pKa Values Span 60 Orders Of Magnitude

Putting Acidity In Perspective

One concept that always seems to have a hard time getting through is that of pK_a. No matter how many times I nag students to “know their pK_a‘s” or tell them that the “pK_a table is your friend” or compare it to a table of hand strengths in poker, I know that in some cases the message is just not getting across.

This drives me bonkers.  pK_a values are important!

pK_a Values Span 60 Orders Of Magnitude

What’s so great about the pK_a table?

Here’s my perspective: What other document can tell you at a glance about the universe of chemical reactivity, neatly arranged on a logarithmic scale?

Isn’t it incredible to be able to quickly determine that hydroiodic acid (pK_a = –10) is about twenty six orders of magnitude more acidic than water (pK_a =14), and that water is likewise another twenty six orders of magnitude more acidic than hydrogen gas (pK_a = 42).*

The absolute scale of chemical reactivity differences is, to me, mind-blowing.

The trouble is, you really need to understand and appreciate log scales on an intuitive level to “get it”, and log tables are not visceral. Dealing with a difference of sixty orders of magnitude is a very difficult thing for the mind to do.

So with the help of the site below (for numbers) I present an augmented pK_a table, with a cue on one side to allow for visualization of the scales involved. Maybe this could help students grasp the relative strengths of acids and bases – and appreciate the mind-blowing differences in chemical reactivity that they possess.

A few fun comparisons:

• Comparing the acidity of a carboxylic acid and an alcohol is like comparing the size of the solar system (Kuiper belt) to that of a human being.
• Comparing thiols to alcohols: like the depth of the Mariana Trench to the height of your average person.
• Acidity of a protonated amine to a neutral amine: like the size of the earth compared to the size of an atomic nucleus.
• Comparing HCl to water is like comparing the size of a galactic supercluster to the size of a house!

[Note – since HI is the most acidic, I decided to make it correspond to the largest number even though HI technically has the lowest pKa. It would not be completely unreasonable to do it the other way, although there is not much detail between the neutrino [10^-25] and the Planck length [10^-35].

*Asterisk is, the solvent it’s measured in affects the pKa (due to the levelling effect) but this is still no less mind blowing.

• Relevant cartoon:

[Source: xkcd  hat tip to Mike Evans @mevans86 for finding this]

• Physicists also grapple with this problem:

Space is big. You just won’t believe how vastly, hugely, mind- bogglingly big it is. I mean, you may think it’s a long way down the road to the chemist’s, but that’s just peanuts to space. – Douglas Adams, the Hitchhiker’s Guide to the Galaxy

* chemist = pharmacist (in Britain)

• The classic 1977 film Powers of Ten wonderfully captured this scale issue. Starting with a shot of a couple eating a picnic in a lakeside Chicago park, the camera zoomed out (and out… and out) by successive increments of 10 to a full 10²⁴ meters, essentially the size of the known universe. The camera then zoomed back in to the couple, and then by powers of ten to the inner world, to cells, organelles, DNA, and eventually to the nucleus of the atom. Breathtaking.
• More recently, this interactive infographic by Primax Studio allows the user to scroll through the absolute limits of inner and outer space.  The scale begins at the Planck length (10^-35m) and ends at the scale of the known universe (10²⁷ m); a total of more than sixty orders of magnitude. The viewer encounters (clickable) atomic nuclei, DNA, dinosaurs, the Apollo space module, planets, stars, and galaxies (and much more)  along the way.

Chemical phenomena happen on a pretty small scale, so it’s hard for us chemists to find images that will compete with planets, galaxies, or blue whales we can use to state our case. So why not just piggyback on what’s been done before?

Notes