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What is the IUPAC name of the given compound: $[Ag{{(N{{H}_{3}})}_{2}}][Ag{{(CN)}_{2}}]$?

Answer
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Hint: The nature of the ligands $N{{H}_{3}}$ and CN- is neutral and negative respectively. Bear this in mind when trying to figure out the cationic and anionic complexes of this compound in particular en-route to finding out the IUPAC name of the given compound.
Complete answer:
Let us first try and understand the rules of the IUPAC nomenclature of coordination compounds before trying to name the given compound.
Remember that coordination compounds are neutral substances (i.e. uncharged) in which at least one ion is present as a complex. The coordination compounds are named in the following way.
A. To name a coordination compound, no matter whether the complex ion is the cation or the anion, always name the cation before the anion. (This is just like naming an ionic compound.)
B. In naming the complex ion:
Name the ligands first, in alphabetical order, then the metal atom or ion. Note: The metal atom or ion is written before the ligands in the chemical formula.
For anionic ligands end in "-o"; for anions that end in "-ide"(e.g. chloride), "-ate" (e.g. sulfate, nitrate), and "-ite" (e.g. nirite), change the endings as follows: -ide $\to $ -o; -ate $\to $ -ato; -ite $\to $ -ito
For neutral ligands, the common name of the molecule is used e.g. \[{{H}_{2}}NC{{H}_{2}}C{{H}_{2}}N{{H}_{2}}\] (ethylenediamine). Important exceptions: water is called ‘aqua’, ammonia is called ‘ammine’, carbon monoxide is called ‘carbonyl’, and the N2 and O2 are called ‘dinitrogen’ and ‘dioxygen’.
With these rules in mind, let us now try to name the given compound.
In the give complex,
The Cation is \[\left[ Ag{{\left( N{{H}_{3}} \right)}_{2}} \right]+\] ion.
And the Anion is \[{{\left[ Ag{{\left( CN \right)}_{2}} \right]}^{-}}\] ion
Therefore, the name of Cation is diammine silver(I) ion
And that of the Anion is dicyanoargentate(I)ion
Making the name of this complex: diamminesilver(I) dicyanoargentate (I)
Now, since $N{{H}_{3}}$ is a neutral ligand and CN- is a negative ligand.
Therefore, the oxidation-number of Ag = +1
Note:
After naming the ligands, name the central metal. If the complex ion is a cation, the metal is named the same as the element. For example, Co in a complex cation is called cobalt and Pt is called platinum.
If the complex ion is an anion, the name of the metal ends with the suffix –ate. For example, Co in a complex anion is called cobaltate and Pt is called platinate. For some metals, the Latin names are used in the complex anions e.g. Fe is called ferrate (not ironate).