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.

THEORIES OF ACIDS AND BASE

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

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  behavior 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 wateras, [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).

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 acid (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 hydronium ion (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 negatively 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 follows:

HCl(aq) + H2O (l) ⇌  H₃O+(aq) + Cl⁻ (aq)
H₂SO₄(aq) + H₂O (l) ⇌  H₃O+(aq) + SO₄²⁻(aq)
CH₃COOH(aq) + H₂O (l) ⇌  H₃O+(aq) + CH­₃COO⁻ (aq)

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

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)

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)

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 aqueous solutions and is the reverse of ionization of water:
H⁺(aq) + OH⁻(aq)  ⇌  H₂O(aq)          (Neutralization)               

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)  
In terms of their ions, the reaction becomes:
H⁺(aq) + SO₄²⁻(aq} ]  +  2 [ Na⁺(aq)  + OH⁻(aq) ]     →    
 [ 2Na⁺(aq)  +  SO₄²⁻(aq) ] +  2H₂O(l)
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 of acids and base is:
                 H⁺(aq) + OH⁻(aq)  ⇌  H₂O(aq)           (Neutralization reaction)

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)  ionizes to give two H⁺ ions, whereas a tribasic acid like H₃PO₄ ionizes to three H⁺ ions in aqueous solutions.

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

H₂SO₄(aq) + 2H₂O (l) ⇌  2H₃O⁺(aq) + SO₄²⁻(aq)  
(COOH)₂(aq) + 2H₂O (l) ⇌  2H₃O⁺(aq) + CH­₃COO⁻ (aq)

  H₃PO₄(aq) + 3H₂O (l) ⇌  3H₃O⁺(aq) + PO₄³⁻(aq)                  

Consequently, for complete neutralization with a monoacidic base like NaOH or KOH, one mole of these acids requires one mole, two moles or three moles respectively of the alkalis:

HCl + NaOH → NaCl + H­₂­O
        HNO₃ + NaOH → NaNO₃ + H­₂­O
       CH₃COOH + 2KOH →  CH­₃COOK + H₂O

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

  H₃PO₄ + 3NaOH → Na₂PO₄ + 3H₂O

Note that boric acid (H₃BO₃) with structure of B(OH)₃, is a monobasic acid as one mole of boric acid is completely neutralized by one mole of NaOH:

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

Limitations of Arrhenius’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.).

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.

BRÖNSTED-LOWRY THEORY OF ACIDS AND BASES

The Brönsted−Lowry definition of acids and bases is based upon the transfer of one or more hydronium ions (H⁺) from an acid to a base. In 1923, Brönsted and Lowry independently defined as follows.

Acids are those molecules or ions which can donate one or more hydronium ions to compounds called bases. Example, hydrochloric acid (HCl), sulphuric acid (H₂SO₄) phosphoric acid (H₃PO₄) or water (H₂O):

HCl ⇌  H⁺ + Cl⁻
H₂SO₄ ⇌  2H⁺ + SO₄²⁻
H₃PO₄ ⇌  3H⁺ + PO₄³⁻
H₂O  ⇌  H⁺ + OH⁻

Note that all Arrhenius acids will be Brönsted acids, but all the Brönsted acids may not be Arrhenius acids.

Bases are those molecules or ions which can accept one or more hydronium ions from acids. For example, ammonia (NH₃), water (H₂O), hydroxide ( OH⁻), or anions like acetate (CH₃COO⁻), sulphide (S²⁻), hydrogensulphide (HS⁻), etc.

   NH₃ + H⁺ ⇌  NH₄⁺
H₂O + H⁺ ⇌  H₃O⁺
OH⁻ + H⁺ ⇌  H₂O
CH₃COO⁻ + H  ⇌ CH₃COOH
S²⁻ + H⁺ ⇌  HS⁻ ;  HS⁻ + H⁺ ⇌  H₂S (two steps)

Note that all Arrhenius bases will be Brönsted bases, but all the Brönsted bases may not be Arrhenius bases.

