## Monday, August 06, 2012

### What Does "pH" Mean?

The term "pH" is used to measure acidity. Strong acids, like hydrochloric acid or sulfuric acid, have very a very low pH while weaker acids, like acetic acid (vinegar), have pH readings that are higher. A "neutral pH" is 7.0, this is close to the pH value of the cytoplasm in living cells.

Higher pH values are "alkaline" rather that acidic. The highest pH value is usually shown as 14 and the lowest pH value is shown as 0.

Acidity is a function of the concentration of hydrogen ions (H+), or protons. The strength of alkaline solutions is measured by the concentration of hydroxide ions (OH-).

There's a reciprocal relationship between the concentrations of these two ions because we're dealing with aqueous solutions (water). Water molecules dissociate into H+ and OH- ions so in pure water there will always be equal concentrations of both ions.

The extent of this dissociation determines the concentration of these ions in pure water. We express the extent of dissociation using a term called the equilibrium constant (Keq) that is defined as the concentration of the products of a reaction over the concentration of the reactant(s).

For the dissociation of water, the actual equation is ...

where H3O+ is a hydronium ion. It's a bit awkward to refer to hydronium ions all the time so it's easier to simply the reaction as ...
Nothing is lost by this simplification except in a few rare cases where it's important to remember that the real positively charge ion is the hydronium ion and not the hydrogen ion.

The equilibrium constant is ...
where the square brackets ([]) simply mean "concentration."

The equilibrium constant has been carefully measured under standard conditions of pressure (1 atm) and temperature (25°C). It's value is 1.8 × 10-16, which means that water doesn't dissociate very much and there are very few hydrogen and hydroxide ions. You can calculate the concentration of these ions knowing that the concentration of pure water is 55.5M.1

Substituting in the equation for the equilibrium constant you get ....
This defines the ion product for water (Kw).
Since the concentrations of H+ and OH- are equal in pure water, this means that the concentration of H+ is ...
This is a very low concentration. At these concentrations the water (and any solution) is said to be "neutral" since the negative and positive charges cancel each other.

Although the concentrations are low, they can have a profound effect on biological processes and biochemical reactions. It's convenient to use a log scale to describe such low numbers; thus, log(10-7) = -7. Using negative numbers isn't convenient so you can convert it to a positive number by taking the reciprocal value; log(1/10-7) = 7.

pH is defined as the negative log of the hydrogen ion concentration.

At neutrality, the pH = 7. It's just a coincidence that the ion product of water turns out to be 1.0 × 10-14. It could have been some other value in which case the pH scale could have ranged from 1 to 16.8 or 12.3 and neutral pH could have been some number other than 7.0.

Since the product of total concentrations of H+ and OH- always has to be equal to 10-14M this means that the concentrations can be easily determined from the pH.

That explains what pH means but there's still the nagging issues of what that little "p" means. This has been a somewhat contentious issue over the past century but today we think we know the answer thanks to some historical detective work.

Here's what I wrote in my book ...
The term pH was first used in 1909 by Søren Peter Lauritz Sørensen, director of the Carlsberg Laboratories in Denmark. Sørensen never mentioned what the little “p” stood for (the “H” is obviously hydrogen). Many years later, some of the scientists who write chemistry textbooks began to associate the little “p” with the words power or potential. This association, as it turns out, is based on a rather tenuous connection in some of Sørensen’s early papers. A recent investigation of the historical records by Jens G. Nøby suggests that the little “p” was an arbitrary choice based on Sørensen’s use of p and q to stand for unknown variables in much the same way that we might use x and y today.

No matter what the historical origin, it’s important to remember that the symbol pH now stands for the negative logarithm of the hydrogen ion concentration.

1. The density of water is 1 gm per millilitre. In one litre there will be 1000 grams of water. The molecular weight of water is 18.01 so the concentration is 1000 ÷ 18.01 = 55.5 M. The density of water depends on the temperature so you have to make a little adjustment at 25°C but it doesn't make much of a difference.

[Image Credits: Moran, L.A., Horton, H.R., Scrimgeour, K.G., and Perry, M.D. (2012) Principles of Biochemistry 5th ed., Pearson Education Inc. (various pages) [Pearson: Principles of Biochemistry 5/E] © 2012 Pearson Education Inc.] Anonymous said...

Larry, a typo. Lowest pH is generally given as 0, as in the graphical scale.

Larry Moran said...

Thanks. Michael M said...

The density of water depends on the temperature so you have to make a little adjustment at 25°C but it doesn't make much of a difference.

Unless, of course, you're doing analytical/quantitative (bio)chemistry. ;) Argon said...

Pedantic point: I don't think it's exactly true that pH = -log[H+], or to put it another way, pH <> p[H]. As a first approximation yes, but pH is more precisely determined by the chemical activity or the 'effective' concentration of H+ in a solution.

Side note: I don't know what the 'p' of 'pH' means either but we often extend it to symbols like 'pIC50' = -log10[I] where 'I' is the molar concentration of an inhibitor that produces 50% inhibition in an assay.

Larry Moran said...

True, but even then it depends on just how accurate you want to be. At 25°C the density of water is 0.997044 grams per milliliter so the concentration of water at 25°C is 55.4M instead of 55.5M. Raul A. Félix de Sousa said...

Actually, the pH scale extends beyond these limits, even for aqueous solutions. A 10 M NaOH solution, for example, has a pH of 15.0, and the pH of a 10 M HCl solution is -1.0. Michael M said...

Actually, no. pH, as Larry prsented it, is only valid for dilute solutions where the activity coefficients of the ions are near unity and the activity is approximately equal to the concentration. Raul A. Félix de Sousa said...

Of course, extreme values of pH cannot occur in dilute solutions, and that is the reason most people are unfamiliar to them. However, the activity coefficients of strong acids and strong bases are near unity in concentrated solutions as well, and the pH of these solutions is very close to the values that can be inferred by the concentration of the solutes.
As a supplement to Larry's discussion of the topic, readers are refered to this short and interesting (and open access) article:

K. F. Lim, Negative pH does exist, J. Chem. Educ. 83 (2006) 1465.

( http://pubs.acs.org/doi/pdf/10.1021/ed083p1465 ) Raul A. Félix de Sousa said...

You will have to make much more significant adjustments to accomodate the fact that kw also varies with temperature.
see: http://en.wikipedia.org/wiki/Dissociation_constant Michael M said...

Yes you can, in theory have negative pH, but, at the concentratrations that you described (>10M), the relationship between the acidity of the solution (which pH is supposed to measure) and the pH is no longer log-linear due to existence of other protonated species in solution.

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