For more than 300 years, substances that behaved like vinegar have been classified as acids, while those that have properties like the ash from a wood fire have been called alkalies or bases. The name "acid" comes from the Latin acidus, which means "sour," and refers to the sharp odor and sour taste of many acids. Vinegar tastes sour because it is a dilute solution of acetic acid in water; lemon juice is sour because it contains citric acid; milk turns sour when it spoils because of the formation of lactic acid; and the sour odor of rotten meat can be attributed to carboxylic acids such as butyric acid formed when fat spoils.

Today, when chemists use the words "acid" or "base" they refer to a model developed independently by Brønsted, Lowry, and Bjerrum. Since the most explicit statement of this theory was contained in the writings of Brønsted, it is most commonly known as the "Brønsted acid-base" theory.

Brønsted argued that all acid-base reactions involve the transfer of an H⁺ ion, or proton. Water reacts with itself, for example, by transferring an H⁺ ion from one molecule to another to form an H₃O⁺ ion and an OH^- ion.

According to this theory, an acid is a "proton donor" and a base is a "proton acceptor."

Acids are often divided into categories such as "strong" and "weak." One measure of the strength of an acid is the acid-dissociation equilibrium constant, K_a, for that acid.

When K_a is relatively large, we have a strong acid.

When it is small, we have a weak acid.

When it is very small, we have a very weak acid.

In 1909, S. P. L. Sørenson suggested that the enormous range of concentrations of the H₃O⁺ and OH^- ions in aqueous solutions could be compressed into a more manageable set of data by taking advantage of logarithmic mathematics and calculating the pH or pOH of the solution.

The "p" in pH and pOH is an operator that indicates that the negative of the logarithm should be calculated for any quantity to which it is attached. Thus, pK_a is the negative of the logarithm of the acid-dissociation equilibrium constant.

The only disadvantage of using pK_a as a measure of the relative strengths of acids is the fact that large numbers now describe weak acids, and small (negative) numbers describe strong acids.

An important features of the Brønsted theory is the relationship it creates between acids and bases. Every Brønsted acid has a conjugate base, and vice versa.

Just as the magnitude of K_a is a measure of the strength of an acid, the value of K_b reflects the strength of its conjugate base. Consider what happens when we multiply the K_a expression for a generic acid (HA) by the K_b expression for its conjugate base (A^-).

If we now replace each term in this equation by the appropriate equilibrium constant, we get the following equation.

Because the product of K_a times K_b is a relatively small number, either the acid or its conjugate base can be "strong." But if one is strong, the other must be weak. Thus, a strong acid must have a weak conjugate base.

A strong base, on the other hand, must have a weak conjugate acid.

Water has a limiting effect on the strength of acids and bases. All strong acids behave the same in water -- 1 M solutions of the strong acids all behave as 1 M solutions of the H₃O⁺ ion -- and very weak acids cannot act as acids in water. Acid-base reactions don't have to occur in water, however. When other solvents are used, the full range of acid-base strength shown in the following table can be observed.

The strongest acids are in the upper-left corner of this table; the strongest bases in the bottom-right corner. Each base is strong enough to deprotonate the acid in any line above it. The hydride ion (H^-), for example, can convert an alcohol into its conjugate base

and the amide (NH₂^-) ion can deprotonate an alkyne.