CONJUGATE ACIDS AND BASES – NEUTRALIZATION OF BRÖNSTED ACID AND BASES

Neutralization is defined as a reaction in which a hydronium ion is transferred from a Brönsted acid HA to a Brönsted base B resulting in the formation of another Brönsted acid BH⁺ and another Brönsted base A⁻:

HA  +  B  ⇌  A⁻  +  BH⁺     (Neutralization of acid HA with base B)

For a complete neutralization of a polyprotic acids (containing more than one ionizable H⁺ ions) or a polyprotic base (capable of accepting more than one H⁺ ions), more than one hydronium ions must get transferred from the acid to the base.

In the above neutralization reaction, the products formed are related to and differ from the original  acid and base by a hydronium ion (H⁺) only. By definition, the species that differ from one another by one hydronium ion only (like A ⁻ and HA, or B and BH⁺) are  called the conjugate base  and conjugate acid respectively. If we write the acid species first, the conjugate acid–base  pairs formed in the above reaction are  HA – A^– and BH⁺– B . Some examples of neutralization reactions are given below:

        Acid   +   Base  ⇌    Conjugated Base + Conjugated Acid
         HA    +    B           ⇌           A⁻            +             BH⁺
HCl +  OH^–        ⇌          Cl^–          +             H₂O    
          HCl   +   NH₃       ⇌           Cl^–          +             NH₄⁺
         HX     +   CN ⁻    ⇌           X^–           +              HCN   
    H₂PO₄^– +   OH⁻    ⇌          HPO₄^2– +             H₂O
     H₂SO₄    +   Cl ⁻     ⇌         HSO₄^–    +             HCl

Some common conjugated acid-base pairs are given below.

Acid (HA or BH⁺)     Conjugate Base (A- or B)       Strength*
Hydrochloric acid (HCl)        Chloride (Cl^–)              Strong – Weak
Nitric acid (HNO­₃)                   Nitrate (NO₃^– )        Strong – Weak
Sulphuric acid (H₂SO₄)  Hydrogensulphate (HSO₄^–)   Strong – Weak
Hydrogensulphate (HSO₄)     Sulphate (SO₄^2–)         Weak – Weak
Acetic acid (CH₃COOH)         Acetate (CH₃COO^–)      Weak – Strong
Hydrogen cyanide (HCN)    Cyanide (CN ⁻)           Weak – Strong
Water (H₂O)                        Hydroxide (OH^–)        Weak – Strong 
Hydronium ion (H₃O⁺)        Water (H₂O)              Strong – Weak
Ammonium ion (NH₄⁺)      Ammonia (NH₃)         Strong – Weak  
Ammonia (NH₃)                   Amide (NH₂^–)          Weak – Strong
Carbonic acid (H₂CO₃)   Hydrogencarbonate (HCO₃^–) Weak – Weak
Hydrogencarbonate (HCO₃^–) Carbonate (CO₃^2–)  Weak – Weak
Phosphoric acid (H₃PO₄) Dihydrogenphosphate (H₂PO₄^–) Weak–Weak
Dihydrogenphosphate (H₂PO₄^2–) Hydrogenphosphate (HPO₄^2–)    
Weak – Weak
Hydrogenphosphate (H₂PO₄^–)  Phosphate (PO₄^3–)
   Weak – Strong
*Strength of acids and bases are discussed later.

The usefulness of Brönsted–Lowry concept is that:

Any protonic solvent like ammonia or sulphuric acid can be handled :
NH₃        +             NH₃       ⇌            NH₄⁺      +             NH₂^–
H₂SO₄    +             H₂SO₄ ⇌          H₃SO₄⁺  +            HSO₄^–
                              Conjugated Acid   Conjugated Base    

2. All hydronium ion transfer reactions (not usually called acid–base reactions) can be treated as such:

NH₄⁺  + S^2–  →   NH₃  +   HS^–
Acid₁    Base₂      Base₁    Acid₂

 However, Brönsted–Lowry definition fails for non-hydronic (non-protonic) solutions like SO₂, POCl₃, BrF₃, etc.

