Box 11-2 What Does a Negative pH Mean

In the 1930s, Louis Hammett and his students measured the strengths of very weak acids and bases, using a weak reference base (B). such as p-nitroaniline (p/C, = 0.99), whose base strength could be measured in aqueous solution. 

The acidity of a solvent that protonates the weak base, B, is defined as the Hammett acidity function  

For dilute aqueous solutions, H0 approaches pH. For concentrated acids, Hu is a measure of the acid strength. The weaker a base, B, the stronger the acidity of the solvent must be to protonate the base. Acidity of strongly acidic solvents is now measured more conveniently by electrochemical methods.12 

Suppose that some p-nitroaniline and a second base, C, are dissolved in a strong acid, such as 2 M HC1. The pK.d of CHH can be measured relative to that of BH by first writing a Henderson-Hasselbalch equation for each acid  

Setting the two equations equal (because there is only one pH) gives 

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