Buffer capacity | Buffers, titrations, and solubility equilibria | Chemistry | Khan Academy

Let's talk about buffer capacity.

Buffer capacity is a property of a buffer, and it tells you how much acid or base you can add before the pH starts changing. Basically, as your buffer capacity goes up (which I'm going to abbreviate as BC), you can add more of your acid or base before the pH starts changing a lot. That might seem like a pretty vague and qualitative definition, so let's go through an example to see what that might look like exactly.

The example we're going to look at is going to be using an acetic acid buffer. Acetic acid is CH₃COOH, and we're going to abbreviate that in this talk using HA. This is in a nucleus solution and that is reversibly reacting to form H⁺ ion and CH₃COO⁻ (or acetate). So we're going to abbreviate acetate in this talk as A⁻.

Some more information about this particular buffer, acetic acid: the Ka is equal to 1.8 times 10 to the minus 5, and if we take the negative log of that, that will give us the pKa, which is also useful. The pKa of acetic acid is 4.74, so that'll tell us a lot about the behavior of this buffer. The last thing we need to know for predicting the behavior of our buffer is what the ratio is between our HA and A⁻.

We're going to be looking at a buffer where A⁻ over HA, this ratio is equal to 1.82. Based on this ratio, we can calculate the pH. So the initial pH of our buffer, before we do anything to it, before we add any acid or we add any base, the initial pH of our buffer we can calculate using the Henderson-Hasselbalch equation.

That equation tells us that pH is equal to pKa plus log of A⁻ concentration (or acetate) over acetic acid concentration. If you're not 100% confident with using this equation or you want to know where it comes from, we actually have separate videos on that. So I would recommend checking those out. In this video, we're just going to use this equation as is.

If we plug in our values here, we get that the initial pKa is equal to 4.74, our pKa plus log of 1.82, which is our ratio of A⁻ over HA. So then we know that our initial pH is equal to 5.00.

What we're going to do next is we're going to look at two different buffers, and both of them are going to be made with acetic acid and with acetate. We're going to call them buffer one and buffer two. Buffer one has a ratio of A⁻ to HA that is 1.82, so the pH is going to be 5, and the A⁻ concentration before we do anything to it, before we add anything, is 0.90 molar, and the HA concentration is going to be 0.49 molar.

Our second buffer that we're going to compare it to, we will call buffer two. Buffer two also has the same ratio of acid to base, except this time both concentrations are going to be 10 times smaller than buffer one. So our A⁻ concentration is 0.09 molar, and our acetic acid concentration is 0.049 molar.

What we're going to do here is we're going to see what happens to the pH of both of these. They both start out with a pH of 5, but how much should they change when we add—we're going to add 0.04 moles of a strong base, sodium hydroxide, to one liter buffer.

So when you do that, well, it's a buffer. We know that it's going to resist the pH change, but what exactly is happening? What's the reaction that goes on when you add this in? When you add your strong base, which is going to dissociate to form OH⁻, it's going to react with the acid in your buffer. So our acid is CH₃COOH, and we always assume that a strong base is going to react irreversibly (so, one-sided arrow) with a weak acid.

What happens is this proton is going to react with OH⁻, and we're going to get H₂O (or water), and we're going to make CH₃COO⁻. So that's our base. We can see that the hydroxide is going to react one-to-one with our weak acid, and it's going to produce one equivalent of our base.

Now we can use this information to calculate what happens to our buffer when we add 0.04 moles of sodium hydroxide. What's going to happen is it's going to react with our acid, which means the concentration of the acetic acid is going to go down by 0.04 molar. Our new concentration after it's reacted is going to be 0.45 molar. Sorry, I tried to do that in my head.

What happens to our concentration of the base? Remember that when the acid reacts with sodium hydroxide, we actually make more base. So we have to adjust the concentration of A⁻ upward. It actually makes 0.04 molar acetate when this reaction happens, so our new concentration of our acetate ion is 0.94 molar.

If these are our final concentrations, we can now plug them back into the Henderson-Hasselbalch equation to get the pH. So the pH of buffer one (I'll put a little subscript one) is going to be 4.74 (the pKa) plus log of 0.94 molar divided by 0.45 molar. If we plug that into our calculator, we get that the pH after we add that hydroxide is 5.06.

So it's a little bit higher; it went up by 0.06. That makes sense. We do imagine it would be higher. If you add base, it becomes more basic, and the pH should go up. But it didn't change a whole lot because it's a buffer.

Now let's compare that with what happens to buffer two. We add 0.04 mol sodium hydroxide to buffer two. Our acetic acid concentration is going to go down by 0.04 molar, so our new concentration of HA is 0.009 molar. By the same reaction, our base concentration is going to go up since when the acid reacts, it makes more conjugate base. So we're going to have to add 0.04 molar to A⁻ concentration, and so the new concentration is going to be 0.13 molar.

We can plug those concentrations into the Henderson-Hasselbalch equation, and we get that the pH of our buffer two is equal to 4.74 (the pKa) plus log of 0.13 molar divided by 0.009 molar. If we plug this into our calculator, this is equal to 1.16.

So if we add that together with our pKa, we get that the new pH is 5.90. The pH changed a whole lot more for buffer two than for buffer one. The pH went up by 0.90 instead of by 0.06.

So if we're comparing the buffer capacities of both of these buffers, we would say that buffer one, well, the buffer changes less when you add the same amount of acid or base. Therefore, buffer one has the higher buffer capacity, since you don't want these concentrations A⁻ and HA to be too low.

The general rule of thumb is that you want your concentrations of HA and A⁻ between 0.10 molar and 1.0 molar. By following that rule of thumb, you can make a buffer where you don't have to worry too much about adding too much acid or base before your pH changes, since that's usually why you're making a buffer in the first place.