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What is the conjugate base of $ N{{H}_{4}}^{+} $ ?

Answer
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Hint :Here, we need to use the concept of Bronsted-Lowry theory for acids and bases, where an acid donates a proton and a base accepts a proton. The conjugate base can be defined as the product formed from a Bronsted-Lowry acid by donating a proton.

Complete Step By Step Answer:
First let us understand the concept of acid and base from the Bronsted-Lowry theory.
As per the theory, a compound that donates a proton in a reaction is said to be acid and is known as Bronsted-Lowry acid.
Similarly, a compound that accepts a proton in a reaction is said to be acting as base and is known as Bronsted-Lowry base.
Now, let us understand the concept of conjugate base and acid.
A conjugate base is the product of a reaction that is formed from a Bronsted-Lowry acid by donating a proton.
A conjugate acid is the product of a reaction that is formed from a Bronsted-Lowry base by accepting a proton.
Here, we are required to find the conjugate base of $ N{{H}_{4}}^{+} $ , which means that we are required to find the product of the reaction where $ N{{H}_{4}}^{+} $ acts as a Bronsted-Lowry acid and donates a proton.
Now, let us suppose a reaction of $ N{{H}_{4}}^{+} $ with water. Here, $ N{{H}_{4}}^{+} $ acts as acid and donates a proton. Hence, water acts as a base and accepts protons.
The balanced reaction can be written as
 $ N{{H}_{4}}^{+}+{{H}_{2}}O\to N{{H}_{3}}+{{H}_{3}}{{O}^{+}} $
Hence, the product of $ N{{H}_{4}}^{+} $ in this reaction is $ N{{H}_{3}} $
Hence, the conjugate base of $ N{{H}_{4}}^{+} $ is $ N{{H}_{3}} $ .

Note :
A conjugate base is formed from a compound that acts as an acid. Similarly a conjugate acid is formed from the compound that acts as base. As an acid donates a proton, the charge of the conjugate base will always be one less than the acid. Similarly for a base, the charge of the conjugate acid is always one more than the base. Here, the given compound $ N{{H}_{4}}^{+} $ has already all electrons shared and electron deficient. Hence, it can never act as a base and accept a proton. However it acts as the conjugate acid for $ N{{H}_{3}} $ .