Question

Question #9356d

Answer 1

`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%")`