# Question eb6dd

Jul 11, 2016

$\text{290 mL isopropyl alcohol}$

#### Explanation:

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

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

$\textcolor{b l u e}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \text{% v/v" = "mL of solute"/"100 mL of solution} \times 100 \textcolor{w h i t e}{\frac{a}{a}} |}}}$

In your case, the solution has a concentration of $\text{70% v/v}$, which means that you get $\text{70 mL}$ of pure isopropyl alcohol for every $\text{100 mL}$ 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 $\text{420 mL}$ 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 $\text{420 mL}$ of rubbing alcohol that is $\text{40% v/v}$.