# If 42.9mL rubbing alcohol is dissolved of in water to make 215mL of solution, what is the concentration expressed in volume/volume % of the solute?

Jul 1, 2016

20.0%

#### Explanation:

A solution's volume by volume percent concentration, $\text{% v/v}$, is a measure of the concentration of the solution in terms of the volume of solute present in $\text{100 mL}$ of solution.

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

This means that all you have to do in order to find a solution's $\text{% v/v}$ concentration is to figure out what volume of solute you get in $\text{100 mL}$ of solution.

In your case, you know that you're adding $\text{42.9 mL}$ of rubbing alcohol, which is your solute, to enough water to make the total volume of the solution equal to $\text{215 mL}$.

Since you know how many milliliters of solute you have in $\text{215 mL}$ of solution, you can use this as a conversion factor to see how many milliliters of solute would correspond to $\text{100 mL}$ of solution

100 color(red)(cancel(color(black)("mL solution"))) * "42.9 mL solute"/(215color(red)(cancel(color(black)("mL solution")))) = "20.0 mL solute"

So, if $\text{100 mL}$ of solution contains $\text{20.0 mL}$ of solute, it follows that the $\text{% v/v}$ concentration is

"% v/v" = "20.0 mL solute"/(color(red)(cancel(color(black)(100)))"mL solution") * color(red)(cancel(color(black)(100))) = color(green)(|bar(ul(color(white)(a/a)color(black)("20.0 %")color(white)(a/a)|)))

The answer is rounded to three sig figs.