## Ionization Constants of Acids and Bases

James Richard Fromm

Since it is known that hydronium ion will react with hydroxide ion to give water, the dissociation of water to hydronium ion and hydroxide ion must be reversible. Any reversible reaction is described by an equilibrium, and for the dissociation of water that equilibrium is:

2H2O H3O+ + OH-.

The position of any equilibrium is given by an equilibrium constant, K, which for the dissociation of water according to the acid-base reaction just described is:

K = a(H3O+)a(OH-)/a2(H2O)

In this equation, the chemical activities a can be approximated by the appropriate molar concentrations, indicated here by the use of square brackets in the form K = [H3O+][OH-]/[H2O]2 Since the concentration of water is approximately constant, it is normally included with the equilibrium constant of water (in other words, the chemical activity of water is taken as that of pure water, which is unity). In that case the equilibrium constant above is known as the ion product of water or the autoionization constant of water and indicated by the subscript w, so that by definition:

Kw = [H3O+][OH-]

The ionization constants of acids and bases other than water are dealt with in a similar way. The ionization of acetic acid in water is described by the equilibrium

CH3COOH(aq) + H2O H3O+(aq) + CH3COO-(aq),

for which the equilibrium constant is

K = a(H3O+)a(CH3COO-)/a(H2O)a(CH3COOH)

From this form of the constant, combining constants and activity coefficients, one obtains the normal or usual form of Ka, the molar ionization constant of an acid:

Ka = [H3O+][CH3COO-]/[CH3COOH]

In the normal form of the ionization constant of an aqueous acid, the concentrations of the hydrogen ion and the base appear in the numerator and the concentration of the acid itself appears in the denominator. The acid is not given the activity of unity because the acid is present as an aqueous solute rather than as the pure liquid acid.

Example. We write the equilibrium constant for the ionization of the aqueous acid HCN, hydrogen cyanide or hydrocyanic acid, as

HCN(aq) + H2O H3O+(aq) + CN-(aq), so

K = a(H3O+)a(CN-)/a(HCN)a(H2O).

If the molar concentrations are taken as good approximations to the activities, which in dilute solutions they are, and the activity of water is taken as unity, then

Ka = [H3O+][CN-]/[HCN]

The constant Ka is referred to as the ionization constant of an acid because the direction of the reaction to which it refers is that of ionization, the formation of the aqueous hydrogen ion or hydronium ion H3O+. Such constants are usually written with [H3O+] as the first term in the numerator so that they can be easily recognized. The constant written for the reverse reaction, that of neutralization, is not commonly used.

If acetic acid loses a proton to form acetate ion, and if this process is reversible, then the acetate ion meets the Bronsted definition of a base. The ionization of an aqueous base is described by the equilibrium

CH3COO-(aq) + H2O CH3COOH(aq) + OH-(aq), so

K = a(OH-)a(CH3COOH)/a(H2O)a(CH3COO-)

From this form of the constant, again combining constants and activity coefficients and taking the activity of water as unity, one obtains the normal form of Kb, the ionization constant of a base:

Kb = [OH-][CH3COOH]/[CH3COO-]

In the normal form of the ionization constant of a base, the concentration of the hydroxide ion and the acid appear in the numerator and the concentration of the base itself appears in the denominator.

Example. We write the equilibrium constant for the ionization of the aqueous base ammonia, NH3, as

NH3(aq) + H2O NH4+(aq) + OH-(aq), so

K = a(OH-)a(NH4+)/a(NH3)a(H2O)

. If the molar concentrations are taken as good approximations to the activities, which in dilute solutions they are, and the activity of water is taken as unity then

Kb = [OH-][NH4+]/[NH3]

The constant Kb is referred to as the ionization constant of a base because the direction of the reaction to which it refers is that of ionization. Such constants must include the molar concentration of hydroxide ion [OH-] and are usually written with [OH-] as the first term in the numerator so that they can be easily recognized.

Aqueous ionization constants of acids and bases are always written in this way regardless of the actual charge on the acid or base. The ionization direction in aqueous solution is the direction of forming hydrogen ions or hydroxide ions without regard to any other ions formed or removed in the reaction.