Conjugated Acid–Base pairs in Polyprotic Acids

In case of polyprotic acid−base system, it is important to remember that the conjugated acid−base pairs differ by one hydronium ion only. Take for example, phosphoric acid (H₃PO₄). It can donate three hydronium ions successively to a base and form anions H₂PO₄^– (dihydrogenphosphate), HPO­₄^2– (hydrogenphosphate) and phosphate (PO₄^3–) respectively. In this system, there are three  conjugate acid–base pairs as shown below:

H₃PO₄ – H₂PO₄^–,    H₂PO₄^– – HPO₄^2– ,   and   HPO₄^2– – PO­₄^3–.

The other acid−base pairs like H₃PO₄ – HPO₄^2–, H₃PO₄ – PO₄^3–  or H₂PO₄^– –  PO₄^3– do not form conjugated acid – base pairs as they differ by two or three hydronium ions.

Similarly, for carbonic acid (H₂CO₃), the conjugated acid−base pairs are H₂CO₃ – HCO₃^– and HCO₃^– – CO₃^2–; the carbonic acid (H₂CO₃) – carbonate ion (CO₃^2–) is not a  conjugated acid – base pair.

Monoprotic or Monobasic Acids

A monoprotic acid or monobasic Brönsted acid can be represented as HA and ionizes to give only one H⁺ ion and one anion A^–. As one molecule of a monobasic acid ionizes to give only one hydronium ion, it can form only one series of salts which contain the anion A^–.

The different types of monobasic  acids are  the following.
1. Neutral molecules like hydrochloric acid (HCl), nitric acid (HNO₃), acetic acid (CH₃COOH) or hydrogen cyanide (HCN), which ionize to form only one anion (chloride, nitrate, acetate and cyanide, respectively). Ionization reactions have been given before.
Therefore, they can donate only one hydronium ion to a base, and their neutralization reactions can be represented as (monobasic means reacting with one equivalent of a base):

  HCl (aq) + NaOH (aq) → NaCl (aq) + H_2­O(l)
                            HNO₃ (aq) + KOH (aq) → KNO₃ (aq) + H₂O(l)
                      CH₃COOH (aq) + NH₃ (aq) → CH₃COONH₄ (aq)

2. Cations like ammonium ion (NH­₄⁺), which can donate a hydronium ion (H⁺) to other bases:

NH₄⁺(aq) ⇌ H⁺ (aq) + NH₃(aq)

Polyprotic or Polybasic Acids

A polyprotic acid can be represented as H_nA. In aqueous solutions, it ionizes to or donates more than one hydronium ion [H⁺(aq)], stepwise, to a base. Based on the value of  n,  these acids  are further classified as diprotic or dibasic acids, triprotic or tribasic acids and polyprotic acids.

Diprotic or Dibasic Acids
A diprotic or dibasic acid can be represented as H₂A. They can donate, or ionize step-wise to give two hydronium ions per molecule and form two distinct series of salts containing the anions HA⁻ and A²⁻. For example sulphuric acid (H₂SO₄), which ionizes step-wise in aqueous solutions to give two H⁺(aq) ions per molecule and forms two series of salts containing hydrogensulphate (HSO₄⁻) and sulphate (SO₄²⁺) ions:

(a)                H₂SO₄ (aq) ⇌ H⁺ (aq) +  HSO₄⁻(aq)
    H₂SO₄ (aq) + NaOH(aq) → Na⁺(aq) +  HSO₄⁻(aq) + H₂O(l)
(b)                HSO₄⁻(aq) ⇌ H⁺ (aq)  + SO­₄^{2 −} (aq) 
HSO₄⁻(aq) + NaOH(aq) → Na⁺(aq)  + SO­₄^{2 −}(aq) + H₂O(l)

Overall ionization reaction and neutralization reaction can be written as:

H₂SO₄ (aq) ⇌ 2H⁺ (aq) +  SO₄²⁻ (aq)
H₂SO₄ (aq) + 2NaOH(aq) → 2Na⁺(aq) +  SO₄²⁻(aq) + 2 H₂O(l)

 Oxalic acid [(COOH)₂], succinic acid [(CH₂COOH)₂]  and tartaric acid [(CHOHCOOH)₂, or C₄H₆O₆) are some other common dibasic acids.

