In this article, we describe the different definitions of acids and bases which have been proposed to explain the acid-base behaviour of the compounds. These so-called ‘theories of acids and bases’ are not theories in the sense as valence bond theory or molecular orbital theory. They are only different definitions and approaches to the same problem.

Since the ancient times, acids are defined as those compounds which show the following typical properties:

1. They have sour taste.
2. They turn blue litmus red.
3. They react with alkalis like sodium hydroxide (NaOH) and form salt and water. The reaction between an acid and a base to form salt and water is called neutralization.
4. They decompose washing soda (sodium carbonate, Na₂CO₃) with effervescence, due to the evolution of carbon dioxide (CO₂).
5. They can dissolve active metals like zinc (Zn), iron (Fe) or tin (Sn) and evolve hydrogen gas (H₂). The metals form their corresponding salts with the acid.The bases, on the other hand, show the following typical properties:

1. They are bitter in taste and slippery to touch.
2. They turn red litmus blue.
3. They react with acids like hydrochloric acid (HCl) or sulphuric acid (H₂SO₄) and form salt and water. (Bases neutralize acids to form salt and water.)
   
   Salt is a chemical compound formed by the complete or partial neutralization of an acid and a base.    A neutralization reaction can be represented as:

 Acid  +  Base  →    Salt  + Water
HCl + NaOH  → NaCl + H₂O
H₂SO₄ + 2NaOH → Na₂SO₄ + 2H₂O

Partial neutralization, e.g. of sulphuric acid with sodium hydroxide gives the acid salt sodium hydrogensulphate (NaHSO₄), which can further react with sodium hydroxide to form sodium sulphate, which is the normal salt:

H₂SO₄ + NaOH → NaHSO₄ + H₂O
NaHSO₄ + NaOH → Na₂SO₄ + H₂O

1.1.1 ARRHENIUS’S THEORY OF ACIDS AND BASES

Arrhenius’s theory for the acids and bases (1883) is based upon his famous theory of electrolytic dissociation or ionization of compounds in solution. It considers the auto-ionization or self ionization of water into hydronium ions (H⁺) (acid) and hydroxide ions (OH⁻) ions (base) as the basis for explaining the acid–base  behaviour of compounds:

H₂O  ⇌  H⁺ + OH⁻

The equilibrium constant for this reaction called the ionic product of water (K_w) and is defined as:

K_w = [H⁺][OH ⁻]/[H₂O]  =  [H⁺][OH ⁻]       (Ionic Product of water)
as [H₂O], being liquid = 1

At 298 K, K_w =1.02 × 10 ⁻¹⁴. The aqueous solutions are acidic when [H⁺] > [OH⁻], neutral when [H⁺] = [OH⁻], and basic when [H⁺] < [OH⁻]. This means that in acidic aqueous solutions, [H⁺] > 1 × 10⁻⁷, in neutral solutions, , [H⁺] =1 × 10⁻⁷, and in basic solutions, [H⁺] < 1 ×10⁻⁷ (all values are in mol.l ⁻¹).

1.1.2 ARRHENIUS’S ACIDS

Arrhenius’s acid is a compound of hydronium, which ionizes in solutions to form a hydronium ion (H+}, e.g., hydrochloric acid (HCl), sulphuric acid (H₂SO₄) formic aid (HCOOH) or acetic acid (CH₃COOOH). These compounds ionize in solutions to form a hydronium ion (H⁺):

HCl(aq) ⇌ H⁺(aq) + Cl⁻(aq)
H₂SO₄(aq) ⇌ 2H⁺(aq) + SO₄²⁻(aq)
HCOOH(aq) ⇌ H⁺(aq) + HCOO⁻(aq)
CH₃COOH(aq) ⇌ H⁺(aq) + CH₃COO⁻(aq)

Note: The H⁺ ion, or the hydronium ion (earlier called, proton) has no electron in its extra nuclear part; it is only a nucleus  of an atom and has extremely small size (that of a nucleus only). Therefore, it has a very high positive charge density and a very high polarizing power. Water, on the other hand, is a polar molecule in which the more electronegative oxygen atom polarizes the O—H bond and carries a partial negative charge.

