Quantifying The Basicity Of Amines, Using “The pKa Of The Conjugate Acid”, a.k.a. “pKaH”
How do you measure the basicity of an amine? Case in point: what’s a stronger base: pyridine or piperidine?
If you said piperidine, congratulations – it is indeed a stronger base.
But why? And how much stronger? How does one go about trying to answer these questions? After all, we can easily compare the strength of acids by examining their pKa’s. Shouldn’t we be able to do the same with bases?
Yes, in a way. Here’s two key points for today:
- The best way to quantify the basicity of an amine is to examine the pKa of its conjugate acid.
- The higher the pKa of the conjugate acid, the stronger the base.
In this post we’ll show some specific examples of how to use pKa values to compare the basicity of amines.
In a subsequent post, we’ll then explore some key trends underlying the basicity of amines. [See: 5 Factors That Affect The Basicity of Amines]
1. Quick Review: Acids, Bases, Conjugate Acids, and Conjugate Bases
First, let’s quickly review some basicity basics.
There are four actors in every acid-base reaction.
- The base is the species which donates a lone pair to H+ (also known as a “proton” or “hydrogen nucleus”). It’s where the new bond to H forms (e.g. pyridine, below)
- The conjugate acid is the species that results after the base forms a bond to H (e.g. “pyridinium” , which has a new N–H bond)
- The acid is the species which loses H+ . It’s where the bond to H breaks (e.g. H–Cl)
- The conjugate base is the species that remains after the acid donates H+ to the base (e.g. Cl-)
Here’s pyridine and piperidine in action. By following the bonds that form and break, you can identify each actor.
2. Using pKa To Measure Acidity
Every acid-base reaction can be written as an equilibrium between a forward and reverse reaction. We’ve seen that the acidity constant, Ka, is a measure of how easily a species dissociates to give H+ and the conjugate base.
For convenience, we use the negative log of Ka, called pKa, which is similar to the familiar pH scale but can extend beyond 14 because it’s not strictly limited to aqueous solvent. pKa values range from –10 or so for very strong acids (e.g. hydroiodic acid, H–I) to 50 and above for certain hydrocarbons (e.g. ethane).
How can we apply these concepts to measure basicity? Couldn’t we switch things around and define a term, Kb, which is the equilibrium for how readily a species combines with H+ , define pKb as its negative log, and compare bases by looking at their pKb values?
Yes…. we could. I guess. If we had to. But generally, organic chemists’ opinion on this subject is “Screw pKb“.
After all, pKa values have been measured for thousands of organic molecules. Does anyone really want to have to remember a huge set of pKb values too? Hell no!
Instead, we can easily use pKa values as an indirect measurement of basicity. Here’s how.
3. Using pKa Values To Quantify Basicity of Amines
Recall these two immortal lines of prose, worth reciting to yourself nightly:
- The stronger the acid, the weaker the conjugate base.
- The weaker the acid, the stronger the conjugate base.
[Don’t leave out the word “conjugate” ! Note 1]
The pKa for the conjugate acid of pyridine (“pyridinium”) has been measured. It’s about 5.2 . [Source – also see Footnote 2]
We also have a value for the pKa for the conjugate acid of piperidine. It’s about 11 .
From these pKa values, we can tell that the conjugate acid of pyridine is stronger than the conjugate acid of piperidine by about 6 pKa units. Since each pKa unit represents a factor of 10, that’s a factor of about 1 million.
Since “the stronger the acid, the weaker the conjugate base”, pyridine is therefore a weaker base than piperidine by a factor of 1 million.
4. “The pKa Of The Conjugate Acid” Can Be Abbreviated as “pKaH”
The term, “pKa of the conjugate acid” is a bit of a mouthful to use on a regular basis. Being naturally lazy, we’d like to condense this a bit for common usage.
Since the conjugate acid of a base (“B”) is “BH”, we can abbreviate “the pKa of the conjugate acid of a base” as its pKaH.
