Question #9356d

1 Answer
Oct 23, 2015

Answer:

#19%"v/v"#

Explanation:

This one is pretty straighforward - all you have to do is not get distracted by the fact that you're mixing the ethanol solution with a methanol solution and not with pure water.

A solution's percent concentration by volume is defined s the volume of the solute divided by the total volume of the solution, and multiplied by #100#.

#"% v/v" = "volume of solute"/"volume of solution" xx 100#

In your case, a #25%"v/v"# ethanol solution means that you get #"25 mL"# of ethanol for every #"100 mL"# of solution.

Calculate what volume of ethanol you have in your #"75-mL"# sample

#75color(red)(cancel(color(black)("mL solution"))) * "25 mL ethanol"/(100color(red)(cancel(color(black)("mL solution")))) = "18.75 mL"#

Now, you mix this sample with a #"25-mL"# sample of #"45% v/v"# methanol solution.

As far as the concentartion of ethanol is concerned, all you need to focus on here is what the total volume of the resulting solution will be.

#"75 mL" + "25 mL" = "100 mL"#

The final solution has avolume of #"100 mL"#. SInce the amount of ethanol remaind unchanged, it follows that the new percent concentration by volume of ethanol will be

#"% v/v" = (18.75color(red)(cancel(color(black)("mL"))))/(100color(red)(cancel(color(black)("mL")))) xx 100 = 18.75%#

Round this to two sig figs to get

#"% v/v" = color(green)("19%")#