Therefore, in water or in aqueous solutions, a bare hydron (proton) or a H⁺ ion  having a very high positive charge density cannot exist in free state. There is a very strong attraction between positively charged hydronium ion and the negaively charged oxygen atom of water molecule. A covalent bond is formed between oxygen atom and the hydronium ion, resulting in the formation of [H₂O—H]⁺, or, H₃O⁺, called a hydrated hydronium ion:

H⁺(aq) + H₂O (l) → H₃­O⁺(aq)

Therefore, more appropriately, the ionization reactions of the acids are written as:

HCl(aq) + H2O (l) ⇌  H₃O+(aq) + Cl⁻ (aq)
H₂SO₄(aq) + H₂O (l) ⇌  H₃O+(aq) + SO₄²⁻(aq)
H₃COOH(aq) + H₂O (l) ⇌  H₃O+(aq) + CH­₃COO⁻ (aq)

(Actual situation may be more complicated and more hydrated ions like H₉O₄⁺ may be present in solutions.)

1.1.3 ARRHENIUS’S BASES

An Arrhenius’s base, or simply a base, is a compound which ionizes in solutions to form a hydroxide ion (OH ⁻). For example, sodium hydroxide (NaOH), ammonium hydroxide (NH₄OH) or calcium hydroxide [Ca(OH)₂], which ionize in aqueous solutions to form hydroxide ions:

NaOH(aq) ⇌  Na⁺(aq) + OH⁻(aq)
NH₄OH(aq) ⇌  NH₄⁺(aq) + OH⁻(aq)
Ca(OH)₂(aq) ⇌  Ca^{²⁺}(aq) + 2OH⁻(aq)

 1.1.4 NEUTRALIZATION REACTION AND ARRHENIUS’S THEORY

Let us consider the neutralization reaction between an acid, hydrochloric acid (HCl), and a base, sodium hydroxide (NaOH), which forms a salt, sodium chloride (NaCl) and water:

HCl(aq) + NaOH(aq) → NaCl(aq) + H­O(aq)⁻   (Neutralization reaction)

In solutions, the acid (HCl), the base (NaOH) as well as the salt (NaCl) are ionized to their ions as shown below:

[ H⁺(aq)  + Cl⁻(aq) ]  + [ Na⁺(aq)  + OH⁻(aq) ]     →
Hydrochloric acid)        (Sodium hydroxide)
[Na⁺(aq)  +  Cl⁻(aq) ] +     H₂O(l)
(Sodium chloride)         (Water)

Cancelling the common ions from both sides we get a net reaction, which is the combination of a hydronium ion and hydroxyl ion to form water. It is therefore, the net neutralization in aquoues solutions and is the reverse of ionization of water:

H⁺(aq) + OH⁻(aq)  ⇌  H₂O(aq)                   (Neutralization reaction)

Now, consider neutralization of sulphuric acid (H₂SO₄) with sodium hydroxide (NaOH). If we cancel out the common ions from the both sides of the reaction involved, we again get the same net reaction:

H₂SO₄(aq) + 2NaOH(aq) → Na₂SO₄(aq) + 2H₂O(l)                (Neutralization reaction)

In terms of their ions, the reaction becomes:

[2H⁺(aq) + SO₄²⁻(aq) ] + 2 [ Na⁺(aq) + OH⁻(aq) ]  →
(Sulphuric acid)          (Sodium hydroxide)
  [ 2Na⁺(aq) + SO₄²⁻(aq) ] + 2H₂O(l)
          (Sodium sulphate)         (Water)

Cancelling the common ions from both sides, and dividing by 2, we again the same net ionic reaction as above.

Therefore, the net neutralization reaction in terms of Arrhenius’s theory is:

H⁺(aq) + OH⁻(aq)  ⇌  H₂O(aq)                     (Neutralization reaction) 

1.1.5 ACIDITY AND BASICITY OF ACIDS AND BASES

The number of hydronium ions (H⁺) released by an acid in aqueous solutions is called the basicity of the acid. A monobasic acid (HCl, HNO₃, HCN, HCOOH or CH₃COOH) ionizes to give one H⁺ ion. A dibasic acid (H­₂­SO_­4­, H₂CO₃, oxalic acid (COOH)₂ or succinic acid (CH₂COOH)₂)  ionizes to give two H⁺ ions, whereas a tribasic acid like phosphoric acid H₃PO₄ or citric acid [HOC(COOH)(CH₂COOH)₂ or C₆H₈O₇] ionizes to three H⁺ ions in aqueous solutions.

