Here’s your typical pKa table with pKa values for a bunch of organic (and inorganic) molecules. You can find a table like that in any organic chemistry textbook. Your instructor has probably given you one of those. A version of this pKa table is most probably given to you on your exam. While the table above only gives the pKa values for more or less commonly seen species in organic chemistry, I often see instructors give students tables with dozens and dozens of molecules!
In reality, it doesn’t matter how big or small the pKa table is. What really matters, is your ability to use it! There are two ways how you can use your pKa table:
- You can look up the pKa values in the table to determine if you’re dealing with a strong or a weak acid or a base.
- You can use the pKa values to estimate the equilibrium constant in an acid-base reaction.
The second way of the pKa table use is what you actually want to focus the most! But first…
What Does pKa Value Represent?
pKa is by definition a -log(Ka), where Ka is the dissociation constant of an acid. Let’s look at the most iconic acid in chemistry: hydrochloric acid (HCl):
In this reaction, HCl dissociates giving you a proton/hydronium ion (depending on the media) and chloride anion. The chloride anion is what we call a conjugate base, while the hydrochloric acid itself is an acid according to the Brønsted-Lowry theory of acids and bases. By the definition, we express the Ka value as the concentrations of the products over the concentration of the reagents. Products in this case are the H+ and the Cl–, while the reagent is HCl.
The pKa value for the HCl dissociation reaction is -8, which means that the Ka value is 108! I assume that you know how to deal with the logarithmic transformations. If you need a refresher, check out the Khan Academy video on this topic. So, the highly negative pKa value means that we’re dealing with a very strong acid.
Qualitatively, we say that anything that has a pKa higher than 3 is a weak acid, while anything with a negative pKa value is a strong acid. In between is sort of a gray area.
High pKa = weak acid
Low pKa = strong acid
The information about the acid strength is useful… kind of, but so what? The pKa values are not very informative outside of context. However, when we have a reaction in mind, then identifying the acid on each side of an equilibrium will help us to estimate the equilibrium constant for this reaction and determine if it’s favorable or not!
Using pKa to Determine the Equilibrium Constant of a Reaction
Why equilibrium constant (Keq) for a reaction is important? If I have a very large constant, it means that my reaction is highly favorable. Generally, a constant higher than 104 means that our equilibrium is completely shifted in the direction of the products. While an equilibrium constant smaller than 10-4 means that our reaction is barely even taking place. Keep in mind, that there’s no “hard” cutoff for what we consider an equilibrium vs non-equilibrium. Rather, think that virtually any reaction can be treated as an equilibrium. The only caveat is going to be that if you have an equilibrium constant higher than 104, the concentration of your starting materials or reagents will be negligible. Likewise, if your equilibrium constant is smaller than 10-4, you’re looking at an equilibrium with the concentration of the products so small, that it might not even matter.
So, how pKa values help us to find the Keq? We first need to identify the acid on each side of our reaction. Let’s look at a fairly typical reaction you might see on a test:
Above, is a reaction between a terminal alkyne and sodium hydroxide. Without going too deep into the acid-base properties of the reagents, this reaction looks just fine. Let’s check it to make sure 😉
Steps to Estimate the Keq
First, I need to identify the acid on each side of the reaction. According to the Brønsted-Lowry theory of acids and bases, acid is the proton donor. So, by checking what loses the proton on the way to the “right” and what loses the proton of the way to the “left,” I see that the alkyne is my acid on the left and water–on the right.
Next, we need to check the pKa values of my acids in the table. Those are 25 and 15.7 respectively.
Now, how exactly does that help me in determining the equilibrium constant? By remembering the definition of the Keq (products over reagents) and doing some simple mathematical manipulations, I get the following expression:
Again, I assume you know how to perform these manipulations. If you don’t feel comfortable with this math, it’s not going to be a dealbreaker. You can always refresh your memory by looking through your gen chem notes or send me a message and I’ll be happy to help you with that. The important thing is, that by using a little more math, we get the following:
So, it all boils down to a simple calculation:
Keq = 10pKa(product) – pKa(reagent)
If you remember that your Keq is always going to be 10 to the power of the right pKa value minus the left pKa value, you’ll always be able to easily estimate the equilibrium constant and tell if your reaction is favorable or not. In this particular case, the reaction is highly unfavorable since we have a very small Keq value.
How to Use Acid-Base Equilibrium for Other Reactions
Acid-Base always happens first!
Remember, that the acid-base reactions have a very low activation energy, so they are very fast. This means that you always have to consider acid-base chemistry before any other step in your reaction or a mechanism. If you forget to check for the acid-base reaction by using the pKa values from your pKa table, you are running a risk of getting a wrong product in your reaction. Let me show you an example:
I’ve seen this reaction on the midterm in the first semester organic chemistry where students have just finished a topic on substitution and elimination reactions in class. Most of the class gave the following answer:
Students treated this reaction as a substitution because they saw a good primary leaving group and a good nucleophile. They forgot to check for acid-base chemistry, so they got it wrong!
Some students gave this answer:
They thought it must’ve been an elimination reaction because methoxide is a base. They forgot to check for acid-base chemistry and they got it wrong as well.
Finally, only a small number of students remembered to check the pKa values from their pKa table and saw an acid-base reaction first!
Since a carboxylic acid has a relatively low pKa value, the first step in this reaction is the acid-base reaction between the carboxylic acid and ethoxide, which is a base. Only then the resulting carboxylate ion does the intramolecular SN2 attack and closes off the ring! If this reaction was given to students with the negatively charged carboxylate from the very beginning, I’m sure most would remember that carboxylates are nucleophilic and react readily with primary alkyl halides.
This only scratches the surface of the various uses for the pKa table and pKa values within it. Hopefully, this post will encourage you to familiarize yourself with your pKa table more and learn how to use it better. If you like the pKa table I have at the top of this page, you can have it in a downloadable pdf format. Just subscribe to my newsletter below and I’ll send it to you with the welcome email along with some other goodies.