A dibasic acid can be a neutral molecule (see above) or a cation of a diacidic base, e.g., hydrazinediium ion (N₂H₆²⁺):
                   (N₂H₆²⁺)(aq) ⇌ 2H⁺(aq) + N­₂H₄(aq)                          

Triprotic or tribasic acids
A triprotic or tribasic acid can be represented as H₃A. They can donate or ionize stepwise, to give three hydronium ions per molecule and form three distinct series of salts containing the anions H₂A⁻ and HA²⁻ and A³⁻. For example, phosphoric (H₃PO₄), which ionizes stepwise in aqueous solutions to give three H⁺ (aq) ions per molecule and forms three series of salts containing dihyrogenphosphate (H₂PO₄⁻) and hydrogenphosphate (HPO₄²⁻) and phosphate (PO₄ ³⁻) ions:

(Step 1)                H₃PO₄ (aq) ⇌ H⁺ (aq) +  H₂PO₄⁻(aq)     
H₃PO₄ (aq) + NaOH(aq) → Na⁺(aq) +  H₂PO₄⁻(aq) + H₃O⁺(aq)
(Step 2)               H₂PO₄⁻(aq) ⇌ H⁺ (aq)  + HPO­₄^{2 −} (aq)  
  H₂PO₄⁻(aq) + NaOH(aq) → Na⁺(aq)  + HPO­₄^{2 −}(aq) + H₃O⁺(aq)
(Step 3) HPO₄²⁻ (aq) ⇌ H⁺ (aq)  + PO­₄^{3 −} (aq)  
  HPO₄²⁻ (aq) + NaOH(aq) → Na⁺(aq)  + PO­₄^{3 −}(aq) + H₃O⁺(aq)

Overall ionization reaction and neutralization reaction can be written as

               H₃PO₄ (aq) ⇌ 3H⁺(aq) +  PO₄³⁻(aq)     
H₃PO₄ (aq) + 3NaOH(aq) → Na₃PO₄(aq) + 3H₂O(l)

Monoacidic or Monoprotic Bases

 A base B is defined as a monoprotic base if one molecule of B can accept  only one H⁺ ion and get neutralized completely. It forms only one protonated species [BH]⁺, which may be a cation or a neutral molecule. (A protonated species is formed by the covalent attachment of one or more hydronium ions to another species.). Some examples are given below.
1. Hydroxides of monovalent cations e.g., sodium hydroxide (NaOH), potassium hydroxide (KOH), thallium(I) hydroxide (TlOH) or ammonium hydroxide (NH₄OH).
2. Molecules containing a lone pair of electrons which can be donated to a hydronium ion, e.g., water, ammonia (NH₃),  organic mono amines [ethyl amine (CH₃CH­NH₂), aniline (C₆H₅NH­₂), etc.]
3. All anions having one unit of negative charge, for example, acetate (CH₃COO ⁻), cyanide (CN ⁻), halides (X ⁻), hydrogensulphate (HSO₄⁻), etc.

When one mole of a monoacid base is treated with a monobasic acid like hydrochloric acid (HCl), the base gets completely neutralized  by one mole of hydrochloric acid:

                     NaOH + HCl → NaCl + H₂O
                                KOH + HCl → KCl + H₂O
                            NH₄OH + HCl → NH₄Cl + H₂O

When a neutral molecule like ammonia or water accepts a hydronium ion, it forms the cation NH₄ ⁺ (ammonium) or  H₃O ⁺ (hydrated hydronium ion) respectively:

                             B(aq) + H⁺(aq)  ⇌ BH ⁺(aq)
                                NH₃(aq) + H⁺(aq)  ⇌ NH₄⁺(aq)
                             H₂O(l) + H⁺(aq) ⇌ H₃O⁺(aq)

When an anion A⁻ carrying one unit of negative charge, like hydroxide ion (OH⁻), or acetate (CH₃COO⁻)  accepts  a hydronium ion, a neutral molecule is formed:

OH⁻(aq) + H⁺(aq) ⇌ H₂O(l)
CH₃COO⁻ + H⁺(aq) ⇌  CH₃COOH
A⁻ (aq) + H⁺(aq) ⇌ HA(aq)

Neutralization Reactions of Monoprotic Bases: The neutralization of one mole of a monoacidic or monoprotic base requires one mole of a monobasic acid (HCl):

NaOH(aq) + HCl(aq) → NaCl(aq) + H₂O(l)
CH₃COONa  + HCl(aq) → CH₃COOH(aq) + NaCl(aq)

A molecule of a polyprotic bases (B) can accept more than one hydronium ion  and form more than one hydronated species (BH_nⁿ⁺), Bases\d on the charge on the base, the hydronated species may be a cation, a neutral molecule or even an anion. Based on the value of n, a polyprotic base can be further classified as follows.

