Equilibrium Constant: Study with Video Lessons, Practice Problems & Examples

The relationship between the equilibrium constant (K_a) and pK_a is crucial in understanding acid strength. Strong acids have high K_a, indicating complete dissociation, while weak acids have lower K_a, leading to partial dissociation. The pK_a scale, ranging from -10 (strongest acids) to 50 (weakest), inversely correlates with acid strength. A lower pK_a signifies a stronger acid, similar to how lower pH indicates higher acidity. Thus, pK_a effectively measures a molecule's tendency to donate protons, essential in organic chemistry.

Why we use pKa instead of pH.

Alright guys. Now I want to talk about the relationship between the equilibrium constant and the pKa. Alright. So remember that in general chemistry we are always talking about something called pH. Okay? And pH was used to measure what? Do you guys remember? It was actually used to measure the concentration of hydronium ions in a solution. Oops. Not is. In solution. Okay. So I know that's really specific, but it was used to basically measure how acidic a solution was. How acidic or how basic. Okay. But it turns out that in organic chemistry, we don't care about the solution at all. We don’t care if it's acidic or if it's basic at all. What we care about is the actual molecule itself and what I care about is how likely is that molecule to donate a proton or how likely is that molecule to accept a proton. pH doesn't tell me that. pH just tells me how many H+ ions are circulating in this test tube. I don't care about that. I care about the molecules inside. I care how much they are likely to give away a proton. Okay? So that means that we're going to use a different measure. We're going to use the negative log of the equilibrium constant or the dissociation constant. Remember that dissociation constant has to do with how likely a bond is to break. Okay? So we're going to use the negative log of how likely that is to happen to figure out the tendency of a molecule to donate protons. Okay? And that's what we actually care about. So that's why in general chemistry you use pH, but now in organic chemistry, we're going to use pKa instead. Okay?

The relationship between equilibrium constant and pKa.

Let's just talk about stuff that you guys should remember, that strong acids are going to have a high dissociation constant. That means that they're very likely to dissociate fully. Okay? And that means, right, they fully dissociate in an aqueous solution. Remember that weak acids are going to have a smaller dissociation constant and what that means is that they're only going to partially dissociate in an aqueous solution. And that makes a huge difference because that means that they're going to have different pKa's. They're going to have different tendencies to donate protons. Now let's remember what is pKa. Well p, remember, stands for the negative log base 10. And then, remember that Ka stands just basically for products over reactants.

Now, I'm not going to make you guys calculate every single thing. But, check it out. I mean, products in this case are just dissociating into H⁺. And reactants are what happens before it fully dissociates. Does that make sense? So the Ka is basically the ratio of how much of my acid is going to actually become a proton. And that's what I care about. So therefore, if we're taking the negative log of this Ka, what that means is that the higher the Ka, basically the higher the chances of the molecule breaking apart and making ions, the lower the pKa is going to be.

So just like we had in pH, remember that your strongest acid was actually the one that was the lowest pH. It was, like, close to 0. Remember that basically pH is on a scale of 0 to 14 and remember that down here was the very acidic solution and then over at 14 was the very basic solution. So remember that if it was very acidic, it would have a very low pH, And in the same way, pKa is going to do the same thing. So your strongest acids are always going to have the lowest numbers for pKa. Does that make sense? And it's because we're using the negative log, not the positive. So it's always going to be the opposite. Cool so far? Awesome.

The pH scale vs. the pKa scale.

Now what I want to do is go over the similarity of the pH scale and the pKa scale. So, for the pH scale, like I said, 0 is very acidic, 14 is very basic, and 7 is neutral. Remember that 7 is just water, neutral, right in the middle. For pKa, we have something very similar, but for pKa, it's just going to be a different scale and it's going to mean something different. So, for pKa, about the lowest pKa that you can get without being a crazy molecule is around negative 10. And these are going to be the most amazing acids. Remember that pKa has to do with how much it wants to be an acid. So, negative 10 is going to be like the most amazing acids ever. It turns out that the scale is about from negative 10 to about 50. So, 50 would be about the same thing as me saying, like, a really high number for pH. And what I'm wondering is what do you think 50 means? Do you think that means that it's a very good base? And the answer is no. It has nothing to do with basicity because we're just trying to see how likely it is to dissociate into an acid. So, what is 50? 50 is just going to be very poor acids. They are terrible at dissociating. So, basically, 50 doesn't mean that you're basic; it just means that you're really bad at being an acid. It means that as an acid, you're never going to dissociate. Then, what is 16? 16 is actually water, and water is going to be kind of your neutral pKa, where basically anything above water, we're going to say that those are the good acids, and then anything below water, we're going to say that those are the bad acids. Does that make sense? With 50 being the worst of all, so much so that I said it was very poor. Does that make sense? So, basically, when we're talking about pKas, we're always looking at things that are lower than 16 as our strong or as our good acids.