HCl(aq) + H2O (l) ⇌  H₃O⁺(aq) + Cl⁻ (aq)       (monobasic acid)
HNO₃(aq) + H2O (l) ⇌  H₃O⁺(aq) + NO₃⁻ (aq)     (monobasic acid)
CH₃COOH(aq) + H₂O (l) ⇌  H₃O⁺(aq) + CH­₃COO⁻ (aq)  (monobasic)

H₂SO₄(aq) + 2H₂O (l) ⇌  2H₃O⁺(aq) + SO₄²⁻(aq)              (dibasic acid)
(COOH)₂(aq) + 2H₂O (l) ⇌  2H₃O⁺(aq) + (COO)²⁻(aq)      (dibasic acid)

H₃PO₄(aq) + 3H₂O (l) ⇌  3H₃O⁺(aq) + PO₄³⁻(aq)              (tribasic acid)
C₆H₈O₇(aq) + 3H₂O (l) ⇌  3H₃O⁺(aq) + C₆H₅O₇³⁻(aq)      (tribasic acid)

For complete neutralization with a monoacidic base like NaOH or KOH, one mole of either of these acid requires one mole, two moles or three moles respectively of the alkalis:

   HCl + NaOH → NaCl + H­₂­O              (monobasic acid)
HNO₃ + NaOH → NaNO₃ + H­₂­O          (monobasic acid)
CH₃COOH + 2KOH →  CH­₃COOK + H₂O       (monobasic acid)

  H₂SO₄ + 2NaOH → Na₂SO₄ + 2H₂O                        (dibasic acid)
(COOH)₂ + 2KOH → (COOK)₂ + 2H₂O                      (dibasic acid)

 H₃PO₄ + 3NaOH → Na₂PO₄ + 3H₃O⁺                      (tribasic acid)
C₆H₈O₇(aq) + 3NaOH ⇌  3H₃O⁺ + C₆H₅O₇Na₃(aq) (tribasic acid)

Other polybasic acids like pentabasic paraiodic acid  (H₅IO₆) and hexabasic telluric acid (H₆TeO₆), etc. are also known.

Note that in aqueous solutions, boric acid (H₃BO₃) and phosphorus acid (H₃PO₃) with structures X(OH)₃, are a monobasic acid and a dibasic acid respectively, as one mole of boric acid is completely neutralized by one mole of NaOH whereas one mole of phosphorus acid requires two moles of NaOH for complete neutralization:

H₃BO₃ + H₂O ⇌ H⁺ + [B(OH)₄] ⁻     H₃BO₃ + NaOH → NaBO₂ + 2H₂O
H₃PO₃  ⇌ 2H⁺ + [HPO₃]²⁻       H₃PO₃ + 2NaOH → Na₂HPO₃ + 2H₂O

1.1.6 LIMITATIONS OF ARRHENIUM’S THEORY

1. A hydronium ion (H⁺), cannot exist in aqueous solutions. It must get hydrated to form monohydrate (H₃O⁺), tetrahydrate (H₉O₄⁺), or even more hydrated [H(H₂O)_n]⁺.
2. There are many compounds which do not contain any hydronium atom or hydroxyl group, but can form hydronium ion or a hydroxide ion in water. Examples include many oxides (both acidic as well as basic oxides) and hydrolyzable salts like anhydrous halides of metals and nonmetals (FeCl₃, AlCl₃, CH₃COONa, Na₂CO₃, PCl₅, SOCl₂, etc.).

AlCl₃ + 3H₂O ⇌ 3H⁺ + 3Cl⁻ + Al(OH)₃
Na₂CO₃ + 2H₂O ⇌ 2Na⁺ + 2OH⁻ + H₂CO₃
CH₃COONa + H₂O ⇌ Na⁺ +  OH⁻ + CH₃COOH
SOCl₂ + 2H₂O ⇌ 4H⁺ + 2Cl⁻ + SO₃²⁻

It is a common Lab exercise to titrate sodium carbonate as a weak base against a strong acid like hydrochloric acid.

3. A hydronium ion (H⁺) can exist in non-aqueous solvents like ether, alcohol or ammonia also. In these solvents, it gets bonded to form hydronated solvent ion (Eddy−Calsey definition of acids and bases).
4. It cannot be extended to non-aqueous solutions.