A weak base is one that, when dissolved in water, only partially dissociates. As a result, the aqueous solution contains a relatively small amount of hydroxide ions and the corresponding base ions, while most of the base remains in its undissociated molecular form. Common examples of weak bases include ammonia (NH3), baking soda (sodium bicarbonate, NaHCO3), pyridine (C5 H5N), and methylamine (CH3NH2).
Non-ionized weak bases (B), exemplified by NH₃, react with water as follows:
$$ B+H_2O⇌OH^-+BH^+ $$
$$ K_b=\frac{\left[OH^-\right]\left[BH^+\right]}{\left[B\right]} $$
Using the symbol c to represent the initial molar concentration of (B), and x to represent the concentration of [OH–]. The latter quantity is also equal to [BH+], as both ions are formed in equimolar concentrations. The concentration of (B) remaining at equilibrium, [B], can be expressed as c − x. The reaction is:
$$ \underset{(c-x)}{B}+H_2O⇌\underset x{OH^-}+\underset x{BH^+} $$
and the equilibrium expression becomes:
$$ K_b=\frac{x^2}{c-x} $$
When c is large in comparison with x, the term c − x can be approximated by c without significant error, leading to the equation:
$$ K_b≅\frac{x^2}{c} $$
which can be rearranged as follows for the calculation of the hydroxyl ion concentration of weak bases:
$$ x^2=K_bc $$
$$ x=\left[OH^-\right]=\sqrt{K_bc} $$
In general, for an anionic base B−:
$$ B^-+H_2O⇌OH^-+BH $$
$$ K_b=\frac{\left[OH^-\right]\left[BH\right]}{\left[B^-\right]} $$
Salts of strong bases and weak acids
Salts of strong bases and weak acids, such as sodium acetate, dissociate completely in aqueous solution to yield ions:
$$ Na^+CH_3COO^-\overset{H_2O}{→}Na^++CH_3COO^- $$
The sodium ion cannot react with water because it would form NaOH, a strong electrolyte that would dissociate completely into its ions. The acetate anion, however, is a Brønsted-Lowry weak base, and:
$$ CH_3COO^-\overset{H_2O}⇌OH^-+CH_3COOH $$
$$ K_b=\frac{\left[OH^-\right]\left[CH_3COOH\right]}{\left[CH_3COO^-\right]} $$
Reference:
- Sinko, P. (2011). Martin’s Physical Pharmacy and Pharmaceutical Sciences. Baltimore, : Lippincott Williams & Wilkins, a Wolters Kluwer business.