Weak acids play a prominent role in organic chemistry. Hydrogen cations (H⁺¹), “protons”, are frequently found in an initial or final step of a sequence of fundamental steps in the process of an organic reaction. Biochemistry also relies heavily on a knowledge of weak acids: catalysis, metabolism, and structural proteins.

 

 

Overview of Strong Acids and Weak Acids

 

 

The best way to understand weak acids is to compare them to strong acids. A strong acid is characterized by the fact it ionizes completely (or nearly so) when dissolved in water.

 

 

 

This means when HCl gas is bubbled through water, the molecule dissociates to form [H⁺¹] and [Cl^-1]:

 

\Large{ \bf{ HCl\longrightarrow H^{+1} + Cl^{-1}\hspace{5em}(1)} }

 

 

As an alternative sometimes you find it written in an equivalent form:

 

\Large{ \bf{ HCl + H_2O\longrightarrow H_3O^{+1} + Cl^{-1}\hspace{5em}(2)} }

 

Notice that when a strong acid dissociates in water one arrow to the right shows this dissociation, for all intents and purposes, goes to completion.

 

In contrast, when a weak acid undergoes dissociation, the molecular species that has not dissociated coexists with the dissociated acid and less reactive base in an equilibrium. As a simple example is HF:

 

\Large{ \bf{ HF + H_2O \rightleftharpoons H_3O^{+1} + F^{-1}\hspace{5em}(3)} }

 

But what does this mean? The actual meaning is expressed in terms of equilibrium constant. 

 

 

The equilibrium constant is a ratio of products to reactant. Think about it in terms of a see-saw where the pivot point of the see-saw, (Figure 1).

 

The reactant is depicted as a red circle while the product is shown as a blue circle. The relative concentrations of reactants and products correspond to the size of the circle. The center of the board has a dashed line to show the relative position of the fulcrum.

 

The weak acid, HF (hydrofluoric acid), has a large amount of reactant and very little product. The equilibrium fulcrum lies closer to the reactants than the products. The acid dissociation constant reflects that fact because it is much smaller than one, 6.8 x 10^-4.

 

 

The center entry shows a hypothetical situation where the concentration of reactants and products are equal at equilibrium. The circles are the same size to reflect the fact the concentrations are equal. That means their relative ratio is 1. The fulcrum resides at the center and coincides with the actual center of the lever.

 

The far-right entry of Figure 1 shows the situation when there is a strong acid like HCl (hydrochloric acid), shows the opposite situation encountered in the case of a weak acid. In this case, the concentration of the products is much greater than the reactants.

A more in-depth  explanation of each term follows below.

 

Strong Acids

 

In the case of a strong acid, it undergoes total dissociation of an anion and proton. They establish an equilibrium mixture of reactants and products, (Eq. 2).

 

HA → H⁺¹ and A^-1                                  (2)

 

Weak Acids

 

 

In contrast, weak acids do not dissociate completely. This leaves a mixture of reactants and products to coexist within the same solution. How much of the molecular species dissociates into anion and cation?

 

 

Acid Dissociation Constant, K_a

 

 

Equilibrium concentrations of each molecular species can be expressed by way of the equilibrium constant K_eq. The dissociation of a weak acid HA when added to water produces H₃O⁺¹ and a weak conjugate base A^-1, (Eq. 3).

 

 

\LARGE{HA + H_2O \longrightarrow H_3O^{+1} + A^{-1}}                         (3)

 

 

Formation of the equilibrium expression results in a standard relationship between the concentration of the products and reactants, (Eq. 4).

 

 

\LARGE{\color{black}{K_{eq}= \frac{[H_3O^{+1}][A^-]}{[HA][H_2O]}}} (4)

 

 

This general expression for equilibrium concentrations can be simplified for the specific application to acid-base reactions. The relative concentration of H₂0 to all the other species remains essentially constant before and after the reaction.

 

 

 

The ratio between the concentration of a dissociated species compared to its undissociated parent molecule is given by the K_a of the mixture at equilibrium. The acid dissociation constant for a weak acid is given by Equation 5.

 

 

\LARGE{\color{black}{K_a= \frac{[H^+][A^-]}{[HA]}}}                            (5)

 

 

Here HA represents the molecular undissociated acid, while H⁺¹ is the concentration of hydrogen ions and A^-1 is the conjugate base in its ionic form. The acid dissociation constant is the fraction of dissociated species over the undissociated species, K_a.

 

 

 

Large and Small, K_a

 

 

A large value of K_a indicates there are many more ions than molecular species. Conversely, a very small K_a shows a relatively small proportion of molecular species that dissociate in solution.

 

 

Comparison of Strong and Weak Acid

 

 

A graphic way to see this is to compare the pH of a 1.00 M solution of a strong acid like HCl to the pH of a weak acid like 1.00 M acetic acid (HC₂H₃O₂).