Basicity of Amines And pKaH

Quantifying The Basicity Of Amines, Using “The pK_a Of The Conjugate Acid”, a.k.a. “pK_aH”

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 pK_a‘s. Shouldn’t we be able to do the same with bases?

Yes, in a way. Here’s three key points for today:

• The best way to quantify the basicity of an amine is to examine the pK_a of its conjugate acid.
• The higher the pK_a of the conjugate acid, the stronger the base. 
• An unofficial but useful shorthand for “the pK_a of the conjugate acid” is the term, pK_aH

Table of Contents

1. Quick Review: Acids, Bases, Conjugate Acids, and Conjugate Bases
2. Using pKa To Measure Acidity
3. Using pKa To Quantify The Basicity Of Amines
4. The “pKa Of The Conjugate Acid” Can Be Abbreviated As “pKaH”
5. Using pKaH To Determine The Relative Basicities Of Amines
6. Some Words Of Caution On pKa Values For Amines
7. What Key Factors Govern The Basicity Of Amines?
8. Notes

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 pK_a 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, K_a, is a measure of how easily a species dissociates to give H+ and the conjugate base.

For convenience, we use the negative log of K_a, called pK_a, which is similar to the familiar pH scale but can extend beyond 14 because it’s not strictly limited to aqueous solvent. pK_a 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 cncepts to measure basicity? Couldn’t we switch things around and define a term, K_b, which is the equilibrium for how readily a species combines with H+ , define pK_b as its negative log, and compare bases by looking at their pK_b values?

Yes…. we could. I guess. If we had to. But generally, organic chemists’ opinion on this subject is “Screw pK_b“.

After all, pK_a values have been measured for thousands of organic molecules. Does anyone really want to have to remember a huge set of pK_b values too? Hell no!

Instead, we can easily use pK_a values as an indirect measurement of basicity. Here’s how.

3. Using pK_a 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 pK_a 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 pK_a for the conjugate acid of piperidine. It’s about 11 .

From these pK_a values,  we can tell that the conjugate acid of pyridine is stronger than the conjugate acid of piperidine by about 6 pK_a units. Since each pK_a 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 pK_a Of The Conjugate Acid” Can Be Abbreviated as “pK_aH”

The term, “pK_a 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 pK_a of the conjugate acid of a base” as its pK_aH.

This lets us say that the pK_aH of pyridine is 5.2, and the pK_aH 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 pK_aH 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 pK_aH with pK_a. The pK_aH of ammonia is 9.2, which measures the acidity of its conjugate acid, NH₄(+).

The pK_a 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 pK_aH of the amide ion NH₂(–), which you may have encountered before as the strong base (NaNH₂)  used to deprotonate terminal alkynes (pK_a =25). Using pK_aH, we can determine that NH₂(–) is about (38 – 9) = 29 orders of magnitude more basic than NH₃ !

5. Using pK_aH to Determine The Relative Basicities Of Amines

Using pK_aH to determine the relative strengths of bases is a pretty useful trick.

Here are some representative examples of nitrogen-containing molecules. Below is the pK_a of their conjugate acids.

What’s the strongest base here? What’s the weakest?

The lowest pK_aH value here is –10 for the nitrile (bottom left). This means the nitrile is the least basic of all of these molecules.

The highest pK_aH 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 pK_a Values For Amines

Two things to watch out for, especially when reading other online sources on this topic.

First,  sometimes the pK_aH values for amines are reported as pK_a values , without explanation. The best pK_a 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 pK_a value for an amine, it’s likely referring to the pK_aH , the pK_a of the conjugate acid.

For instance, you might see a pK_a table where the pK_a of methylamine (CH₃NH₂) is listed as 10.63.

That’s low. Hopefully by this point, such a value of 10 for a pK_a of an amine should strike you as weird, especially since the pK_a of the closely related NH₃ is 38.

The value of 10.63 actually refers to the pK_a of the conjugate acid of methyl amine, NOT methylamine itself. It’s a pK_aH value.

Similarly, the same table lists trimethylamine as having a pK_a of 9.8 . Again, this is actually its pK_aH.  I can’t find an actual pK_a 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 pK_aH of an amine is reported as its pK_b, such as in this table which reports the pK_b of NH₃ as 9.2 .   This is inaccurate.

[The pK_b of NH₃ can be calculated from the formula pK_aH + pK_b = 14 . The pK_b of NH₃ is 4.8  (aqueous solution). ]

Again, pK_b 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 pK_a 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

Notes

Note 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.

Note 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 pK_a Tables (DMSO)