Acid Dissociation Constant

Did you know that most food items like apples and lemons contain naturally occurring acids? Have you ever wondered what makes an acid 'strong' or 'weak'? You will learn that, here.

Acid dissociation constant definition

We know that an acid dissociates into an H⁺ ion and the corresponding anion. We also know that the reaction of acid and water is an ionisation reaction. These reactions are reversible and reach an equilibrium state where the rates of forward and backward reactions are the same. The equilibrium constant calculated for an acid solution at equilibrium is called the acid dissociation constant.

You must remember how to find the equilibrium constant of a chemical reaction. The dissociation constant is nothing else but the equilibrium constant of the ionisation reaction of any acid in a solution. For any acid HA, the equilibrium reaction for the solution of HA would be:

$\mathrm{HA}\rightleftharpoons {\mathrm{H}}^{+}+{\mathrm{A}}^{-}$

Here, H⁺ is a Hydron, or Hydrogen ion, which gives any acid its acidic nature. The anion formed (A^-) after HA releases H⁺. This is called the conjugate base of the acid HA. As you might remember, a solution is said to be in a state of equilibrium when the rate of the forward reaction is equal to the rate of the backward reaction. The acid dissociation constant is calculated at equilibrium. It is denoted by K_a.

$K_{eq}=K_a=\frac{\left[H^{+}\right]\left[A^{-}\right]}{\left[HA\right]}$

Usually, the value of K_a is very large, so a logarithm of K_a is taken. This is called pK_a.

pH of a solution

You might have come across the term pH while studying Chemistry. pH is a measure of the acidic strength of a solution. For the sake of understanding, it can be considered as a scaled quantity of concentration of H⁺ ions in a solution.

$pH=-{\log }_{10}\left(\left[H^{+}\right]\right)$ $=-{\log }_{10}\left[{\mathrm{H}}^{+}\right]$

The pH of a solution can range from 0 to 14. Solutions with pH less than 7 are acidic, while those with a pH above 7 are basic. The characteristic sour taste of lemons is due to the presence of citric acid, giving it a pH of ≈ 2. The black coffee you have in the morning has a pH of ≈ 5. Saliva has a pH of ≈ 6.6. On the basic side, the baking soda you have in the kitchen has a pH of 9.5. Liquid drain cleaners have a pH of ≈ 14 (very strong, which is why we use them with care; they can hurt skin).

Acid dissociation constant of HCl

A common example of a strong acid is hydrochloric acid (HCl). For HCl, the ionisation reaction would be written like this:

$\mathrm{HCl}+{\mathrm{H}}_2\mathrm{O}\rightleftharpoons {\mathrm{H}}_3{\mathrm{O}}^{+}+{\mathrm{Cl}}^{-}$

The equilibrium constant for the above reaction would be calculated as:

$K_a=\frac{\left[H_3{O}^{+}\right]\left[C{l}^{-}\right]}{\left[HCl\right]\left[H_{2}O\right]}$

The H⁺ ions are transferred to H₂O and form hydronium ions (H₃O⁺). This is because free H⁺ ions do not exist in an aqueous solution. For simplicity, we can replace [H₃O⁺] with [H⁺]. Also, [H₂O] is equal to 1 as the concentration of water is 1. Hence, the equation for K_a becomes:

$K_a=\frac{\left[H^{+}\right]\left[C{l}^{-}\right]}{\left[HCl\right]}$

HCl is a strong acid. This means that it dissociates completely into H⁺ and Cl^- ions in solution. For example, if 1 mol of HCl is added to 1 L of water, it will give out 1 mol of H⁺ ions and 1 mol of Cl^- ions.

This can be represented with the help of an ICE table (Initial, Change, Equilibrium), where we can write the concentrations of the reactants and the products of the reaction at the initial stage (Initial), the change in their concentration from initial stage till equilibrium (Change), and their final concentrations at equilibrium (Equilibrium).

In the ICE table for the ionisation reaction of HCl, we have written the concentrations of the reactants and the products at the initial stage, and the final stage. We can now substitute these values in the formula for K_a for HCl.

$K_a=\frac{1·1}{(verysmallnumber)}$

There is a very small number in the denominator, as there is always a very small amount of undissociated acid at equilibrium. Therefore, the value of K_a for strong acids is very large. K_a for HCl is very high, at 1.3 x 10⁶.

In this subsection, we learnt that strong acids are so-called because they dissociate completely into H⁺ ions and the corresponding conjugate bases.

But what about acids that cannot dissociate completely in a solution? Those acids are called weak acids.

Determination of the dissociation constant of a weak acid

Let us consider an acid HB. The ionisation reaction equation will be written as:

$HB\rightleftharpoons H^{\mathit{+}}+B^{\mathit{-}}$

Consider HB as a weak acid. Weak acids do not dissociate completely, i.e. if 1 mol of HB is added to water, at equilibrium the solution will have less than 1 mol of H⁺ and B^-, and will also contain a certain concentration of undissociated HB at equilibrium (unlike the case of strong acid, which only contained H⁺ and the conjugate base at equilibrium). Due to incomplete dissociation/ionisation of the weak acid, the solution is not as acidic as it would be if an equal quantity of a strong acid was added to the solution.

Let us take the example of acetic acid (CH₃COOH), a weak acid. Consider adding 1 mol of acetic acid to 1 L of water. The concentration of acetic acid would be 1 mol/L or 1M. The equation of the reaction can be written as: