To what volume should 25 mL of 15 M nitric acid (HNO3) be diluted to prepare a 3.0 M solution?

Answer 1

See other answers to your questions privided by @Tonya G.

M1V1 = M2V2

(25 ml)(15 M) = (x ml)(3 M)

Solve for x mls

Answer 2

When you do a dilution, the quantity of your solute is the same in both solutions. The only thing you are doing is adding more solvent and making the concentration lower. This allows for a nice "shortcut" formula to be used here, sometimes it is written C₁V₁ = C₂V₂ where C stands for concentration and V stands for volume. Several different common concentration units will work in this formula, but not all of them!

The most common and versatile concentration unit used in general chemistry is molarity, which is defined as "moles of solute per liter of solution". This one definitely works in the formula, so sometimes you see the dilution formula written as M₁V₁ = M₂V₂. If you multiply a molarity times a volume, your answer ends up being in moles of solute, which is the underlying concept for the formula! Your moles of solute doesn't change just because you are adding water.

Pick one situation to be "situation 1" 25 mL of 15 M nitric acid (HNO3) for example, since this is a volume of a solution you are starting with. This will be M₁ and V₁, so M₁ is 15 M and V₁ is 25 mL.

Then the other volume and concentration is "situation 2". You have the new concentration you are trying to reach, so that is M₂ = 3.0 M, but we don't know V₂, that is what we are looking for.

Take the equation and solve for V₂, you will get this new equation:

V₂ = M₁V₁ / M₂ and plugging in the values we know:

V₂ = (15 M) (25 mL) / (3.0 M)

Notice the molarity units will cancel out, and in this case notice the original molarity is 5 times the final molarity. This is sometimes referred to as a "5x dilution". When we calculate the volume, it comes out to be V₂ = 125 mL which is (not coincidentally!) 5 times the original volume!

To actually do the dilution, we would have to add ~100 mL of water to reach this, but the best way to do this in a lab is to dilute it in a volumetric flask to a final volume of 125 mL. This is because volumes are not always additive, and if you take 25 mL of solution and add 100 mL of water, you might not get exactly 125 mL of new solution. This concept is called "volume of mixing", and it varies, so the safe and correct way to get the final volume to be 125 mL is to use the volumetric flask.

So we can see that when we multiply the volume by 5, we decrease the concentration by a factor of 5, or we could say we divide the concentration by 5. After you work a few of these you can start to see the pattern - to cut a concentration in half, you need to double the volume of the solution. For a 1/3 concentration, triple the volume!

Hope this helps - good luck with your chemistry class! 😊