# Ph pka and pkb relationship

### pKa and pKb relationship (video) | Khan Academy

Regarding the last equation, it is only applicable to the sum of the pKa of a species HX and the pKb of its conjugate base, X-. Since both the pK. Im having trouble determining the relationship between pH and pKa and pKb. Is a low pKa representative of a low pH and a high pKb. Learn what pH, pKa, Ka, pKb, and Kb mean for acids and bases, plus understand the pKa and pKb are related by the simple relation: pKa +.

So with that said, let's see if we can find a relationship between Ka and Kb. What do we have here? We have an A minus on both sides of this. We have H over-- OH over A minus.

### Henderson-Hasselbalch

Let's solve for A minus. If we multiply both sides of this equation by HA over H plus, on the left-hand side we get Ka times the inverse of this. So you have your HA over H plus is equal to your concentration of your conjugate base. And let's do the same thing here. Solve for A minus. So to solve for A minus here, we might have to do 2 steps. So if we take the inverse of both sides, you get 1 over Kb is equal to A minus over H, the concentration of my conjugate acid times the concentration of hydroxide.

Multiply both sides by this. And I get A minus is equal to my concentration of my conjugate acid times concentration of hydroxide. All of that over my base equilibrium constant. Now, these are the same reactions. In either reaction for given concentrations, I'm going to end up with the same concentration.

This is going to equal that. These are two different ways of writing the exact same reaction.

So let's set them equal to each other. So let me copy and paste it, actually. So I'm saying that this thing, copy, is equal to this thing right here. So this is equal to-- let me copy and paste this-- that.

That's equal to that. So let's see if we can find a relationship between Ka and Kb. Well, one thing we can do is we can divide both sides by HA. So if we divide both sides by HA. Actually, I could probably have that earlier on to the whole thing. If we ignore this part right here, this is equal to that.

Let me erase all of this. I'm using the wrong tool. So we could say that they both equal the concentration of A minus.

So that's equal to that. We can divide both sides by HA. This over here will cancel with this over here. And we're getting pretty close to a neat relationship. And so we get Ka over our hydrogen proton concentration is equal to our hydroxide concentration divided by Kb. You can just cross-multiply this. So we get Ka, our acidic equilibrium concentration, times Kb is equal to our hydrogen concentration times our hydroxide concentration.

Remember, this is all in an aqueous solution. What do we know about this? What do we know about our hydrogen times our hydroxide concentration in an aqueous solution? For example, let me review just to make sure I'm jogging your memory properly. We could have H2O. It can autoionize into H plus.

And this has an equilibrium.

**pKa - Why most drugs are weak acids or weak bases**

You just put the products. So the concentration of the hydrogen protons times the concentration of the hydroxide ions. And you don't divide by this because it's the solvent. And we already figured out what this was. If we have just completely neutral water, this is 10 to the minus 7. And this is 10 to the minus 7. So this is equal to 10 to the minus Now, these two things could change. I can add more hydrogen, I could add more hydroxide.

And everything we've talked about so far, that's what we've been doing. That's what acids and bases do. They either increase this or they increase that. But the fact that this is an equilibrium constant means that, look, I don't care what you do to this. At the end of the day, this will adjust for your new reality of hydrogen protons. And this will always be a constant. As long as we're in an aqueous solution, a solution of water where water is a solvent at 25 degrees.

## pH and pKa relationship for buffers

I mean, in just pure water it's 10 to the minus 7. But no matter what we do to this and this in an aqueous solution, the product is always going to be 10 to the minus 14th power. So that's the answer to this question. This is always going to be 10 to the minus If you multiply hydrogen concentration times OH concentration.

Now they won't each be 10 to the minus 7 anymore, because we're dealing with a weak acid or a weak base. So they're actually going to change these things. But when you multiply them, you're still going to get 10 to the minus And let's just take the minus log of both sides of that. Let me erase all this stuff I did down here. I'll need the space. Let's say we take the minus logs of both sides of this equation.

So you get the-- let me do a different color-- minus log, of course it's base 10, of Ka. Let me do it in the colors.

- CHEMISTRY COMMUNITY
- pH, pKa, Ka, pKb, Kb
- pKa and pKb relationship

Ka times Kb is going to be equal to the minus log of 10 to the minus So what is this equal to? The log of 10 to the minus 14 is minus 14, because 10 to minus 14th power is equal to 10 to the minus You take the negative of that, so this becomes So the right-hand side of your equation just becomes And this one, we could use log properties. This is same thing as the minus log of Ka. We use the colors. Ka plus the minus log of Kb. Or, though you could think of this-- this is your pKa, this is your pKb.

We can rearrange the Henderson-Hasselbalch equation to get a lot of different kinds of information. One kind of problem you see a lot is for some buffer, you know, they might ask you, oh, what's the pH?

The other thing that you can use the Henderson-Hasselbalch equation to tell you is the relationship between A minus and HA which is something you might wanna know. A lot of times, you just wanna know, you know, what's in your solution, depending on what you wanna do to your solution, if you wanna add things to it, maybe you wanna add some acid, you wanna add some base.

You wanna know what's going on. The Henderson-Hasselbalch equation gives you a really quick and easy way of doing that. So what we're gonna do, is we're gonna rearrange this equation to solve for this ratio that we might be interested in. And I don't know about you, but I actually find, well, laughs I find logs not super-intuitive sometimes.

So I'm actually going to get rid of the log by raising both sides to the 10th power. So what does this tell us?

It may not look like it tells us a whole lot more, but actually, it tells us a lot. It tells us about the relative relationship and size between A minus and HA concentration.

So if we look at this, we can derive a couple relationships.

So let's go ahead and look at all the possible scenarios for these three things. So anything to the zeroth power is equal to one. Which tells us that this ratio is equal to one. And if A minus concentration over HA concentration is equal to one, that means that they have the same concentration.

I forgot a minus sign there.