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Negative pH

Dateline: 05/01/00

By Alan Bruzel

The concentration of hydrogen ions in an aqueous solution is conveniently represented as pH, the negative log of the hydrogen ion concentration:

pH = -log [H⁺]

However, pH is actually the negative log of the activity coefficient of hydrogen ions. Most of the time, this distinction causes no difficulty because activity coefficients and concentrations serve equally well when describing dilute aqueous solutions of acids.

Problems arise when one needs to represent acidities of either concentrated acids or of acids in non-aqueous environments. For example, although a 10^-2 N solution of sulfuric acid in water is pH 2 (assuming complete ionization), is it valid to consider the pH of 100% sulfuric acid (a 36 N solution which is not completely ionized) to be the negative log of 36; that is, pH -1.6?

Negative pH values can occur, but come as a surprise to those accustomed to working within the confines of the 0 to 14 pH scale used to measure dilute aqueous acids and alkalis. From a practical standpoint, the commonly used glass electrode, which is satisfactory for measuring hydrogen ion concentrations in the 0 to 14 pH range, gives non-linear responses when confronted with solutions of pH less than zero. Those investigators measuring a pH of -3.6 in acidic mine waters from Iron Mountain, California needed to carefully calibrate their glass electrodes down to pH -4.

Consequently, defining values for extreme acidity in non-aqueous systems, as in the above example of 100% sulfuric acid, requires a supplementary measurement scale. The Hammett acidity function, H_o, expresses the relative strengths of acids by monitoring the color changes of indicators such as mono-, di-, and trinitroanilines. Using this approach, HF has been assigned an H_o of -11, H₂SO₄ an H_o of -12, HSO₃F an H_o of -15, and the superacid HSO₃F + SbF₅ an H_o of -19.

What the Web Has to Say about:
Negative pH

Acids and Bases
Behavior of acids in aqueous and non-aqueous environments. From Joseph MacNeil, Chatham College.

Acidity Function
Using the Hammett acidity function to measure acidity outside of the normal pH range. From Eva Jiraskova, Palacký University at Olomouc, Czech Republic.

Introduction to pH
Theory of pH, how pH electrodes work, and their maintenance and calibration. From Edwin Bohr/Electronics.

Is a Negative pH Possible?
Factors affecting true measurement of hydrogen ion concentration. From Fred Senese, General Chemistry Online.

Negative pH and Extremely Acidic Mine Waters from Iron Mountain, California
Naturally occurring water with a negative pH. Article by Darrell Kirk Nordstrom et al. from Environmental Science & Technology.

Nobel Prize in Chemistry 1994
To George A. Olah for his work on stable carbocations (positively charged hydrocarbons) generated by superacids.

Solvents, Solutions, Acids and Bases
Definitions of pH terminology with a treatment of important strong acids and superacids. From Peter Bird, Concordia University.

Superacids
Examples of these substances and some applications. From Kenneth A. Goldsby, Florida State University.

Trifluoromethanesulfonic Acid and Derivatives
Properties and reactions of this strong acid (H_o = -13). Reprint of an article by R.D. Howells and J.D. McCown appearing in Chemical Reviews.

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