How much water should be added to 16 ml of? 12% alcohol solution to reduce the concentration to? 8%?

Question

Question on a math quiz I got wrong but would like to know what the correct answer is.

Answer 1

Hello, thank you for taking the time to post your question!

You want to solve this one using the dilution equation, which states that the amount of solute remains constant before and after dilution, meaning that

C1V1 = C2V2     where C represents concentration and V represents volume

If you plug in the given values from the equation that becomes

0.12(16) = 0.08*V2

V2 = 0.12(16) / 0 .08 = 24

That value tells us that the end volume is 24 mL, meaning that

24 mL – 16 mL = 8 mL was added to the original solution

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

Gilbert,

Concentrations can be calculated in several different ways that all give different answers. The most common types of concentrations are by moles, mass, and volume. If this is really the entire question, I would have to assume they want the volume answer because we can't determine the mass or the moles of alcohol without knowing the actual formula of the alcohol. So this is how you do volume concentration:

 

concentration% = volume of pure substance / total volume of combination * 100

                                         or

                     12% = .12(16)/16 * 100           (just a restatement of the given)

 

So starting with 16 ml of solution, we add x ml of water to get a total volume of (16+x). And the amount of pure alcohol is found from .12(16).

 

Now we calculate:    8% = .12(16)/(16+x) * 100            Solve for x.

 

.08 = 1.92/(16+x)

.08(16+x) = 1.92

16 + x = 1.92/.08 = 24

x = 24 - 16 = 8 ml

 

I hope that helps.

Answer 3

)The amount of alcohol is unchanged, so

(16ml)(0.12) = x(0.8)

(16ml) (0.12)/(0.8) = x        

(16ml)(1.5) = 24 ml= x

 

The 24ml is the total volume of the new solution, including the 16ml you started with, so (24 - 16)ml or 8ml of water was added.