# Relationship between pka and pkb definition

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

The pKa and pKb values are measurements of the strengths of acids and bases The equilibrium constant of a base, Kb, is found using the following equation. Learn what pH, pKa, Ka, pKb, and Kb mean for acids and bases, plus understand the differences between each term's definition. indicates a stronger base. pKa and pKb are related by the simple relation: pKa + pKb = There is a lot of misuse going on with the term p K a since many people are too lazy to say. The p K a of N H X 3 's conjugate acid is

So we could write the same reaction both ways. And we can write equilibrium constants for both of these reactions. So let's do that. Let me erase this, just because I can erase this stuff right there, and then use that space. So an equilibrium reaction for this first one.

I could call this the K sub a, because the equilibrium reaction for an acid. And so this is going to be equal to its products. So the concentration of my hydrogen times my concentration of whatever my conjugate base was, divided by my concentration of my original acid. So this would be the concentration of HA. I could also write an equilibrium constant for this basic reaction.

## pKa and Dissociation Equilibrium

Let me do it right down here. So I'll call that my K sub b. This is a base equilibrium. And so this is equal to the concentration of the products. It's becoming tedious to keep switching colors. Actually, I'll do it. Because it makes it easier look at, at least for me.

HA times the concentration of my hydroxide ions divided by my concentration of my weak base. Remember, this can only be true of a weak base or a weak acid. If we were dealing with a strong acid or is or a strong base, this would not be an equilibrium reaction. It would only go in one direction. And when it only goes in one direction, writing this type of equilibrium reaction makes no sense-- or equilibrium constant-- because it's not in equilibrium.

It only goes in one direction. If A was chlorine, if this was hydrochloric acid, you couldn't do this. You would just say look, if you have a mole of this, you're just dumping a mole of hydrogen protons in that solution and then a bunch of chlorine anions who are not going to do anything. Even though they are the conjugate base, they wouldn't do anything. So you can only do this, remember, for weak acids and bases.

So with that said, let's see if we can find a relationship between Ka and Kb. What do we have here?

### Relationship between Ka and Kb (article) | Khan Academy

We have an A minus on both sides of this. We have H over-- OH over A minus. 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.

### pKa and pKb – jingle-bells.info

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.

**pKa vs Ka and Relative Acid Strength**

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.

- pKa and pKb
- pH, pKa, Ka, pKb, Kb
- Relationship between Ka and Kb

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. 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.

Activity level should be used rather than concentration, but concentration was used instead of activity because concentration often corresponds to activity level in analytical concentrations and it is simpler the same applies below. When an acid dissociates, it releases a proton to make the solution acidic, but weak acids have both a dissociated state A- and undissociated state AH that coexist according to the following dissociation equilibrium equation.

The concentration ratio of both sides is constant given fixed analytical conditions and is referred to as the acid dissociation constant Ka. Ka is defined by the following equation.

The square brackets indicate the concentration of respective components. Based on this equation, Ka expresses how easily the acid releases a proton in other words, its strength as an acid. Carboxylic acids containing -COOHsuch as acetic and lactic acids, normally have a Ka constant of about to Consequently, expressing acidity in terms of the Ka constant alone can be inconvenient and not very intuitive.

Therefore, pKa was introduced as an index to express the acidity of weak acids, where pKa is defined as follows. In addition, the smaller the pKa value, the stronger the acid.