(3) Acid-base

pH: pH = −log₁₀[H₃O⁺] The quantity most measured in aqueous acid-base equilibrium is the oxonium (hydronium) ion concentration (but usually called the hydrogen ion concentration in this context) [H₃O⁺(aq)]. As this is often very small it is common to express the hydrogen ion concentration as pH.

The operation of taking a logarithm can only be performed on a pure number. Thus [H₃O⁺] is divided by the standard unit of concentration, 1 mol L⁻¹

K_w: K_w = [H₃O⁺][OH¯ ].
In water the very important equilibrium
H₂O + H₂O H₃O⁺(aq) +OH¯(aq)
always exists, with the equilibrium constant
K_w = [H₃O⁺][OH¯ ]
= 1.0 × 10⁻¹⁴ at 25 ^oC and pK_w = 14.
In very pure water at 25 ^oC; [H₃O⁺] = [OH¯ ] = 1 × 10⁻⁷ mol L⁻¹.

Neutral solution: An aqueous solution with [H₃O⁺] = [OH¯]; at 25 ^oC pH = 7.

Acidic solution: An aqueous solution with pH < 7.

Basic or alkaline solution: An aqueous solution with pH > 7.

Acidity constant: symbol K_a, (older term, the acid dissociation constant), the equilibrium constant for the reaction
HA(aq) + H₂O H₃O⁺(aq) + A¯(aq)

As the values of K_a are often very small, then pK_ais used.
pK_a = −logK_a

HA represents any acid. In many books,K_a is shown as
The (aq) are not shown and the oxonium, H₃O⁺, is simplified to H⁺.
This convention is used where appropriate for simplicity in this section from now on.

Weak acids: Acids with small values of K_a
(K_a < 1, pK_a positive, position of equilibrium well to left, only a small fraction of acid molecules reacted).

Strong acids: Acids with large values of K_a (K_a »1, pK_a negative, equilibrium well to right, almost all acid molecules reacted).

Weak base: A base for which the equilibrium position for the reaction
B(aq) + H₂O BH⁺(aq) + OH¯(aq)
lies well to the left, only a small fraction of molecules have accepted a proton from water.

Strong base: A base for which the equilibrium position for the above reaction lies well to the right, only a small fraction of molecules remain in the solution.

Basicity constant: symbol K_b, the equilibrium constant for the reaction:

Qualitatively, this expression says that the stronger an acid the weaker its conjugate base. Strong acids have very weak conjugate bases and very weak acids have strong conjugate bases.
Examples:
HNO₃ is a strong acid (pK_a −1.3), NO₃¯ is a very very weak base;
HS¯ is a very weak acid (pK_a 19), S²¯ is a strong base.
Tables of K_b are unnecessary, tables of K_a or pK_a of the corresponding conjugate acids being sufficient to state base strength.
For an acid HA, where pK_a(HA) = 7, pK_b(A¯) is also 7,
and it can be said that the strengths of the acid and its conjugate base are the same.

Polyprotic acids and bases: Acids with two, three or more hydrogens which can undergo proton transfer. Polyprotic acids can be diprotic, triprotic etc.
Similarly bases which can accept more than one proton are said to be polyprotic bases. For polyprotic acids successive acidity constants can be written as shown for phosphoric acid:

some polyprotic acids

Buffer solution: A solution which is resistant to change in pH (when small amounts of acid or base are added or it is diluted). A buffer solution contains significant amounts of both an acid and its conjugate base. If H₃O⁺ is added to or produced in the solution, it is removed by reaction with the base. Likewise any OH¯ is removed by reaction with the conjugate acid:
H₃O⁺ + A¯ HA + H₂O
OH¯ + HA A¯ + H₂O

The pH of a buffer solution can be controlled by taking the appropriate amounts of HA and A¯
From the expression , , it is easily seen that when [HA] = [A¯]
K_a = [H⁺] and therefore pH = pK_a

Brønsted acid: A proton donor; the molecule or ion must contain H.
Example: HCl and all the acids above in this section.

Brønsted base: A proton acceptor; the molecule or ion must have a pair of non-bonding electrons to form a bond with a proton
Example: NH₃ and all the bases above in this section.

Lewis acid: A species (molecule or ion) which can accept a pair of electrons from a base and form a bond.
This is a broader definition of an acid.
Carbon dioxide in its reaction with the hydroxide ion to give the hydrogencarbonate ion is an example:
CO₂ + OH¯ HCO₃¯
A proton is a Lewis acid by this definition.

Lewis base: An electron pair donor.
Example: the hydroxide ion in the above example
Brönsted bases are also Lewis bases as they donate a pair of electrons to the proton.

(4) Complex ion formation

Complex ion: An ionic species consisting of ligands (Lewis bases) (see section 13) bonded to a metal cation
(which is acting as a Lewis acid).
Cu(NH₃)₄²⁺ and CrCl₆³⁻ are examples.
The ligands may be neutral molecules such as NH₃ or anions such as Cl¯.

Stability constant (Formation constant): The equilibrium constant for the overall reaction between the aquated metal cation and the free ligands to form the complex ion.

Note: The formal convention for arrows in chemical equations is that represents a reaction in the forward direction, represents a reversible reaction, and represents a reaction at equilibrium.