# What is pH?

 Vocabulary acid activity base buffer hydroxide IUPAC pH

### The Simple Definition

pH is a logarithmic measure of hydrogen ion concentration, originally defined by Danish biochemist Søren Peter Lauritz Sørensen in 1909 [1].

pH = -log[H+]

where log is a base-10 logarithm and [H+] is the concentration of hydrogen ions in moles per liter of solution. According to the Compact Oxford English Dictionary, the "p" stands for the German word for "power", potenz, so pH is an abbreviation for "power of hydrogen" [2].

The pH scale was defined because the enormous range of hydrogen ion concentrations found in aqueous solutions make using H+ molarity awkward. For example, in a typical acid-base titration, [H+] may vary from about 0.01 M to 0.0000000000001 M. It is easier to write "the pH varies from 2 to 13".

The hydrogen ion concentration in pure water around room temperature is about 1.0 × 10-7 M. A pH of 7 is considered "neutral", because the concentration of hydrogen ions is exactly equal to the concentration of hydroxide (OH-) ions produced by dissociation of the water. Increasing the concentration of hydrogen ions above 1.0 × 10-7 M produces a solution with a pH of less than 7, and the solution is considered "acidic". Decreasing the concentration below 1.0 × 10-7 M produces a solution with a pH above 7, and the solution is considered "alkaline" or "basic".

pH is often used to compare solution acidities. For example, a solution of pH 1 is said to be 10 times as acidic as a solution of pH 2, because the hydrogen ion concentration at pH 1 is ten times the hydrogen ion concentration at pH 2. This is correct as long as the solutions being compared both use the same solvent. You can't use pH to compare the acidities in different solvents because the neutral pH is different for each solvent. For example, the concentration of hydrogen ions in pure ethanol is about 1.58 × 10-10 M, so ethanol is neutral at pH 9.8. A solution with a pH of 8 would be considered acidic in ethanol, but basic in water!

### The Theoretical Definition

pH has been more accurately defined as

pH = -log aH+

where aH+ is the hydrogen ion activity. In solutions that contain other ions, activity and concentration are not the same. The activity is an effective concentration of hydrogen ions, rather than the true concentration; it accounts for the fact that other ions surrounding the hydrogen ions will shield them and affect their ability to participate in chemical reactions. These other ions effectively change the hydrogen ion concentration in any process that involves H+.

In practice, Sørenson's original definition can still be used, because the instrument used to make the measurement can be calibrated with solutions of known [H+], with the concentration of background ions carefully controlled.

### The Experimental Definition

IUPAC has endorsed a pH scale based on comparison with a standard buffer of known pH using electrochemical measurements. The IUPAC pH scale is very slightly different from the theoretical definition, since it considers factors that are not included in the (thermodynamic) theoretical pH.

### Notes

1. In Sørensen 's original paper, pH is written as PH. According to the Compact Oxford English Dictionary, the modern notation "pH" was first adopted in 1920 by W. M. Clark for typographical convenience.
2. "p functions" have also been adopted for other concentrations and concentration-related numbers. For example, "pCa = 5.0" means a concentration of calcium ions equal to 10-5 M, and pK_a = 4.0 means an acid dissociation constant equal to 10-4.

Author: Fred Senese senese@antoine.frostburg.edu

General Chemistry Online! What is pH?