Weak Acids

A weak acid is one that does not dissociate completely in solution; this means that a weak acid does not donate all of its hydrogen ions (H⁺) in a solution. Weak acids have very small values for K_a (and therefore higher values for pK_a) compared to strong acids, which have very large K_a values (and slightly negative pK_a values).

The majority of acids are weak. On average, only about 1 percent of a weak acid solution dissociates in water in a 0.1 mol/L solution. Therefore, the concentration of H⁺ ions in a weak acid solution is always less than the concentration of the undissociated species, HA. Examples of weak acids include acetic acid (CH₃COOH), which is found in vinegar, and oxalic acid (H₂C₂O₄), which is found in some vegetables.

Vinegars

All vinegars contain acetic acid, a common weak acid.

Dissociation

Weak acids ionize in a water solution only to a very moderate extent. The generalized dissociation reaction is given by:

$HA(aq) \rightleftharpoons H^+ (aq) + A^- (aq)$

where HA is the undissociated species and A^- is the conjugate base of the acid. The strength of a weak acid is represented as either an equilibrium constant or a percent dissociation. The equilibrium concentrations of reactants and products are related by the acid dissociation constant expression, K_a:

$K_a = \frac{[H^+][A^-]}{[HA]}$

The greater the value of K_a, the more favored the H⁺ formation, which makes the solution more acidic; therefore, a high K_a value indicates a lower pH for a solution. The K_a of weak acids varies between 1.8×10⁻¹⁶ and 55.5. Acids with a K_a less than 1.8×10⁻¹⁶ are weaker acids than water.

If acids are polyprotic, each proton will have a unique K_a. For example, H₂CO₃ has two K_a values because it has two acidic protons. The first K_a refers to the first dissociation step:

$H_2CO_3 + H_2O \rightarrow HCO_3^{-} + H_3O^+$

This K_a value is 4.46×10⁻⁷ (pK_a1 = 6.351). The second K_a is 4.69×10⁻¹¹ (pK_a2 = 10.329) and refers to the second dissociation step:

$HCO_3^- + H_2O \rightarrow CO_3^{2- } + H_3O^+$

Calculating the pH of a Weak Acid Solution

The K_a of acetic acid is $1.8\times 10^{-5}$. What is the pH of a solution of 1 M acetic acid?

In this case, you can find the pH by solving for concentration of H⁺ (x) using the acid's concentration (F) and K_a. Assume that the concentration of H⁺ in this simple case is equal to the concentration of A^-, since the two dissociate in a 1:1 mole ratio:

$K_a = \frac{[H^+][C_2H_3O_2^-]}{[HA]} = \frac{x^2}{(F-x)}$

This quadratic equation can be manipulated and solved. A common assumption is that x is small; we can justify assuming this for calculations involving weak acids and bases, because we know that these compounds only dissociate to a very small extent. Therefore, our above equation simplifies to:

$K_a=1.8\times 10^{-5}=\frac{x^2}{F-x}\approx \frac{x^2}{F}=\frac{x^2}{\text{1 M}}$

$1.8\times 10^{-5}=x^2$

$x=3.9 \times 10^{-3}\text{ M}$

$pH=-log[H^+]=-log(3.9\times 10^{-3})=2.4$

Although it is only a weak acid, a concentrated enough solution of acetic acid can still be quite acidic.