# Question #9932a

##### 1 Answer

The solution is

#### Explanation:

A solution's *volume by volume percent concentration*, **volume of solute**, which in your case is the alcohol, expressed in *milliliters*, present in **of solution**.

#color(blue)(|bar(ul(color(white)(a/a)"% v/v" = "mL of solute/100 mL solution"color(white)(a/a)|)))#

In your case, you know that you get

#100 color(red)(cancel(color(black)("mL solution"))) * overbrace("225 mL alcohol"/(400color(red)(cancel(color(black)("mL solution")))))^(color(purple)("information given")) = "56.25 mL alcohol"#

Since this is how many milliliters of solute you get in

#"% v/v" = color(green)(|bar(ul(color(white)(a/a)color(black)("56% alcohol")color(white)(a/a)|)))#

I'll leave the answer rounded to two **sig figs**, but keep in mind that you only have one sig fig for the volume of the solution.

Now, you know that your solution contains **for every** **solvent**, which in this case is water, will be

#V_"solvent" = "100 mL" - "56 mL" = "44 mL"#

This tells you that **every** **water**.

For your solution, this is equivalent to

#400 color(red)(cancel(color(black)("mL solution"))) * "44 mL water"/(100color(red)(cancel(color(black)("mL solution")))) = "176 mL water"#

Keep in mind that we've **rounded** the volume of alcohol from

#V_"water" = V_"solution" - V_"alcohol"#

#V_"water" = "400 mL" - "225 mL" = "175 mL water"#