Dilution Chemistry: How to Calculate and Perform Molarity Dilutions
- This is lesson 1.5, and today, we're going to be talking about dilutions. Our goal today is to learn how to calculate the molarity of a dilution and how to perform a dilution.
So what is molarity? If you guys recall, molarity is the moles of solute divided by the total volume of solution. And we have the equation M equals n over V, where n is the number of moles of the solute, V is the total volume of solution in liters-- keep in mind, the volume is always in liters. And it's the total volume of the solution, not just the volume of the water. And M is the molarity, and the melody has the units of moles per liter.
So that's the equation. We've spent some time already talking about how to calculate molarity and how to calculate different parts of that equation. But today, we're going to talk about dilution. Dilution is the process of adding water to a solution and thereby reducing its concentration. If you're adding water, your volume is going to increase, and the molarity is going to decrease.
But the number of moles will stay the same. Keep that in mind, right, you're not actually taking any moles away. The number of moles of your solute should stay the same. So you can say that n1 equals n2. Your initial moles is going to equal your final moles. And recall that m equals n over v. And so, we can rearrange that to solve for n.
So n equals M times V. We multiply both sides of that equation by V. That gives us n equals M times V. So we can replace n on both sides of that equation with MV. That's going to get us M1V1 equals M2V2. And that is our dilution equation.
To perform a dilution, use a pipette to transfer the correct amount of concentrated solution into a volumetric flask. If you are diluting a concentrated acid, be sure to put most of the water in first. Always add acid to water when diluting acids. Otherwise, it can actually boil and blow up in your face, which would be a bad thing.
A volumetric flask and volumetric pipette are shown here. You will typically always want to use a volumetric flask, because they have the best precision of any kind of glassware that you could use for this dilution. Now, sometimes you might want to use a volumetric pipette. Or sometimes, you'll probably use a graduated pipette, which will allow you to get more or less any volume that you want.
Once you have put the solute and most of the water into the volumetric flask, what you're going to want to do is mix it up some. Then, you're going to cap the flask and carefully invert it a few times, with your thumb firmly on the cap. Make sure you don't shake it, because that might lead to accidents. Check the liquid level and then carefully add distilled water until it reaches the mark. Every volumetric flask has a mark, and at that mark, it means the total volume equals whatever that volumetric flask has.
Then, you're going to recap the flask and mix it again. And of course, you're not going to shake it up, but simply invert it multiple times. When you invert it multiple times, it's going to mix very efficiently, and it's going to be much safer.
Don't forget to keep your thumb on the cap. Because you might think that the cap is there firmly, but the next minute, it starts leaking. And then you've got to start everything over. Or, you might even have acid on your hands, which wouldn't be a good thing. So make sure you keep your thumb firmly on the cap.
Let's try a few problems to see how this works. A 12.5 milliliter solution of 2.2 molar copper(II) sulfate was diluted with distilled water to a final volume of 300 milliliters. Calculate the molarity of the final solution. So to do that, we are going to be using the equation M1V1 equals M2V2. And we need to think, OK, what are we solving for? It says calculate the molarity of the final solution. So we're solving for that M2, the final molarity.
So we're going to want to divide both sides of the equation by V2 in order to solve for that. That's going to get us M2 equals-- the V2 over V2 are going to cancel. And so we're left with M1V1 over V2.
Now we get to plug in some numbers. So our initial similarity was 2.2 molar. Our initial volume was 12.5 milliliters. And we can leave this in milliliters. I know that the molarity is in moles per liter, but we can leave this in milliliters. Because our final volume also has milliliters as units. So the milliliters over milliliters are going to cancel. So that final volume is 300 milliliters. And so, our milliliters over milliliters cancel to leave us with molarity as our final answer.
And so, let's do that in a calculator. That's going to be 2.2 times 12.5 divided by 300. And that gives us a final molarity of point-- well, how many sig figs do we have here? Notice, in our problem, we've got three sig figs for that, three for that, and four for that. And so, our final answer should have only three significant figures. And so, that's going to give us-- that 6 right here is going to round up to a 7, because it's followed by 6. So that's going to be 0.0917 molar. Or, you could write 0.0917 moles per liter. Because molarity, that capital M, stands for moles per liter.
Next, you want to make 2.5 molar ammonia by diluting 20 milliliters of 18 molar ammonia. What should your final volume be? All right, once again, this is a dilution problem. So we're going to write down an equation, M1V1 equals M2V2. And what are we solving for? It says, what should your final volume be? So we're solving for V2, which means we're going to divide both sides of the equation by M2. That's going to have M2 over M2 cancel, and so, we're left with V2 equals M1V1 over M2.
Now we can plug in some numbers. Our initial molarity is that 18 molar, right? That's what we're starting off with. So we have 18 molar. And our initial volume is 20 milliliters. Our final molarity, which is what we want to make, is that 2.5 molar. So in your calculator, you got 18 times 20 divided by 2.5, which gives us 144. 144. My molar over molar cancels, leaving me with milliliters as our units for our answer.
