# Question 9356d

Oct 23, 2015

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 $100$.

$\text{% v/v" = "volume of solute"/"volume of solution} \times 100$

In your case, a 25%"v/v" ethanol solution means that you get $\text{25 mL}$ of ethanol for every $\text{100 mL}$ of solution.

Calculate what volume of ethanol you have in your $\text{75-mL}$ 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 $\text{25-mL}$ sample of $\text{45% v/v}$ 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.

$\text{75 mL" + "25 mL" = "100 mL}$

The final solution has avolume of $\text{100 mL}$. 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%")#