Recap of Fundamental Acid-Base Concepts

An acid is a chemical species that can donate a proton (H⁺), and a base is a species that can accept (gain) a proton, according to the common Br ø nstead-Lowry definition. (A subset of the Br ø nstead-Lowry definition for aqueous solutions is the Arrhenius definition, which defines an acid as a proton producer and a base as a hydroxide (OH^-) producer.) Hence, the conjugate base of an acid is the species formed after the acid loses a proton; the base can then gain another proton to return to the acid. In solution, these two species (the acid and its conjugate base) exist in equilibrium.

Recall from this and earlier experiments in Chem 151 and 152 the definition of pH:

where [H⁺] is the molar concentration of protons in aqueous solution. When an acid is placed in water, free protons are generated according to the general reaction shown in Equation 3. Note: HA and A^- are generic symbols for an acid and its deprotonated form, the conjugate base.

Equation 3 is useful because it clearly shows that HA is a Br ø nstead-Lowry acid (giving up a proton to become A^-) and water acts as a base (accepting the proton released by HA). However, the nomenclature H₃O⁺ is somewhat misleading, because the proton is actually solvated by many water molecules. Hence, the equilibrium is often written as Equation 4, where H₂O is the base:

The Law of Mass Action and Equilibrium Constants

Using the Law of Mass Action, which says that for a balanced chemical equation of the type

in which A, B, C, and D are chemical species and a, b, c, and d are their stoichiometric coefficients, a constant quantity, known as the equilibrium constant (K), can be found from the expression:

where the brackets indicate the concentrations of species A, B, C, and D at equilibrium.

Equilibrium Constant for an Acid-Base Reaction

Using the Law of Mass Action, we can also define an equilibrium constant for the acid dissociation equilibrium reaction in Equation 4. This equilibrium constant, known as K_a, is defined by Equation 7:

Equilibrium Constant for the Dissociation of Water

One of the simplest applications of the Law of Mass Action is the dissociation of water into H⁺ and OH^- (Equation 8).

The equilibrium constant for this dissociation reaction, known as K_w, is given by

(H₂O is not included in the equilibrium-constant expression because it is a pure liquid.) Hence, we can see that increasing the OH^- concentration of an aqueous solution has the effect of decreasing the H⁺ concentration, because the product of these two concentrations must remain constant at a given temperature. Thus, in water, the equilibrium in Equation 8 underlies the equivalency of the Brønstead- Lowry definition of a base (an H⁺ acceptor) and the Arrhenius definition of a base (an OH^- producer).