How to Use a pKa Table

A Key Skill – How To Use A pK_a 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 pK_a values to tell if an acid base reaction is favorable or unfavorable.

• pK_a is the negative logarithm of the acid dissociation constant, K_a, which can be measured experimentally.
• pK_a values have been measured for a large number of molecules and are largely related to the most acidic functional group present in the molecule. A pK_a table is a useful complication of pK_a values.
• A low value of pK_a (e.g. -10) indicates a strong acid. A high value of pK_a (e.g. 50) indicates a weak acid.
• Acid base reactions have four components: an acid and a base exchange a bond to H to give a conjugate acid and a conjugate base.
• Acid-base reactions can always be written as equilibria; that is,  occurring in a forward or a reverse direction. The favored direction for an acid-base reaction is when a stronger acid and a stronger base give a weaker acid and a weaker base.
• One can tell which direction is favored by comparing the pK_a of the acid and the conjugate acid. Formation of the weaker acid (i.e. molecule with the higher pK_a) will be favored.
• These concepts can also be applied to other reactions you will learn about later on in the course (e.g. substitution reactions)

Table of Contents

1. 1. The Acidity Constant K_a and Its Negative Logarithm pK_a
   2. The Four Components of an Acid Base Reaction
   3. The Principle of Acid-Base Mediocrity
   4. Using pK_a values and the Principle of Acid-Base Mediocrity To Predict Acid-Base Reactions
   5. How to Use pK_a Values to Determine Basicity 
   6. How to Use a pK_a Table To Determine If An Acid-Base Reaction Is Favorable
   7. How To Determine The Acidity of Compounds That Aren’t On A pK_a Chart
   8. Applying pK_a In Substitution Reactions
   9. Summary
   10. Notes
   11. Quiz Yourself!
   12. (Advanced) References and Further Reading

1. The Acidity Constant Ka and Its Negative Logarithm pKa

Let’s review some key principles of acidity constants to make sure we’re all on the same page.

The acidity constant, K_a, is a measurement of the equilibrium between an acid, H-A and its dissociation to give H+ and its conjugate base, A(-). (This value has to be measured experimentally).

1. 1. • A strong acid has complete or nearly complete dissociation, so a large K_a.
      • A weak acid has incomplete dissociation, and a small K_a.

Not shown in the equation for K_a is the solvent, which is generally assumed to be water for our purposes. There are limits to using water as a solvent for K_a measurements at extreme acidities and basicities. [Note 1]

Can you tell which acid is stronger based on its K_a?

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In order to get a better grasp on these numbers, we often take the negative logarithm of the acidity constant and call this pK_a.

pK_a = – log K_a

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1. 1. • The higher the pK_a, the weaker the acid.
      • The lower the pK_a, the stronger the acid.

One of the strongest acids, H-I has a pK_a of -10.

Water has a pK_a of 14. [Note 2]

Alkanes have a pK_a of about 50.

[Note 3]

2. The Four Components Of An Acid-Base Reaction

In an acid-base reaction, a bond is formed at H and a bond is broken at H.

Every acid-base reaction has four components.

1. 1. • The acid (where the bond to H breaks),
      • the base (where the bond to H forms),
      • the conjugate acid (the species that results when the base forms the new bond to H)
      • and the conjugate base (the species that results when the acid breaks its bond to H).

This is drawn in the forward direction (left to right) but the reverse reaction (right to left) is also an acid-base reaction. We just flip around the identities.

To see the reverse acid-base reaction, hover here or click this link.

Note that by drawing something up as an acid-base reaction does not imply that it actually happens at a reasonable rate.

That can only be determined through experiment.

We’re just saying that the pattern of an acid-base reaction is followed (i.e. form and break a bond at the same H).

3. The Principle of Acid-Base Mediocrity

In what direction do you think acid-base reactions are favored?

Do they spontaneously go from stronger acids to weaker acids, or do they go from weaker acids to stronger acids?

What correlates more with your experience: does adding salt (NaCl) to water result in harmless salt water, or result in the exothermic formation of HCl gas and caustic NaOH?

Acid base reactions spontaneously proceed in a direction that gives weaker acids from stronger acids

I like to call this The Principle of Acid-Base Mediocrity. [Note 4]

How do we know which acid is stronger and which is weaker? By identifying the acid and the conjugate acid, and comparing their two pK_a values!

Acid base reactions will favor formation of the acid with the higher pK_a value. It’s not completely unlike how areas of high pressure will flow to areas of low pressure.

