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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.
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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.
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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.
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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 \(mol/kg\).
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The expansion of \(pH\) then becomes:
\[\text{pH} = -log_{10}\left(m_{H+}\times\gamma_{H^+}\right)\]
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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.
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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. |