## Weak Acids

#### Learning Objective

• Solve acid-base equilibrium problems for weak acids.

#### Key Points

• The dissociation of weak acids, which are the most popular type of acid, can be calculated mathematically and applied in experimental work.
• If the concentration and Ka of a weak acid are known, the pH of the entire solution can be calculated. The exact method of calculation varies according to what assumptions and simplifications can be made.
• Weak acids and weak bases are essential for preparing buffer solutions, which have important experimental uses.

#### Terms

• weak acidone that dissociates incompletely, donating only some of its hydrogen ions into solution
• conjugate basethe species created after donating a proton.
• conjugate acidthe species created when a base accepts a proton

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 Ka (and therefore higher values for pKa) compared to strong acids, which have very large Ka values (and slightly negative pKa 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.

## 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, Ka:

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

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

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

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

This Ka value is 4.46×10−7 (pKa1 = 6.351). The second Ka is 4.69×10−11 (pKa2 = 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 Ka 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 Ka. 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.