4. Using pKa values and the Principle of Acid-Base Mediocrity To Predict Acid-Base Reactions

With these two mental tools – the higher the pK_a, the weaker the acid, and the Principle Of Acid Base Mediocrity, we are all set to use pK_a values to predict the directions of acid-base reactions.

The acid-base reaction that results in a compound with a lower pK_a going to a higher pK_a will be favored.

The compound with the lower pK_a will be the stronger acid and the compound with the higher pK_a will be the weaker acid.

Ready for some quizzes?

Let’s start with an acid base reaction involving a terminal alkyne (pK_a 25) and acetic acid (pK_a 4)

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Now let’s look at water (pK_a 14) and acetic acid (pK_a 4)

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Note that each unit of difference in pK_a indicates an order of magnitude difference in acidity.

We can get a rough idea of the position of the equilibrium by measuring the difference in pK_a values.

So the acid-base reaction in the quiz above favors water (pK_a 14) by about 10 orders of magnitude (10¹⁰) over acetic acid (pK_a 4). That means there are roughly 10 billion molecules of water for every molecule of acetic acid.

This quiz asks you to calculate the ratio of each acid present at equilibrium.

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A good rule of thumb is that a difference in pK_a of more than 10 pK_a units will represent an irreversible acid-base reaction for the purposes of carrying out a chemical reaction. [Note 5]

So acetate ion (the conjugate base of acetic acid, pK_a 4) is perfectly capable of deprotonating water (pK_a 14) but the equilibrium will be very unfavorable (a difference of 10 pK_a units).

It’s unreasonable to expect that acetate ion will be able to deprotonate a ketone like acetone (pK_a 17) to any significant extent.

5. pKa Values Are Also A Guide To Basicity

pK_a values are also a useful guide to basicity, but maybe not in the way that you’d normally think.

There’s one common misconception that needs to get cleared up.

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It’s true that the higher the pK_a, the weaker the acid.

Does that mean that the higher the pK_a, the stronger the base?

No! 

In order for a species to act as a base, it has to have a lone pair of electrons that could reasonably remove a proton. That’s not the case for alkanes (pK_a = 50), alkenes (pK_a = 42), or ammonium salts (pK_a = 10) and many others.

Instead, it’s true that the higher the pK_a, the stronger the conjugate base.

You can use pK_a values to predict the strength of the base that will result when a proton (H+) is removed.

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Here is another quick quiz:

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6. How To Use a pKa table

The ultimate guide to acidity is a pK_a table, which represents a collection of actual measurements of the acidity of various molecules.

A typical pK_a table covers the acidity of species ranging from hydroiodic acid H-I (pK_a = -9) to alkanes (pK_a = 50)  representing about 60 orders of magnitude in reactivity. [Note 6]

Using a pK_a table, you can apply the Principle of Acid-Base Mediocrity and examine any random acid base reaction, once you have identified the main functional group.

It’s very powerful.

For example, will CH₃CH₂S(-), the conjugate base of ethanethiol  deprotonate hydrogen gas (H₂) to give H(-) ?

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To figure this out, we draw out the four components of our acid base reaction. We then look on our pK_a table for the pK_a of a thiol and H₂ . The pK_a of the thiol is about 10 and the pK_a of H₂ is about 35.

Since going from CH₃CH₂S(-) to H(-) would result in a significantly stronger acid (and stronger base), we can say this reaction is unfavorable.

With a little bit of thought, you will soon reach the conclusion that a pK_a table is not unlike the ranking of hands in poker.

It is particularly useful for ranking the strengths of bases.

For example, just like a royal flush beats all other hands in poker, a deprotonated alkane like CH₃(-) will have a favorable acid-base equilibrium for the deprotonation of  anything below it in the pK_a table.

Since pretty much everything is less acidic than an alkane, this means that the conjugate base of an alkane can remove a proton from a huge variety of functional groups. [Note 7]

7. How To Determine The Acidity Of Compounds That Aren’t on the pK_a chart

One of the keys to using a pK_a table is to start by identifying the key functional group(s) present and be familiar with their acidities.

Two of the molecules below might look a little scary because they are so huge and complex, but their acidity will mostly be determined by the functional group, not all the alkyl carbons.

The pK_a of cholic acid isn’t so different from acetic acid. The pK_a of cocaine’s conjugate acid isn’t so different from ammonium. So start by focusing on the most acidic functional group.

What about the key trends that influence acidity? Aren’t they important?

Yes, of course. But when we’re changing two or more variables at once (e.g. when we’re comparing the acidities of two different functional groups), it’s difficult to judge which variable is more important without an experimental measurement.

That’s why pK_a measurements are so useful.

If we’re examining the same functional group, then applying trends to determine the relative acidities is helpful.