Calculate the pKa of acetic acid

So now what I want you guys to do is calculate the pKa's of the following acids using the dissociation constant. Okay? So, in this case, I'm already giving you the dissociation constant. This is really easy. All you have to do is just take the negative log of it. So I'm just really, like, organic chemistry has very little math in it, but I just want you guys to practice this so you remember the definition of negative log. So, in your calculator, what you should do is just type in and you guys can follow along with me. So maybe pause the video if you need to get your calculator. Okay. You guys all got it. You have your iPhone sideways. Perfect. Awesome.

So what we're gonna do is we're gonna say \( 1.75 \times 10^{-5} \). Okay? And we're just going to take the negative log of that. So I'm gonna basically type in that number and then I'm going to type in log base 10, if it says that. Okay. And then I'm going to type in the negative sign. okay? Remember that you basically have, like, a positive-negative button on your calculator. So you're gonna type in the negative sign on your calculator and what that's gonna give you is a pKa of 4.75. Okay? So is that a good acid? What do you guys think? Yeah, that's actually a pretty good acid because remember I said anything below 16 is pretty good. So it turns out this is actually a carboxylic acid. Remember carboxylic acid? So it turns out carboxylic acids are actually pretty good acids. Duh. Right? That's why they're called carboxylic acids.

Calculating pKa and comparing acidity

Let's try this next one. Notice that it has a dissociation constant of that, slightly different. Go ahead and take the negative log of that number and see what you get. So now what you should have gotten is you should have gotten the number 9.24 if you round it. Okay? And that's the pKa. So now I want to ask you guys, which of these is the stronger acid? Is acetic acid stronger, or is ammonium stronger? And the answer is it has to be acetic acid. Okay? This is my stronger one because of the fact that it has a lower pKa. Okay? In fact, every time that you drop 1 in pKa, that actually means it's 10 times stronger because it's a log scale. So it turns out that acetic acid is actually like probably like almost like 100000 times better of an acid than ammonium. Isn't that crazy? Like, the numbers get really big really fast when it comes to acidity. So I hope that makes sense. So it's just a quick review. What's most important about this entire page is you guys knowing this trend right here where your lowest pKas are going to be your strongest acids, your highest pKas are going to be your worst acids. Never say that they are bases because pKa has only to do with acids and not with anything else. So let me know if I can clear that up for you in any other ways, but if not, let's keep going.

Here’s what students ask on this topic:

What is the relationship between Ka and pKa in organic chemistry?

The relationship between Ka and pKa is crucial in understanding acid strength. Ka, the acid dissociation constant, measures how completely an acid dissociates in solution. A high Ka indicates a strong acid that dissociates fully, while a low Ka indicates a weak acid that only partially dissociates. pKa is the negative logarithm of Ka, given by the equation:

${\mathrm{pK}}_a=\; -log$₁₀(Ka)

Thus, a lower pKa corresponds to a higher Ka, indicating a stronger acid. This inverse relationship helps chemists understand and compare the acid strengths of different molecules.

How does pKa differ from pH in measuring acidity?

pKa and pH are both measures related to acidity, but they serve different purposes. pH measures the concentration of hydronium ions (H₃O⁺) in a solution, indicating how acidic or basic the solution is. It ranges from 0 (very acidic) to 14 (very basic), with 7 being neutral. pKa, on the other hand, measures the tendency of a specific molecule to donate a proton, reflecting its intrinsic acid strength. It is the negative logarithm of the acid dissociation constant (Ka). While pH is about the solution's acidity, pKa is about the molecule's proton-donating ability. Lower pKa values indicate stronger acids, similar to how lower pH values indicate higher acidity.

Why do strong acids have low pKa values?

Strong acids have low pKa values because pKa is the negative logarithm of the acid dissociation constant (Ka). For strong acids, Ka is high, meaning they dissociate completely in solution, releasing a large number of protons (H⁺). The equation for pKa is:

${\mathrm{pK}}_a=\; -log$₁₀(Ka)

Because Ka is large for strong acids, the negative logarithm results in a low pKa value. This low pKa indicates a high tendency to donate protons, which is characteristic of strong acids. Therefore, the lower the pKa, the stronger the acid.

What is the pKa scale and how is it used in organic chemistry?

The pKa scale is a numerical representation of acid strength, ranging from about -10 to 50. It is used in organic chemistry to compare the proton-donating abilities of different molecules. The scale is inversely related to acid strength: lower pKa values indicate stronger acids, while higher pKa values indicate weaker acids. For example, a pKa of -10 represents a very strong acid, while a pKa of 50 represents a very weak acid. This scale helps chemists predict reaction outcomes, understand molecular behavior, and design synthesis pathways by providing a clear measure of how likely a molecule is to donate a proton.

How do you calculate pKa from Ka?

To calculate pKa from Ka, you use the following equation:

${\mathrm{pK}}_a=\; -log$₁₀(Ka)

First, determine the value of Ka, the acid dissociation constant, which represents the ratio of the concentration of dissociated ions to the concentration of the undissociated acid. Once you have Ka, take the negative logarithm (base 10) of this value to find pKa. For example, if Ka = 1.0 x 10^-5, then:

${\mathrm{pK}}_a=\; -log$₁₀(1.0 x 10^-5) = 5

This calculation shows that the pKa is 5, indicating the acid's strength.