# What is the percent by volume of isopropyl alcohol in a solution made by dissolving 18.9mL of isopropyl alcohol in 412mL of water?

Jul 28, 2016

4.39%

#### Explanation:

We express a solution's volume by volume percent concentration, $\text{% v/v}$, by calculating how many milliliters of solute are present in $\text{100 mL}$ of solution.

In essence, all you have to do to determine a solution's volume by volume percent concentration is figure out how many milliliters of solute you get in $\text{100 mL}$ of solution, then tag along a % sign to that value.

In your case, you know that you get $\text{18.9 mL}$ of isopropyl alcohol, your solute, in a total volume of

${V}_{\text{total" = V_"solute" + V_"solvent}}$

${V}_{\text{total" = "18.9 mL" + "412 mL" = "430.9 mL}}$

of solution. In order to find the solution's $\text{% v/v}$ concentration, you must pick pick a $\text{100 mL}$ of this solution and use its known composition to calculate how many milliliters of isopropyl alcohol it contains

100 color(red)(cancel(color(black)("mL solution"))) * overbrace("18.9 mL isopropyl alcohol"/(430.9color(red)(cancel(color(black)("mL solution")))))^(color(blue)("the solution's composition")) = "4.39 mL isopropyl alcohol"

Now all you have to do is replace the $\text{mL}$ symbol with a % sign

"% v/v" = "4.39 mL isopropyl alcohol"/"100 mL solution" = color(green)(|bar(ul(color(white)(a/a)color(black)(4.39%)color(white)(a/a)|)))

The answer is rounded to three sig figs.