In this case, apply the trend that the more electronegative electron-withdrawing groups help to stabilize the negative charge in the conjugate base. The weaker the conjugate base, the stronger the acid.

8. Not Just For Acid Base Reactions

A good working knowledge of pK_a isn’t just useful for acid-base reactions.

It can also be useful for predicting whether certain reactions will be favorable, even if you don’t know the mechanism.

For example,  substitution reactions involve formation and breakage of bonds at a carbon atom.

Here is an example.

Just based on relative basicities, in which direction would you predict this reaction to be favorable? Don’t worry about anything else for now. 

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We would not expect this reaction to be favorable, because it results in a much stronger base.

But the reverse reaction, where it does form a weaker base, works perfectly fine.

Here is another examnple of a substitution reaction, known as nucleophilic acyl substitution. Don’t worry about the name or the mechanism for now.

Just based on relative pK_a values, in which direction would you predict this reaction to be favorable?

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All else being equal, we should expect that the reaction will favor the formation of the weaker base.

9. Summary

If you have a pK_a table, you essentially have a ranking of the stabilities of different molecules. (The stronger the base, the more unstable it is).

You can start to make predictions about which direction reactions will be favorable (or unfavorable).

When you hear instructors say things like, “don’t memorize, learn the concepts! “, this is one of those concepts that is extremely powerful when you understand it and apply it.

Notes

Note 1. The limit to using water as solvent for pK_a measurements is the levelling effect. That is, no base can exist that is stronger than HO(-), and no acid can exist that is stronger than H₃O(+). For this reason, pKa values for weaker acids than H₂O are often measured in DMSO.

Note 2. The pK_a of pure water is 14. The relative acidity of water relative to alcohols can change in other solvents. For example, in 2-propanol, methanol is 3 times more acidic than water.  See Ref 1.

Note 3. How are pK_a values measured? See reference six.

Note 4. Related to the Principle of Acid-Base Mediocrity is the Principle of Pressure Mediocrity (high pressure flows to low pressure, to give a mediocre pressure) and the Principle of Concentration Mediocrity (high concentration diffuses to areas of low concentration to give a mediocre concentration).

Note 5. One example of this rule of thumb in practice is the Claisen Condensation, where alkoxide bases (pK_a of alcohols = 15-16) are capable of deprotonating esters (pK_a = 25).

Note 6. 60 orders of magnitude is a lot. It is roughly the difference between the smallest possible length (the Planck length, about 10^-35 m) and the size of the known universe (4.4 × 10²⁶ m).

Note 7. Assuming no side reactions interfere, which is generally a good assumption since, for the most part, acid-base reactions are fast, relative to other reactions.

Quiz Yourself

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(Advanced) References and Further Reading

A collection of pKa values is presented on the Organic Chemistry Data site (formerly Hans Reich’s site)

1. What Is The pKa of Water? from Libretexts is a very accessible article on this topic.
2. pKa Values in the Undergraduate Curriculum: What Is the Real pKa of Water?
   Todd P. Silverstein and Stephen T. Heller
   Journal of Chemical Education 2017 94 (6), 690-695
   DOI: 10.1021/acs.jchemed.6b00623
3. Confusing Quantitative Descriptions of Brønsted-Lowry Acid-Base Equilibria in Chemistry Textbooks – A Critical Review and Clarifications for Chemical Educators
   Meister, E.C., Willeke, M., Angst, W., Togni, A. and Walde, P.
   Helvetica Chimica Acta, 2014 97: 1-31.
   DOI: 10.1002/hlca.201300321
   Full discussion of why the pK_a of water (in water as solvent) should be 14.0 and the pKa of H3O(+) should be 0.
4. Acid Ionization Constants of Alcohols. II. Acidities of Some Substituted Methanols and Related Compounds
   P. Ballinger and F. A. Long
   Journal of the American Chemical Society 1960 82 (4), 795-798
   DOI: 10.1021/ja01489a008
   This is the paper giving the pK_a of water as 15.7 whose methods are criticized in the above articles. Read it for yourself.
5. The Relative Acidity of Water, Methanol and Other Weak Acids in Isopropyl Alcohol Solution
   Jack Hine and Mildred Hine
   Journal of the American Chemical Society 1952 74 (21), 5266-5271
   DOI: 10.1021/ja01141a009
6. Equilibrium acidities in dimethyl sulfoxide solution
   Frederick G. Bordwell
   Accounts of Chemical Research 1988 21 (12), 456-463
   DOI: 10.1021/ar00156a004
   A very accessible account on the measurement of pKa values.

[Sigificantly updated Oct 2022]