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### Theory:

When two compounds react, if their ions are interchanged, the reaction is called a double displacement reaction.
Ions with identical charges can only be interchanged, which means that a cation can be replaced by another cation. This reaction is also called ‘Metathesis reaction’.

Many displacement reactions occur between the ionic compounds that are dissolved in water. A double displacement reaction is shown schematically as follows:

Double displacement reaction

Atoms from two different compounds swap places in a double displacement reaction. The two reactants and products are different compounds. For example:

$$2NaOH+CuSO_4→Cu(OH)_2+Na_2SO_4$$

Double displacement reaction

In a double displacement reaction, one of the products must be either a precipitate or water. In this way, double displacement reaction is further classified as follows:

(i) Precipitation reactions
(ii) Neutralization reactions

Precipitation reactions:
When aqueous solutions of two compounds are mixed, if they react to form an insoluble compound and a soluble compound, it is called a precipitation reaction.
Since one of the products is an insoluble compound, the reaction is called a precipitation reaction.

Example:
Mixing the clear aqueous solutions of potassium iodide with lead (II) nitrate is an example of a double displacement reaction.

$$Pb(NO_3)_{2(aq)}+2KI_{(aq)}→PbI_{2(s)}↓+2KNO_{3(aq)}$$

Precipitation of $$PbI_2$$

In this reaction, potassium and lead displace or replace one another and form a yellow precipitate of lead (II) iodide.

Neutralization reactions:

The reaction between an acid and a base result in the formation of salt and water is called a neutralisation reaction. This is another type of displacement reaction in which both acid and base neutralise each other.

Example: $$1$$

A common neutralisation reaction is the reaction of sodium hydroxide with hydrochloric acid. Here, sodium replaces hydrogen from hydrochloric acid, forming sodium chloride (neutral soluble salt).

$$NaOH_{(aq)} + HCl_{(aq)} → NaCl_{(aq)} + H_2O_{(l)}$$

Neutralisation reaction

Example: $$2$$

The reaction of ammonium hydroxide with nitric acid forms ammonium nitrate and water.

$$HNO_{3(aq)}+NH_4OH_{(aq)}→NH_4NO_{3(aq)}+H_2O_{(l)}$$
Reference:
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