Question

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

Answer 1

`4.39%`

Explanation:

We express a solution's volume by volume percent concentration, `"% v/v"`, by calculating how many milliliters of solute are present in `"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 `"100 mL"` of solution, then tag along a `%` sign to that value.

In your case, you know that you get `"18.9 mL"` of isopropyl alcohol, your solute, in a total volume of

`V_"total" = V_"solute" + V_"solvent"`

`V_"total" = "18.9 mL" + "412 mL" = "430.9 mL"`

of solution. In order to find the solution's `"% v/v"` concentration, you must pick pick a `"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 `"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.