Question

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?

Answer 1

`20.0%`

Explanation:

A solution's volume by volume percent concentration, `"% v/v"`, is a measure of the concentration of the solution in terms of the volume of solute present in `"100 mL"` of solution.

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

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

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

Since you know how many milliliters of solute you have in `"215 mL"` of solution, you can use this as a conversion factor to see how many milliliters of solute would correspond to `"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 `"100 mL"` of solution contains `"20.0 mL"` of solute, it follows that the `"% 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.