Weak acids & bases

Strong acids ionize quantitatively, so we use a normal, one-directional arrow. Weak acids do not, so we have to use an equilibrium arrow. Acetic acid is an example of a weak acid:

CH₃COOH_(aq) ⇌ H⁺_(aq) + CH₃COO⁻_(aq).

Since the equilibrium position is not the same for all weak acids, we have to care about the equilibrium constant, which in this case we call the acid ionization constant. For the general reaction HA_(aq) ⇌ H⁺_(aq) + A⁻_(aq), the acid ionization constant is

$K_{\text{a}}=\frac{[{\text{H}}^{+}][{\text{A}}^{-}]}{[\text{HA}]}\text{.}$

Similarly, weak bases have B_(aq) + H₂O_(l) ⇌ HB⁺_(aq) + OH⁻_(aq) as their general reaction. The base ionization constant is

$K_{\text{b}}=\frac{[{\text{HB}}^{+}][{\text{OH}}^{-}]}{[\text{B}]}\text{.}$

Another way of representing the position of the equilibrium for weak acids is percent ionization:

$p=\frac{[{\text{H}}^{+}]}{[\text{HA}]}\times 100\%⟺[{\text{H}}^{+}]=[\text{HA}]\left(\frac{p}{100\%}\right)\text{.}$

The following equation is true for all conjugate acid–base pairs:

$K_{\text{a}}{K}_{\text{b}}=K_{\text{w}}\text{.}$

Example

Given a solution of 0.082 mol/L phosphoric acid (a weak acid) whose pH is 1.68 upon reaching equilibrium, find the hydrogen ion concentration, the percent ionization, and the value of the acid ionization constant.

Finding the hydrogen ion concentration is easy enough:

$[{\text{H}}^{+}]={10}^{-\text{pH}}\text{mol/L}={10}^{-1.68}\text{mol/L}=0.021\text{mol/L}\text{.}$

We can use this to find the percent ionization:

$p=\frac{[{\text{H}}^{+}]}{[\text{HA}]}\times 100\%=\frac{0.02089\text{mol/L}}{0.082\text{mol/L}}\times 100\%=26\%\text{.}$

Our dissociation reaction is H₃PO_4(aq) ⇌ H₂PO₄⁻_(aq) + H⁺_(aq). We need to use an ICE table to find the equilibrium concentrations.

Now we can calculate the acid ionization constant:

$K_{\text{a}}=\frac{[{\text{H}}^{+}][{\text{A}}^{-}]}{[\text{HA}]}=\frac{(0.02089\text{mol/L})(0.02089\text{mol/L})}{0.06111\text{mol/L}}\text{,}$

which evaluates to 7.1 × 10⁻³.