User:Milton Beychok/Sandbox

Formal definition

The concentration, in moles per litre of solution) of hydrogen (H⁺, ions in an aqueous solution can be written simply as [H⁺] or as hydronium [H₃O⁺] and both describe the same entity.

For very dilute solutions, the pH value can be defined by this simple expression:

(1)      ${\rm {pH}}=-\log _{10}\left[{\rm {H^{+}}}\right]=\log _{10}{\frac {1}{\left[{\rm {H^{+}}}\right]}}$

and the corresponding expression for the hydroxide (OH^-) ions can be expressed as:

(2)      ${\rm {POH}}=-\log _{10}\left[{\rm {OH^{-}}}\right]=\log _{10}{\frac {1}{\left[{\rm {OH^{-}}}\right]}}$

Since the product of the concentration of hydrogen ions and the concentration of hydroxide ions is a constant, namely:

(3)       $\left[{\rm {H^{+}}}\right]\left[{\rm {OH^{-}}}\right]=1\times 10^{-14}$

taking logarithms gives:

(4)       $\left({\rm {pH}}+{\rm {pOH}}\right)=14$

As the theory behind chemical reactions became more sophisticated, the definition of pH was reexamined. Specifically, as the role of electrical charge in chemical reactions became better understood, the definition of pH was changed to refer to the active hydrogen ion concentration. The more theoretical definition of pH, while not generally covered in many introductory chemistry textbooks,is the definition adopted by the International Union of Pure and Applied Chemistry (IUPAC):

(5)       ${\rm {pH}}=-\log _{10}\,(a_{\rm {H^{+}}}$)

pH = -log aH+Only in dilute solutions (about 0.001 mols per litre) are all anion and cations so far apart that they free to be at their maximum activity.

i.e. [H+] =

aH+. At higher acid/alkaline concentrations, the physical spacing between cations and anions decreases, so that they begin to obstruct each other, and shield each other’s charge. Therefore, the mobility of the any particular ion is impaired by interactions with other ions and their associated electrical fields. These local electric field interactions affect the extent to which the ions can participate in chemical reactions, and give an apparent concentration that is always smaller than the real concentration. In this case, the ion activity is “slowed down”; specifically, [H+] > aH+. This discrepancy between ion activity and concentration increases with the acid concentration. Therefore, for acid concentrations greater than ~ 1mM it is generally advisable to use activities instead of concentrations in order to accurately predict pH and thus the reaction dynamics.