This lets us say that the pKaH of pyridine is 5.2, and the pKaH of piperidine is 11.
We can then dig into the literature to find other bases to compare it to.
For instance, exactly how basic is ammonia (NH3) ? The conjugate acid of ammonia, NH4(+), is 9.2 . Equivalently, we can say that the pKaH of ammonia is 9.2. This puts it in-between pyridine and piperidine on the basicity scale.
Note that it’s very important not to confuse pKaH with pKa. The pKaH of ammonia is 9.2, which measures the acidity of its conjugate acid, NH4(+).
The pKa of ammonia itself is 38, which measures the equilibrium constant for dissociation of NH3 to give its conjugate base, NH2(-) and H+.
That means that 38 is the pKaH of the amide ion NH2(–), which you may have encountered before as the strong base (NaNH2) used to deprotonate terminal alkynes (pKa =25). Using pKaH, we can determine that NH2(–) is about (38 – 9) = 29 orders of magnitude more basic than NH3 !
5. Using pKaH to Determine The Relative Basicities Of Amines
Using pKaH to determine the relative strengths of bases is a pretty useful trick.
Here are some representative examples of nitrogen-containing molecules. Below is the pKa of their conjugate acids.
What’s the strongest base here? What’s the weakest?
The lowest pKaH value here is –10 for the nitrile (bottom left). This means the nitrile is the least basic of all of these molecules.
The highest pKaH value here is 10.8 for triethylamine. That makes triethylamine the strongest base out of all of those listed.
6. Some Words Of Caution On pKa Values For Amines
Two things to watch out for, especially when reading other online sources on this topic.
First, sometimes the pKaH values for amines are reported as pKa values , without explanation. The best pKa tables won’t do this, but it’s hard to sort the wheat from the chaff when you are just starting out.
If you see an anomalously low pKa value for an amine, it’s likely referring to the pKaH of the conjugate acid.
For instance, here’s a pKa table where the pKa of methylamine (CH3NH2) is listed as 10.63.
That’s low. Hopefully by this point, such a value of 10 for a pKa of an amine should strike you as weird, especially since the pKa of the closely related NH3 is 38.
The value of 10.63 actually refers to the pKa of the conjugate acid of methyl amine, NOT methylamine itself. It’s a pKaH value.
Similarly, the same table lists trimethylamine as having a pKa of 9.8 . Again, this is actually its pKaH. I can’t find an actual pKa value for trimethylamine, but I would guess that it is >40, since the conjugate base of trimethylamine is the carbanion (CH3)2N–CH2(–) ).
A second, less common source of confusion is that sometimes the pKaH of an amine is reported as its pKb, such as in this table which reports the pKb of NH3 as 9.2 . This is inaccurate.
[The pKb of NH3 can be calculated from the formula pKaH + pKb = 14 . The pKb of NH3 is 4.8 (aqueous solution). ]
Again, pKb values don’t really come up much in undergraduate organic chemistry, although I’m told that they sometimes make an appearance on the DAT/MCAT.
7. What Key Factors Govern The Basicity Of Amines?
Now that we’ve learned at least how to quantify and interpret the pKa values of amines and their conjugate acids, we can start to ask the key question: why? What key factors govern the basicity of amines? What are the important trends?
For instance, why is pyridine a weaker base than piperidine? Why are nitriles even weaker bases? Why do electron withdrawing groups tend to make amines weaker bases?
The good news is that if you already understand the factors that govern acidity, you simply have to apply the exact same principles – but in reverse!
We’ll cover that in the next post. Five Factors That Affect The Basicity of Amines
Footnote 1. There are many acids which are non-bases (such as NH4 which lacks a lone pair) and many bases which are non-acids, such as Cl(–), which is incapable of accepting a lone pair. Hence, saying “the stronger the acid, the weaker the base” is wrong.
Footnote 2. That’s the measurement obtained using water as solvent. You might see another value, 3.4, which is obtained when dimethylsulfoxide (DMSO) is used as a solvent. See Bordwell pKa Tables (DMSO)