 Diprotic or Diacidic Base: A diprotic or a diacidic base B can accept two hydronium ions [H⁺(aq)] per molecule and form  salts containing BH⁺ and BH₂²⁺ ions. A diprotic or diacidic base can be:

1. Hydroxide of divalent metal cation, e.g., calcium hydroxide (Ca(OH)₂) or barium hydroxide (Ba(OH)₂).
2. Organic compounds containing two basics groups, e.g., ethylene diamine (NH₂CH₂CH₂NH₂), p-phenylene diamine or 1,4-diaminobenzene (C₆H₄(NH₂)₂).
3. All A²⁻  anions (having two units of negative charge), like sulphide S²⁻, carbonate (CO₃²⁻), etc.

The typical reactions of diprotic or diacidic bases with a monobasic acid like hydrochloric acid are given below.

Ca(OH)₂ + 2HCl  → CaCl₂ + 2H₂O
                              Ba(OH)₂ + 2HCl → BaCl₂ + 2H₂O
                     NH₂CH₂CH₂NH₂ + 2HCl → (NH₃CH₂CH₂NH₃]²⁺  +  2Cl ⁻

The reactions of the A^{2 −} anions showing the step-wise addition of hydronium ions can be written as:

              S^{2 −} (aq) + H⁺(aq) ⇌ HS ⁻ (aq)   ;       HS ⁻ (aq) + H⁺(aq) ⇌ H₂S (aq)
         CO₃^{2 −} (aq) + H⁺(aq) ⇌ HCO₃ ⁻ (aq) ; HCO₃^– (aq) + H⁺(aq) ⇌ H₂CO₃ (aq)

Note that the anion HS ^– is named as hydrogensulphide (as one word) whereas H₂S is named as hydrogen sulphide (two words).

Similar abbreviated reactions can be written for any other divalent anion.

Polyprotic  or Polyacid Bases

The above definition of a diprotic base can be extended further. Thus, a triprotic base B can accept, stepwise, three protons per molecule and form the ultimate species BH³⁺. Examples of triprotic bases include the following.

1. Hydroxides of trivalent metals like iron(III) hydroxide, Fe(OH)₃, or aluminium hydroxide, Al(OH)­₃.
2. Organic compounds containing three basic amino groups, e.g., 1,2,3-triaminopropane.
3. Anions with three units of negative charge, e.g., phosphate, PO₄^{3 −}.

The phosphate ion being a triprotic Brönsted base, can accept three H⁺ ions successively and -step-wise, and forms hydrogenphosphate (HPO₄²⁻), dihydrogenphosphate (H₂PO₄⁻) and phosphoric acid (H₃PO₄): 

H⁺ (aq)  + PO­₄^{3 −} (aq) ⇌ HPO₄²⁻ (aq) 
   H⁺ (aq)  + HPO­₄^{2 −} (aq) ⇌ H₂PO₄⁻(aq)
  H⁺ (aq) +  H₂PO₄⁻(aq) ⇌ H₃PO₄ (aq)

Overall complete hydronation (protonation) reaction of phosphate ions with three H⁺(aq) ions can be written as:

PO₄^{3 −} (aq) + 3H⁺(aq) ⇌ H₃PO₄ (aq)

AMPHOTERIC COMPOUNDS

Amphoteric compounds are those compounds which react or get neutralized with both acids as well as bases and, in both the cases, form a salt and water. Therefore, an amphoteric compound can function both as an acid as well as as a base. Thus, zinc hydroxide (Zn(OH)₂) is an amphoteric hydroxide. It reacts with acids like hydrochloric acid or sulphuric acid and gets neutralized to form salts (zinc chloride or zinc sulphate) and water. On the other hand, it reacts with a base like sodium hydroxide,  and gets neutralized to form another salt, sodium zincate (Na₂ZnO₂),  and water. The reactions are:

