume.

The volume by volume percent concentration, `"% v/v"`, tells you how many milliliters of solute, which in this case is isopropyl alcohol, you get per `"100 mL"` of solution.

`color(blue)(|bar(ul(color(white)(a/a)"% v/v" = "mL of solute"/"100 mL of solution" xx 100color(white)(a/a)|)))`

In your case, the solution has a concentration of `"70% v/v"`, which means that you get `"70 mL"` of pure isopropyl alcohol for every `"100 mL"` of solution, i.e. of rubbing alcohol.

You can thus use the volume by volume percent concentration as a conversion factor to calculate how many milliliters of isopropyl alcohol you have in your `"420 mL"` bottle of rubbing alcohol

`420 color(red)(cancel(color(black)("mL rubbing alcohol"))) * overbrace("70 mL isopropyl alcohol"/(100color(red)(cancel(color(black)("mL rubbing alcohol")))))^(color(blue)("= 70% v/v")) = color(green)(|bar(ul(color(white)(a/a)color(black)("290 mL isopropyl alcohol")color(white)(a/a)|)))`

I'll leave the answer rounded two two sig figs.

You can use the same technique to figure out how many milliliters of isopropyl alcohol you have in `"420 mL"` of rubbing alcohol that is `"40% v/v"`.