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$\ce{Ag^{+}_{(aq)}}$ can be written as $\ce{[Ag(H2O)2]+}$ but how would you know that it bonds with 2 water molecules?

I don't get when ligands randomly form 6, 4, 2 bonds.

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There is no way to absolutely predict the co-ordination number in any complex entity, without knowing say for example, magnetic or geometric properties of the complex. All we can do is give a probable configuration based on intelligent guesses. The co-ordination number depends on the characetristics of the ligands and the central ion.

Silver ion, $\ce{Ag+}$ usually forms complexes with Co-ordination Number two. This is partly because the silver ion is small sized, making it difficult to accommodate higher co-ordination numbers around itself owing to increased ligand-ligand repulsion, and partly due to the low charge on silver ion which makes it difficult to hold more than two ligands together. Therefore, in most of its complexes, silver ion co-ordinates with two ligands to form a linear entity. But to confirm this, you need to study solvated silver ions spectroscopically, magnetically or geometrically (diffraction), without which the above arguments can only give you, at best, a good guess.

Other examples include $\ce{[Ag(NH3)_2]+}$, and the polymeric $\ce{[Ag(en)]ClO4}$, both of which have co-ordination number of the silver ion 2.

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