Now, pause here and think about this. Notice that we have only two significant figures here for this 2.5, two significant figures here for this 18. So you might think that we should put two significant figures here for this 144 milliliters. But that would be incorrect, because this 144 milliliters-- that's a volume that you want to get as precise and accurate as possible. So you're not going to limit yourself and say, OK, I'm just going to use 140. Well, 140 might get you the correct-- more or less-- molarity of the solution. But it's not going to be the best amount of volume.
In general, when you're going to weigh something out-- when you're going to measure a volume or something like that in the lab-- you're not going to want to limit yourself by significant figures. You want to get the best number possible that you can measure out in the lab-- even more significant figures than you probably need when you're making a solution, when you're weighing something out for a chemical reaction, or anything like that. So when you're planning out when to make something, don't limit yourself by significant figures. Always use the most precise number possible.
All right, let's try one last problem together. Suppose you needed 100 milliliters of 0.1 molar nitric acid. You have concentrated nitric acid, which is 15.8 molar. How should you make it? All right, let's start off with the dilution equation. That's M1V1 equals M2V2. So what do we know so far? You know that final volume, right? That 100 milliliters, that's what you need. That's that final volume. You know your final molarity, but you don't know your initial volume. You know your initial molarity, but you don't know your initial volume.
So we're going to go ahead and solve for V1 here. But we're going to notice that there's going to be a little bit of a twist here to the problem what-- I'll get to that here in a minute. So we're going to solve for V1. So let's go ahead and divide both sides by M1. And that's going to get us M1V1 equals M2V2 over M1.
So I can plug in some numbers. My final molarity is 0.1 molar. Our final volume is 100 milliliters and our initial molarity is 15.8. So we can put that in our calculator. We have 0.1 times 100-- well, that, of course, is just 10 divided by 15.8. And we're left with this number right here. It's a number that's less than one. This is 0.633 milliliters.
Now, the problem with this is, you might not be able to easily measure this out in the lab. You might be able to use a micropipette, but you might not actually have access to a micropipette. And typically, you're not going to want to use a micropipette when dealing with concentrated acids.
So instead, the typical thing that we're going to want to use is, we're going to use glassware. We're going to use a glass graduated pipette to get the acid out. And then, we're going to do an initial dilution and a final dilution. So typically, what we do here is, we do a series of two separate dilutions.
So what's useful in this case would be to actually first make a solution that is, let's say, one molar, and then you can dilute that down to 0.1 molar. Because 0.633 milliliters would be a very difficult volume to measure in any kind of glass graduated pipette.
All right, so let's do it this way. Let's go ahead and make a stock solution of one molar nitric acid. And so, to do that, we're going to use the same equation that we used before, only this time, our V1-- which is still going to be M2V2 over M1-- is now going to be an M2 of 1. We still have 100 milliliters that we can make 15.8 molar. And that is simply going to be 10 times as much as this number that we calculated before. So we have 6.33 milliliters of our concentrated nitric acid that we're going to measure out.
Now we're going to need to do another dilution in addition to that to get our final volume. But that dilution is going to be much easier to do. So once we have our stock solution, then we're going to want to dilute that down. And so, once again, we're going to solve for another V1. So V1 is going to be M2V2 over M1. And now, our new M2 is going to be 0.1 molar. That's our final molarity that we want to solve for.
And let's go ahead and put everything into a 100 milliliter volumetric flask, because that's probably the glassware that we have. And it's fairly reasonable. And now, our M1, rather than 15.8, is simply 1. Because we made a stock solution of this 1 molar nitric acid, and now we can use that to make more dilute solutions. And so, we can do this math in our heads, right? So this is going to be 0.1 times 100. So that's going to be 10 divided by 1 is just 10.
So what you're actually going to do in the lab is, you're going to take a 100 milliliter volumetric flask, and you're going to put some water in it. In fact, you're going to put a lot of water in it. Not all the way up to the mark, but probably about 80 milliliters of water into that. It doesn't matter exactly how much. And then, you're going to use a glass graduated pipette to get 6.33 milliliters of that concentrated nitric acid. And you're going to add your acid to that volumetric flask that has water in it already. And then you're going to cap it, invert it several times, and you're going to put more water up to the mark, until you have a nice stock solution that's one molar nitric acid.
Then you're going to take that stock solution, and you're going to do this again. And you're going to put 10 milliliters of that stock solution into another 100 volumetric flask. And you're going to add water-- distilled water-- to put that up to 100 milliliters. And you're going to now have 100 milliliters of that 0.1 molar solution of nitric acid, which is exactly what you wanted.
Oftentimes, when you want to make a highly dilute solution-- such as 0.1 molar something-- and you're starting off with a highly-concentrated solution-- such as 15.8 molar-- you're going to need to do a series of dilutions. Sometimes two different dilutions and sometimes even more. All right, have a great rest of your day. Stay curious.