                              Acid       +   Base      →      Salt    +  Water
2HCl      +  Zn(OH)₂   →   ZnCl₂  +  2H₂O
                              Zn(OH)₂ +  2NaOH  →  Na₂ZnO₂ + 2H₂O

Some other common amphoteric compounds include oxides and hydroxides of zinc, aluminium, lead(II), and tin(II), e.g., ZnO, Al₂O₃, Al(OH)₃, PbO, Pb(OH)₂, SnO and Sn(OH)₂.

LUX–FLOOD DEFINITION                                                              

The definition proposed by Lux (1939) and extended by Flood (1947) considers the acid–base reaction on the basis transfer of oxide ions. Acid is a substance that can accept oxide ions (O^2–) whereas bases are the oxide ion donors. Thus the reactions

                                             CaO + SiO₂ → CaSiO₃
                                             ZnO + SO₃ → ZnSO₄

involve basic oxides (CaO, ZnO) and acidic oxides (SiO₂, SO₃) to form salts (CaSiO₃, ZnSO₄).

The acids need not always be oxides as can be seen in the interaction of pyrosulphates with oxides of titanium, niobium or tantalum at 1100 K:

                                             TiO₂  +Na­₂S₂O₇  → TiOSO₄ + Na₂SO₄
                                             (Base)           (Acid)    (Salt)

Substances are called amphoteric if they tend to both lose and gain oxide ions:

  ZnO ⇌ Zn²⁺  + O^2– (Base) ; ZnO + O^2– ⇌ ZnO₂^2- (Acid)
Al₂O₃ ⇌ Al³⁺ + 3O^2– (Base) ; Al₂O₃ + O^2– ⇌ 2AlO₂^–  (Acid)

The Lux−Flood definition can be extended to include any anion transfer like halide or sulphide. It is applicable to systems where no solvents involved like molten melts or non-protonic solvents.

LEWIS ACIDS AND BASES

According to G N Lewis (1923):

A base is a neutral molecule or an ion that can donate a pair of electrons  to other molecules or ions. For example, ammonia (NH₃), water (H₂O), hydroxide (OH⁻) or chloride (Cl⁻) ions.

An acid is a molecule or an ion that can accept a pair of electrons from an electron pair donor (Lewis base). Examples include hydronium ion (H⁺), ammonium ion (NH₄⁺), boron trifluoride (BF₃), etc.

Neutralization is the process of donation of a pair of electrons from a Lewis base to an Lewis acid. In the process, a coordinate bond is formed. Hence, in addition to the usual Brönsted acid–base neutralization reactions, the Lewis definition considers the formation of a coordinate bond also as a neutralization reaction:

BF₃    +     NH₃      →   H­₃N⁺–BF₃ ^–
Lewis acid + Lewis base  → Coordinated adduct

 Lewis Acid
Lewis acids are defined as those compounds or ions, which cannot be classfied as acids on the basis of Arrhenius or Brönsted definition, but can accept a pair of electrons from other molecules or ions. Thus, the following species are Lewis acids:

1. All cations, as they can combine with electron pairs:

Ag⁺ + 2CN^– → [Ag(CN)­₂] ^–
Ni²⁺ + 4NH₃ → [Ni(NH₃)₄]²⁺
Fe³⁺ + 6CNS^– → [Fe(CNS)­₆]^{3 –}
Al³⁺ + 4OH^– → [Al(OH)­₄] ^–
Co³⁺ + 6NH₃  → [Co(NH₃)­₆]³⁺

2. Electron deficient compounds, in which the central atom does not have a complete octet of electrons. For example, boron trifluoride (BF₃) or aluminium chloride (AlCl₃). In these molecules, the boron atom or aluminium atom has only six electrons in its outermost valence shell. Therefore, these atoms do not have the stable  octet of electrons, and the compounds are termed electron deficient compounds. . In order to complete their octet and attain stability, these atoms can accept a pair of electrons from other electron pair donors (bases) like ammonia or chloride ion, complete their octet and form a stable species, called adducts:

