When the number of molecules, atoms, or ions of a particular type (here we consider H⁺ ions) is in the hundreds of millions, we can confidently speak of concentrations and analyze an average behavior. However, when the number is very small, random fluctuations in the actual number present become important.

As a rule of thumb we need a different type of description (stochastic equations!) when describing 10 or fewer atoms, molecules, or ions. Consider two compartments of comparable size but very different function inside eukaryotic cells: mitochondria and lysosomes (#9 and #12 in the schematic at right). These have very different pH from the rest of the cell. Mitochondria have a pH of ~8. This means that there are about 10^-8 moles/liter of H⁺ ions. Lysosomes on the other hand have a pH of ~5.

Figure source: Wikimedia Commons