The concentration of hydrogen or hydroxyl ions in solutions of acids or bases may be expressed as gram-ions per liter or as moles per liter. A solution containing 17.008 g of hydroxyl ions or 1.008 g of hydrogen ions per liter is said to contain 1 gram-ion or 1 mole of hydroxyl or hydrogen ions per liter. Owing to the ionization of water, it is possible to establish a quantitative relationship between the hydrogen and hydroxyl ion concentrations of any aqueous solution.
The concentration of either the hydrogen or hydroxyl ion in acidic, neutral, or basic solutions is usually expressed in terms of the hydrogen ion concentration, or more conveniently, in pH units.
In a manner corresponding to the dissociation of weak acids and bases, water ionizes slightly to yield hydrogen and hydroxyl ions. As previously observed, a weak electrolyte requires the presence of water or some other polar solvent for ionization. Accordingly, one molecule of water can be thought of as a weak electrolytic solute that reacts with another molecule of water as the solvent. This autoprotolytic reaction is represented as:
$$ H_2O+H_2O⇌H_3O^-+OH^- $$
The law of mass action is then applied to give the equilibrium expression:
$$ k=\frac{\left[H_3O^+\right]\left[OH^-\right]}{\left[H_2O\right]^2} $$
The term for molecular water in the denominator is squared because the reactant is raised to a power equal to the number of molecules appearing in the equation, as required by the law of mass action. Because molecular water exists in great excess relative to the concentrations of hydrogen and hydroxyl ions, [H2O]2 is considered a constant and is combined with k to give a new constant, Kw, known as the dissociation constant, the autoprotolysis constant, or the ion product of water:
$$ K_w=k×\left[H_2O\right]^2 $$
The value of the ion product is approximately 1×10-14 at 25°C; it depends strongly on temperature. In any calculations involving the ion product, one must be certain to use the proper value of Kw for the temperature at which the data are obtained.
Substituting the two equations gives the common expression for the ionization of water:
$$ \left[H_2O\right]×\left[OH^-\right]=K_w≅10^{-14} $$
In pure water, the hydrogen and hydroxyl ion concentrations are equal, and each has the value of approximately 1×10-7 moles per liter at 25°C.
$$ \left[H_2O\right]=\left[OH^-\right]≅\sqrt{10^{-14}}≅10^{-7} $$
When an acid is added to pure water, some hydroxyl ions, provided by the ionization of water, must always remain. The increase in hydrogen ions is offset by a decrease in hydroxyl ions so that Kw remains constant at approximately 1×10-14 at 25°C.
Reference:
- Sinko, P. (2011). Martin’s Physical Pharmacy and Pharmaceutical Sciences. Baltimore, : Lippincott Williams & Wilkins, a Wolters Kluwer business.