# pH and Activity Corrections

pH Value

pH (Potential Hydrogen) is defined as the negative decimal logarithm of the hydrogen ion activity:

 (1) pH = – log {H+}

Curly brackets {..} symbolize the activity, whereas rectangular brackets [..] are reserved for concentrations. Inserting the relationship, {H+} = γ ∙ [H+], one gets

 (2) pH = – log γ – log [H+]

Formulas for the activation coefficient (log γ) are presented here. In diluted solutions we have γ = 1, and Eq.(2) simplifies to (because log 1 = 0):

 (3) pH = – log [H+] (only for diluted solutions)

Example

What is the pH of a 0.1 molar HCl solution without and with activity corrections?

HCl is a strong acid. The hydrogen ion concentration is then given by [H+] = 0.1 M. Inserting it into Eq.(3) yields an approximate pH value of

 (4) pH = – log 0.1 = 1.0 (without activity correction)

Now with activity correction. For this purpose we adopt the extended Debye-Hückel equation

 (5) $$log \, \gamma_{i} = -\dfrac{Az^{2}_{i}\sqrt{I}}{1+Ba\sqrt{I}}$$

with A = 0.5085 M-1/2, B = 3.281 M-1/2 nm-1 and the effective ion-size parameter a = 0.9 nm. With z = 1 and the ionic strength I = 0.1 M we obtain log γ = – 0.083. Inserting this result into Eq.(2) gives us the exact pH value:

 (6) pH   = – log γ – log [H+]   =   0.083 + 1.0   =   1.083

The pH of the 0.1 molar HCl solution is 1.083 (rather than 1.0 as often assumed). This exact pH value is also predicted by aqion – see the initial pH in the titration example.