Strengths of Acids and Bases

If an acid is an H⁺-donor, then the stronger an acid is, the more effectively it will be able to donate H⁺. If that acid is in aqueous solution, we can think of “strength” by the following equilibrium for the generic acid, HA(aq):

HA(aq) + H₂O(l) ↔ H₃O⁺(aq) + A^-(aq)

In equilibrium terms, the stronger an acid is, the more product-favored the equilibrium will be. Since this equilibrium expression can be applied to any acid, and acids are an important and diverse class of compounds, we define this equilibrium as an acid dissociation equilibrium and call its corresponding equilibrium constant the acid dissociation constant, or K_a.:

Similarly, we can think of the strength of a base using the equilibrium for the generic base, B(aq):

B(aq) + H₂O(l) ↔ OH^-(aq) + BH⁺(aq)

With its corresponding base dissociation constant, Kb:

Looking at the K_a equilibrium equation, the water that appears on the reactant side is accepting H⁺ to become H₃O⁺(aq). If water is accepting a proton, it is acting as a Bronsted-Lowry base. Considering the reverse reaction, H₃O⁺(aq) is a proton-donor so it is acting as an acid, while A^-(aq) is accepting a proton as B-L base. These acids and bases are not independent of each other, they are conjugate acid-base pairs. A^-(aq) is the conjugate base of HA(aq), and HA(aq) is the conjugate acid of A^-(aq); H₂O(aq) is the conjugate base of H₃O⁺(aq), and H₃O⁺(aq) is the conjugate acid of H₂O(aq). A conjugate acid-base pair are related by the addition or removal of a single H⁺. The same relationships can be described for the K_b equilibrium expression.

In the K_a equilibrium, water is acting as a base, while in the K_b equilibrium, water is acting as an acid. So what is water, an acid or a base? The answer is BOTH! The acid or base behavior of a substance is dependent upon its environment because acid and base are relative terms. In the case of water, if the water molecules are interacting with something that is more acidic than water, then water will act as a base. Likewise, if the water molecules are interacting with something that is more basic than water, the water will act as an acid. This brings up an interesting question: is water an acid or a base when it's not interacting with any other substance? Consider the following equilibrium:

H₂O(l) + H₂O(l) ↔ H₃O⁺(aq) + OH^-(aq)

Once again, water is acting as both an acid and a base. This process is called autoionization. Since water is such an important substance for life on Earth, this equilibrium also has a specific letter assigned to it, K_w, the autoionization constant for water:

Like almost all equilibria, K_w is dependent upon temperature. At 25°C, K_w = 10^-14. For pure water, this means that at 25°C, [H₃O⁺] = [OH^-] = 10^-7M. If this equilibrium constant only applied to pure water, it would be interesting but of limited use. Fortunately, it can be applied to any relatively dilute aqueous solution to understand the relative amounts of hydronium and hydroxide ions present in the solution. Consider an acid, HA(aq), and its conjugate base, A^-(aq), both interacting with water:

HA(aq) + H₂O(l) ↔ H₃O⁺(aq) + A^-(aq)

A^-(aq) + H₂O(l) ↔ OH^-(aq) + HA(aq)

If these equilibrium equations are added together, the result is the K_w equilibrium equation. When two (or more) sequential equilibria are added together, the equilibrium constant for the overall process is the product of the equilibrium constants for the individual steps. This means that for any conjugate acid – conjugate base pair, K_a x K_b = K_w. This also implies a general relationship, the stronger an acid is, the weaker its conjugate base, and vice versa.

This has been a lot of acid and base information wrapped up in a big discussion of equilibrium. K_a, K_b, and K_w all describe specific systems, but the most important thing to remember is that at their core, these are all equilibrium constants. They behave like every other equilibrium constant, they follow all the same rules as every other equilibrium constant, and they can be manipulated just like any other equilibrium constant. The only thing special about them is that they refer to a specific type of chemical equation.