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What is the valency of ammonia and ammonium ions?

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Hint: In order to answer this question we should first get some idea about valency. The valency of an atom refers to its ability to combine with other atoms. The number of bonds that an atom can make as part of a compound is represented by the element's valency.

Complete answer:
Valency refers to an element's ability to combine with other elements. The valency of elements belonging to the same periodic table group is the same. The number of electrons in an element's outer shell determines its valency.
Noble gases have a valency of 0 because they rarely mix with other elements.
Ammonia is a nitrogen-hydrogen chemical with the formula \[N{H_3}\] Ammonia is a colourless gas with a strong odour. It is the simplest pictogen hydride and a stable binary hydride. It's a common nitrogenous waste, particularly among aquatic organisms, and it aids terrestrial organisms in meeting their nutritional needs by serving as a precursor to food and fertilisers.
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The ammonium cation has the chemical formula \[NH_4^ + \] and is a positively charged polyatomic ion. The protonation of ammonia produces it \[\left( {N{H_3}} \right).\] Ammonium also refers to positively charged or protonated substituted amines and quaternary ammonium cations \[\left( {NR_4^ + } \right),\] which have one or more hydrogen atoms replaced by organic groups (indicated by\[R\])
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Ammonia has the formula \[N{H_3}\] and is a compound. It has a valency of \[0\] because it satisfies the Octet rule, which states that the outermost orbit has \[5{\text{ }} + {\text{ }}3{\text{ }} = {\text{ }}8\] electrons. It has an oxidation number of zero, indicating that it is an extremely stable chemical that does not lose or receive any additional electrons.
The valency of the ammonium ion is \[ + 1\]. It takes the form of a cation or a positive ion.

Note:
Ammonia is a colourless gas with a distinctly unpleasant odour. It has a density of \[0.589\] times that of air, making it lighter than air. Because of the strong hydrogen bonds between molecules, it is quickly liquefied; the liquid boils at \[33.3{\text{ }}^\circ C{\text{ }}\left( {27.94{\text{ }}^\circ F} \right)\] and freezes to white crystals at \[77.7{\text{ }}^\circ C{\text{ }}\left( {107.86{\text{ }}^\circ F} \right).\]