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?

1 Answer
Jul 1, 2016

Answer:

#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.