The Arrhenius dissociation model

The Arrhenius theory defines acids and bases as isolated species in solution giving rise respectively to hydrogen ions H⁺ and hydroxyl ions OH^-. Interaction with solvents is ignored. The theory cannot begin to explain acidic and alkaline properties in non-aqueous solvents. Despite its shortcomings the theory is widely used to calculate equilibrium data for weak electrolytes, including acids and bases, in water.

For a generalized binary weak electrolyte MX (e.g., HCl) at concentration C, a fraction a ionizes. There will be an equilibrium mixture of (1-a)C of MX and aC of both M⁺ and X^-. The equilibrium for the dissociation process

MX = M⁺ + X^-

is given by

K = ( [M⁺] [X^-] ) / [MX] = a²C / (1-a)

If a <<1for a very weak electrolyte, K ~ a²C. This is called the Ostwald Dilution Law.

The Bronsted-Lowry concept of acids and bases

Acids are defined as proton donors and bases as proton acceptors regardless of whether the species are are ionic or neutral. In general

acid = base + proton

Specific examples are

H₂SO₄ = HSO₄^- + H⁺

HSO₄^- = SO₄^2- + H⁺

H₃O⁺ = H₂O + H⁺

OH^- = O^2- + H⁺

The species on the right, along with the proton is known as the conjugate base. Conjugate acids are defined in a similar way. In aqueous solution the concept includes solvent interaction.

Dissociation constants of acids

Given the general form of a weak acid as HA we can write the dissociation reaction as

The equilibrium constant is written

or

K_a is K[H₂O]. K_a is used since the concentration of water is very large in a dilute solution.

Self-ionization of water

In pure water a small amount of the water molecules are ionized.

Since the proton does not exist as a free particle in water it is more accurate to represent the proton as attached to a water molecule.

The equilibrium constant for this reaction is

As the concentration of water is usually so large (55.5M for pure water) and rather constant in dilute solutions it is usual to absorb the water term into the constant K and write

K_W has the value of 10^-14 at 25° C.

Dissociation constants of bases

For the general dissociation reaction of a weak base (such as NH₃)

the dissociation constant K_b is written

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