Acidity

In chemistry the unit $\textit{pH}$, also referred to as $\textit{acidity}$ or $\textit{basicity}$, is the negative logarithm (base 10) of the concentration of free protons (or hydronium ions). The definition of $pH$ in terms of hydrogen ions in solution is: $$\text{pH}=-\log_{10}(a_{H^+})\equiv-\log_{10}\left(\left[H^+\right]\right)$$ Where $a_{H^+}$ is the equilibrium molar concentration of $H^+$ in the solution, the activity of the hydrogen ion in the solution. $$$$ This definition is appropriate for concentrations equal to, or less than $1\ mol/l$, where $aH+ \equiv [H+]$, that is, $1\ mol/L\ HCl$ has a $pH$ of zero. $$$$ To relate this to standard molality ($b^\circ$), typically taken as $1 \ mol/kg$, consideration is given to the activity ($a_{H^+}$) of the hydrogen ions. $$$$ The activity can be expressed as: $$a_{H^+} = \gamma_{H^+} \times m_{H^+}$$ Where, $\gamma_{H^+}$ is the activity coefficient, which adjusts the molality to account for non-ideal behavior due to interactions between ions in the solution. $m_{H^+}$ is the molality of hydrogen ions in the solution relative to the standard molality, expressed in $mol/kg$. $$$$ The expansion of $pH$ then becomes: $$\text{pH} = -log_{10}\left(m_{H+}\times\gamma_{H^+}\right)$$ $$$$ This definition is relevant in more concentrated solutions or when precise thermodynamic calculations are required. It reflects how the properties of the solution deviate from ideal behavior and provides a more accurate understanding of the $pH$ under various conditions. $$$$ While $pH$ is a universally recognized scale for expressing hydrogen ion activity, its appropriateness and accuracy can diminish under conditions of extremely high ionic strength, non-aqueous environments, high temperatures, or very high or low $pH$ values. In such cases, alternative measurement strategies might be required to obtain meaningful and accurate descriptions of acidity or basicity.