Fundamentals of Acids and Bases

For more than two-hundred years, chemists have struggled to come up with a way to describe acid-base reactions that is at the same time physically relevant, specific enough to be accurate, and general enough to include everything that should be considered an acid-base relationship.

Svante Arrhenius first defined acids to be proton (H⁺) donors and bases to be hydroxide ion (OH^-) donors in aqueous solution. The Arrhenius model of acids and bases is summarized by the following two reactions:

At the time that Arrhenius proposed these definitions, water was virtually the only solvent used in chemistry, and nearly all known acids and bases contained protons (H⁺) and hydroxyl groups (OH), respectively. His definition was sufficient for the chemistry that was understood then. But progress in chemistry necessitated new definitions: it was discovered that ammonia behaves like a base, and HCl donates protons in non-aqueous solvents. The Bronsted-Lowry model of acids and bases serves that need by describing acids as proton donors and bases as proton acceptors. These definitions remove the role of solvent and allow bases like ammonia and fluoride ion to be classified as bases, so long as they bond to protons. The Bronsted-Lowry model implies that there is a relationship between acids and bases (acids transfer protons to bases) and allows us to define conjugate acids and conjugate bases, as seen in .

You should note in the figure above that the conjugate acid of the base, BH⁺, acts as an acid in the reverse reaction by donating a proton to the conjugate base, A^-, of the acid HA.

Despite the usefulness of the Bronsted-Lowry definition, there is an even more general definition of acids and bases provided by G. N. Lewis. The Lewis model of acids and bases proposes that an acid is an electron pair acceptor while a base is an electron pair donor. This model of acidity and basicity broadens the characterization of acid-base reactions to include reactions like the following which do not involve any hydrogen transfers. The nitrogen atom in ammonia donates an electron pair to complete the valence octet of boron.

Because we are more interested now in describing terms and processes that involve proton transfers (pH, titration), we will focus on the Bronsted-Lowry definitions of acids and bases. We will leave consideration of the Lewis model of acids and bases for studying reactions in organic chemistry.

As you may have noted already in the acid-base reactions above, we use arrows in both reaction directions to indicate that these are equilibrium processes. Proportions of reagents and products at equilibrium can be described by an equilibrium constant. The equilibrium constant given in is for the reaction of an acid, HA, with water as shown.

Although water is a reactant in the above reaction and belongs in the equilibrium constant, its value of 55.6 M in aqueous solution is so large in comparison with the change in water concentration at equilibrium that we will assume that the value of [H₂O] is constant. Using that assumption, we will define the acid dissociation constant, K_a, in to be the following:

From the form of the above equation we can see that stronger acids, those that dissociate to a greater extent, will have larger values of K_a whereas weaker acids will have smaller values of K_a. A practical range for K_a values runs from 10^-12 for very weak acids to 10¹³ for the strongest acids. Knowing this practical range of acidity constants will aid in judging how reasonable your answers are when you calculate values for K_a in problems.

In an analogous way, we define K_b, the base constant in to be the following:

Stronger bases have larger values of K_b while weaker bases have smaller values of K_b. K_b's of typical bases in inorganic chemistry tend to have a range of values between 10^-11 and 10³.

As you may have discovered in our above discussion, water can act as both an acid and as a base. For this reason water is said to be amphiprotic. Water is often incorrectly termed amphoteric. An amphiprotic species like water can either donate or accept a proton. Amphoteric species can both donate and accept hydroxide ions, as water cannot. The following reaction in , called the autoionization of water, has the equilibrium constant K_w defined in the manner of K_a and K_b. The dissociation constant K_w for water is 1 x 10^-14 at room temperature (298 K), and tends to rise with higher temperatures.

Knowing that K_w = 1 x 10^-14 is useful because the relationship between K_a and K_b for a conjugate acid-base pair is K_a * K_b = K_w. Therefore, you can calculate the K_a of the conjugate acid of a base when given its K_b. This point is proved in below.

From the proven expression, we see that strong acids (large K_a's) form weak conjugate bases and weak acids form strong conjugate bases. In the following section, we will discuss acid and base strength in more depth.