# How to Use a pKa Table

Today we’ll talk about an incredibly important skill that might take some time to grasp but pays tremendous dividends. We’ll go through the exact details of how to use a pKa table. [Background for pKa – read this post ]   Understanding the proper use of a pKa table will give you the ability to recognize which acid-base reactions will happen and which will not. This will come up a lot as you progress through Org 1 and Org 2. It might be helpful to go back and review some of the factors that affect acidity that were talked about earlier.

Let’s say you’re given the following question:

By acidity, we’re talking about Bronsted acidity here – in other words, the ability to donate a proton.

Let’s say we’re given a pKa table with the following values.

1. Remember that a pKa table ranks molecules in order of their acidity, from strongly acidic (e.g. HCl with pKa of –8) to weakly acidic (e.g. methane, pKa of ~50).
2. What determines whether or not an acid-base reaction will happen in the first place? We apply the following principle to acid-base reactions: A stronger acid will tend to react with a stronger base to produce a weaker acid and a weaker base.
3. It’s easy enough to use a pKa table to determine acid strength – we can see at a glance that H2O (pKa of 15) is a stronger acid than NH3 (pKa of 38). The question is, how do we determine base strength?

Here’s how we do it. Draw out the conjugate bases of the acids on your pka table by removing a proton.

E.g. NH3 –> NH2(-) or   CH4 –> CH3 (-).

Here’s the key principle: The order of base strength is the inverse of acid strength. The weaker the acid, the stronger the conjugate base. Using this principle, you can also use the pKa table to give you the strengths of bases. I call this the inverse pKa table.

Here’s a pKa table with the conjugate bases included:

4. Here’s how we apply this knowledge to the problem.

Find the acid on the pKa table. Find the base on the inverse pKa table. Do the acid base reaction – that is, add a proton to the base and remove a proton from the acid.

5. Evaluate: Is the new acid stronger or weaker? Is the new base stronger or weaker?

6. Examples.

Example A : We have CH4 and HO(-) We can find CH4 on the pKa table – it has a pKa of 50. Hydroxide ion, HO(-) is not on the left side of the pKa table, but it is on the “inverse” pKa table – it is the conjugate base of water, H2O. So CH4 is the acid and HO(-) is the base in this reaction.

Doing the proposed acid base reaction, we transfer a proton from CH4 to HO (-). The products of this reaction would therefore be CH3(-) and water.

Now we ask the question – how do these compare in strength to our starting acids and bases? Water has a pKa of ~15, and CH4 has a pKa of 50. Our product is a stronger acid. From the inverse pKa table, we also note that CH3(-) is a stronger base than HO(–). Our product is a stronger base.

Verdict – the reaction won’t happen. We need to go to a weaker acid-base pair (see #2, above). So we write “NR”.

Here’s another example.

Example B – Take HCΞCH and NH2(–). HCΞCH has a pKa of 25; on the other hand, NH2(–) is on the conjugate base table. Drawing out the products of the acid base reaction will give us NH3 (weaker acid than HCΞCH) and HCΞC(–) (weaker base than NH2(–). This reaction will go.

Example C : Take NH3 and HCl. This time, we can find both HCl and NH3 on the pKa table. But HCl has a pKa of (–8) and NH3 has a pKa of 38. HCl will clearly act as an acid here, and NH3 will act as a base.

We can write out our acid base reaction: HCl + NH3 → NH4(+) Cl(–)

Our acidic product, NH4, has a pKa of 9. Our product is a weaker acid than HCl. Our basic product, Cl(-) ranks below NH3 on our inverse pKa scale. Our product is a weaker base than NH3. Conclusion: this reaction is also a go. And, indeed, if you find yourself in a freezing hut with only a bottle of concentrated HCl and aqueous ammonia to keep you company, adding them together will definitely warm up your day. This is about the only situation in which I would recommend this.

Q. How do you deal with a compound that is similar but not on the table? Take hexane, for instance. Even though it is not technically on the list, its behavior is similar enough to methane – they’re both alkanes, after all – that we make the assumption that the pKa’s are roughly the same. Similarly, an amine like trimethylamine (NMe3) will have similar behavior to NH3 in the reaction with HCl.

One final point on the big-picture type view. Note the pattern. The conjugate base of methane (H3C(–) ) is strong enough to deprotonate anything below it on the pKa table (that is, pretty much everything). Methyllithium, CH3Li, is an incredibly strong base. Conversely, acetylide ion, HCC(–) is strong enough to effectively deprotonate any acid with a pKa under ~25, and acetate ion (CH3COO(–)) is weaker still, only able to deprotonate any acid with a pKa lower than 5.

That’s why I compare a strong base like methyl lithium to a royal flush in poker – it will essentially defeat  any hand (acid) it encounters.