              BF₃ + NH₃ → [H­₃N⁺–BF₃ ^–]
AlCl₃ + Cl ^–  → [AlCl₄] ^–

3. Covalent compounds in which the central atom has a complete octet of electrons, but can expand its valence shell by accepting one or more pairs of electrons. This is called the expansion of valence shell to more than an octet. Covalent halides of element of third to sixth period in group 14 to 17 like SiCl₄, SnCl₂, SnCl₄, PCl₅, AsF₅, SbF₅, SF₄, BrF₃, etc.  are Lewis acids, as they can accept one or more electron pairs from say, the halide ions, and form coordinated complexes:

SnCl₄ + 2Cl ^–  → [SnCl₆]^{2 –}
PCl₅ + Cl ^–    → [PCl₆] ^–
AsF₅  +  F ^–     → [AsF₆] ^–
SbF₅ + Cl ^–    → [SbClF₅] ^–
IF₅  +  F ^–     → [IF₆] ^–

4. Multiple bonded covalent compounds SO₂, SO₃, or CO₂, which can form a covalent bond with anions like halide or hydroxide:

SO₂ + OH ^–  → [SO₃(OH)] ^–
SO₃ + F ^–  → [SO₃F] ^–
CO₂ + OH ^–  → [CO₂(OH)] ^–

Lewis Bases
Lewis bases are defined as those compounds or ions, which cannot be classified as a base on the basis of Arrhenius or Brönsted definition, but contain lone pair(s) of electrons that can be donated to Lewis acids, and form a coordinate or covalent bond.

Due to the presence of lone pairs of electrons, almost all the Lewis bases are Brönsted bases.

Lewis bases can be classified as follows:
1. Molecules having an unshared or lone pair of electrons, i.e., water, ammonia, ethers (R₂O), alcohols (ROH), amines (RNH₂, R₂NH, R₃N), etc. Lewis base strength increases wirh the increase in the availability of the electron pair.
2. All anions like OH ^–, S^{2 –}, Cl ^– or NO₂ ^–  as all anions have (a) an atom with free electron pairs and (b) a negative charge density. Lewis base  strength increases with increase in charge density on the atom having the lone pair making it easier for donation.
3. Compounds having multiple-bonded atoms like carbon monoxide, nitric oxide, alkenes, alkynes;  (multiple bonded molecules) and conjugated organic compounds having multiple bonds, e.g., benzene or allyl radicals. These species can combine with transition metals and their ions and form complexes containing coordinate bonds e.g., [Ni(CO)₄], [Fe(H₂O)₅(NO)]²⁺, [Ag(CH₂=CH₂)]⁺, [Cr(C₆H₆)₂], etc.

USANOVICH DEFINITION

Usanovich removed the condition that bases should donate a pair of electrons as such and extended the Lewis definition by proposing that  any number of electrons can be transferred in an acid−base  reaction. According to Usanovich’s definition, acid is a chemical species that can accept one or more electrons (not necessarily electron pairs), whereas base is the chemical species that can donate or release any number of electrons.

 Therefore, in addition to Arrhenius, Brönsted and Lewis acids, the Usanovich’s acids include all the oxidizing agents (electron acceptors), whereas bases include all the reducing agent (electron donors). When a species accepts electrons, it is said to undergo reduction, and acts as an oxidizing agent. Thus, in reactions

Ag⁺ + e^– ⇌ Ag    
S + 2e^– ⇌ S ^{2 –}  
Fe³⁺  + 3e ^–  ⇌ Fe²⁺

In these examples, silver ions, sulphur and iron(III) ions are accepting electrons and are getting reduced. However, according to Usanovich definition, these reactions show the acidic behavior of these ions.

Similarly, when a species loses electrons, it undergoes oxidation and acts as a reducing agent. Thus, hydrogen and metals are reducing agents – they  lose electrons and undergo oxidation:

                              H₂ ⇌ 2H⁺ + 2e^–
                              Na ⇌ Na⁺ + e ^–
Mg ⇌ Mg²⁺ + 2e ^–

 But Usanovich considers such species as  bases as they lose electrons in the reactions and are electron donors.

