How many mL of alcohol and how many mL of water are needed to prepare a 35.0%
alcohol solution containing 15.0 mL

Here we want to mix a volume of water and a volume of alcohol in such a way that we end with a 35.0% alcohol solution.

We will conclude that we must use 9.75 mL of water and 5.25 mL of alcohol.

Now let's see how to get the solution:

First, we should define the variables:

We want to have a 15 mL solution, then we will have:

x + y = 15 mL

And the 35% of this must be alcohol, then we will have that the quotient between the volume of alcohol and the total volume should be equal to 0.35

y/15mL = 0.35

That can be rewritten as:

y = 0.35*15ml = 5.25mL

Now we can reaplace this in the first equation to get the volume of water that we must use:

x + y = 15mL

x + 5.25mL = 15mL

x = 15mL - 5.25 mL = 9.75mL

So we can conclude that we must use 9.75 mL of water and 5.25 mL of alcohol.

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15.00 ml ROH + 27.86 ml H₂O => 42.86 ml of solution

Explanation:

Assuming the 15.0 is the volume of alcohol ...

Vol ROH = 15.00 ml = 35% of X where X = total volume of solution

X = 15.00 ml/0.35 = 42.86 ml total volume of solution

∴ Volume of water in 42.86 ml of solution = 42.86 ml - 15.00 ml = 27.86 ml