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

1 Answer
Jul 28, 2016

Answer:

#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.