A bit of a while ago, friend of the blog, Simon Donner who studies Pacific Island corals posted a tweet
Projected CO2-driven decrease in ocean pH - increase in 'acidity' - under a low (RCP2.6) and high (RCP8.5) emissions scenario. Source: IPCC — Simon Donner (@simondonner) October 20, 2016
and indeed, on the next day when talking with an organiker colleague, Eli mentioned this and in response heard some, not all in his class thought that the difference in acidity which is the [H+] ion concentration between two acid solutions was the difference between their pHs.@simondonner pH is a log scale, a linear scale would make more sense. Had long discussion w. class about logs,log tables & slide rules & pH— eli rabett (@EthonRaptor) October 20, 2016
Since pH = -log [H+], this common mistake can have consequences whether one is thinking about organic reactions or ocean biochemistry.
Looking at the chart above, the difference in [H+] ion concentration between pH = 8.2 and pH = 7.7 is
pH= 8.2 [H+] = 10-8.2 = 6.3 x 10-9
pH= 7.7 [H+] = 10-7.7 = 2.0 x 10-8
That's a factor of more than 3 greater
Anyhoo, this set off a train of thought bringing Eli back to yesteryear, actually bask to before his yesteryear and even Mom Rabett's yesteryear. Why do we use pH rather than just the [H+] concentration. The Rabett expects that Russell will chime in on this, but what the heck
It goes back to how acidity is measured, specifically the insturment(s) used to measure pH and to more than a little extent to the log tables of yesterday. Allow Eli to explain
pH is mostly measured through the electrical potential developed across a thin glass window at the bottom of an electrode. A potential difference is developed between the H+ ions in the solution and the ions on the inside. The voltage difference between this electrode and a standard electrode is in the mV range over pH scale and is proportional to the pH, that is the logarithm of the H+ ion concentration.
Fritz Haber and Zygmunt Klemensiewicz were the first to develop a usable pH electrode in 1909, but usable was a stretch because they depended on a a galvanoscope to read out the voltage difference and required patience, luck and skill. The big step forward was made by Arnold Beckman who hooked up a vacuum tube amplifier to read out the voltage difference and got rich. He also gave it away to good causes, something that must be mentioned
While vacuum tube amplifiers were pretty good at amplifying, and the scale of the meter could read out the now larger voltage difference, they really could not take antilogs to turn the pH into an [H+] ion concentration. Besides which pH meters are not very precise, even with care, luck and skill, so there really was no advantage to abandoning pH.
On the other side of this, calculators were at best adding machines, and while there were beasts that could multiply (on the old IBM comptometers you set up the multiplication, walked away and had a cup of coffee before coming back for your result), most did multiplications by hand or converted numbers into logs using log tables, at which point multiplication becomes addition of logs and division subtraction of logs much easier things to do. Some had nice K&E slide rules, slide rules are essentially log tables on a stick. A nice stick sometimes, but a stick none the less and if you were lucky two significant figures with a third sometimes possible by squinting.
So there really was no reason to abandon pH for numerical [H+] ion concentrations.
Till today, driven by two things. First, even refrigerators have implanted digital computers and lcd screens so converting pH to concentrations and displaying them is no longer an issue. Second, new kinds of [H+] probes are hitting the market which are both precise and accurate