In some cases, there is not much difference between the Usanovich definition and the Lewis definition. For example, the reaction between pyridine and oxygen to form pyridine-N-oxide is an oxidation reaction of pyridine as well as the adduct formation in which pyridine nitrogen atom donates an electron pair to oxygen atom:

2C₅H₅N + O₂ → [C₅H₅N→O] or [C₅H₅N⁺–O^–[C₅H₅N→O].

CADEY – ELSEY DEFINITION

Cadey – Elsey definition of acids and bases is based upon the auto-ionization of solvents. In liquid state, all the ionizing solvents undergo auto-ionization, i.e., dissociate into their ions:

 Solvent (l) ⇌ Cation (Acid) + Anion (Base)
 2H₂O         ⇌       H₃O⁺      +             OH ^–
2NH₃(l)      ⇌      NH₄⁺      +             NH₂ ^–
2SO₂(l)      ⇌        SO²⁺       +          SO₃ ^2–  
                         CH₃CO₂H(l) ⇌    CH₃CO₂H₂⁺  +     CH­₃CO₂ ^–

In an ionizing solvent like water, liquid ammonia, liquid sulphur dioxide or acetic acid, acids are defined as those species that increase the concentration of the cation of the solvent , whereas bases are defined as those species that increase the concentration of the anion of the solvent. Thus, in water as solvent, all the species that increase the concentration of hydronium ions (H₃O⁺) are acids, whereas the species that increase the concentration of hydroxide ions (OH ^–) are bases.

However, in liquid ammonia as the solvent, the acids are compounds like ammonium chloride (NH₄Cl), ammonium nitrate (NH₄NO₃) and ammonium acetate (CH₃COONH₄) which ionize to form ammonium ions and increase the concentration of the cation of the solvent:

                               NH₄Cl  ⇌ NH₄⁺  + Cl^–
                              NH₄NO₃ ⇌ NH₄⁺  + NO₃^–
CH₃COONH₄ ⇌  NH₄⁺ + CH₃COO ^–

 Similarly, in liquid ammonia as solvent, bases are compounds like sodamide (NaNH₂) or potassium amide (KNH₂), which  ionize to form NH₂^–, the amide anion:

NaNH₂ ⇌ Na⁺ + NH₂^–

The advantage of such a definition is that all the ionizing systems AB can be treated analogously. The ionic product of the solvent can be defined as K_AB
                              K_AB = [A⁺][B ^–]
And a pA scale, analogous to the pH scale can be set for each solvent where the neutral point when [A⁺] = [B ^–] wiill be given by –(1/2)K_AB,

Limitations: The limitations of the solvent system definition are the following.

1. Emphasis is only on the auto-ionization of the solvent; other physical characteristics are completely ignored.
2. Due to low dielectric constants of many of these solvents, existence of ions in the solvent are is not conceivable.
3. For many solvents like POCl₃, auto-ionization is stretched too far.   
4. For many reactions, ionic reactions are too emphsized where other mechanisms are sufficient to explain the reaction.

A GENERALIZED ACID–BASE CONCEPT

In all the systems, an acid is defined as a substance that donates a positive species  or accepts a negative species, whereas a base is defined as a substance that donates a negative species  or accepts a posotive species. All these concepts can be generalized by defining acidity and basicity. Acidity is a positive character of a substance which decreases when it combines with a base.

All these concepts do not explain the acidic or basic behavior; they only help in correlating the observed phenomena. All the concepts are compatible with one another. The real explanation, however, lies in the the theories of structure and bonding.

It can be inferred that the stronger acid will have a more positive character and a stronger base will have a more negative character. The choice of strongest acid is therefore limited to a bare proton as it is species with the highest positive charge density. This can be justified on the grounds that even though a bare proton does not exist in solutions, it does exist in gaseous state and can attach itself to any compound containing electrons (anions as well  as molecules, including methane, graphite, etc.). The strongest base must be the smallest anions, oxide ion (O^2–) or fluoride (F^–) ion. However, counterpart of a proton, the electron, must be the strongest base. It is worth noting that free electrons exist in some non-aqueous solvents (ammonia) and make the solutions highly alkaline.