The pH scale

Water ionizes to a small extent.

It ionizes to form equal concentrations of hydronium ions and hydroxyl ions. At 25° C the concentration of each is 10^-7 mol/liter.

Addition of acids will increase the hydronium ion concentration and decrease the hydroxyl ion concentration. The product of the two (K_W) is always 10^-14 at 25° C. Thus if the concentration of hydronium ion is 10^-6M the hydroxyl ion is 10^-8M. K_W is given by

The value of K_W is a function of temperature to some extent.

pH is defined as the negative exponent of the hydronium ion concentration or more accurately activity rather than concentration. If the concentration of hydronium ion is 10^-5M, the pH is 5. It is sometimes expressed as the negative logarithm of the hydrogen ion (or hydronium ion) activity or concentration.

For most practical purposes the pH scale can be considered to range from 0 to 14.

Calculation of pH for solutions of strong acids and bases

With strong acids and bases the pH or (pOH) can be calculated from the concentration. If the concentration of a strong acid like HCl is 10^-1M the pH is 1. At 10^-2M the pH is 2. But as the concentration of strong acid or base approaches that of the self-ionization of water, the contribution from the ionization of water must be taken into account.

Hydrolysis

Hydrolysis refers to a reaction with water. Reactions such as

CH₃COO^- + H₂O = CH₃COOH + OH^-

and

NH₄⁺ + H₂O = NH₃ + H₃O⁺

are hydrolysis reactions for salts of a weak acid and base, respectively. In the first case it was necessary to have cations such as sodium that do not hydrolyze, i.e., sodium acetate, which dissolves to form sodium ions and acetate ions. Most of the acetate ions react with water molecules to form molecular acetic acid, CH₃COOH. In the second case it is necessary to have anions such as chloride (NH₄Cl) that do not hydrolyze.

Calculation of pH for solutions of weak acids and bases

The acid dissociation constant for a weak acid

can be rewritten as

since [A^-] = [H₃O⁺} and [HA] ~ C, the analytical concentration of acid if the extent of ionization is small. Thus

So the pH is given by

which can also be written

Buffer systems

Buffer systems consist of weak acids or bases dissolved with one of their completly ionized salts. The purpose of these solutions is to maintain an almost constant pH only slightly affected by the addition of acid or base. In the system ethanoic acid/sodium ethanoate the presence of the salt suppresses the protolysis of the acid so that it remains virtually undissociated. This means that the concentrations of both the acid and salt are very close to the original concentration. The acid dissociation constant is

or

or, taking logarithms

This is a form of the Henderson-Hasselbach equation. For a weak base with one of its completely ionized salts, e.g., ammonia in the presence of ammonium chloride, after a similar development the final equation is

Addition of small amounts of acid or base convert small amounts of weak acid or base and the salt so that the concentration ratio remains almost constant.

Salts of weak acids and strong bases

Given the hydrolysis constant for sodium ethanoate

since [CH₃COOH] = [OH-], then

If the degree of hydrolysis is small (K_b < 0.01), [CH₃COO^-] is approximately the original concentration C of salt dissolved. Thus

and /p>

Therefore

Or, in logarithms