That's the definition of p[H]. The definition of the "real" pH is the -log of H+ activity. H+ activity is the concentration of H+ * a coefficient. In practice,

That's the definition of p[H]. The definition of the "real" pH is the -log of H+ activity. H+ activity is the concentration of H+ * a coefficient. In practice, the coefficient is considered to be 1, however there are cases (such as extreme concentrations) when that approximation isn't valid.