To determine the coordination number of the complex \([Pt(NH_3)_4][PtI_4]\), we need to analyze the coordination environment of each platinum center in the complex.
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[Pt(NH₃)₄]²⁺ complex: In this part of the complex, platinum (Pt) is coordinated to four ammonia (NH₃) ligands. Each NH₃ is a monodentate ligand that binds through a single donor atom (nitrogen). Therefore, the coordination number of Pt in this complex is 4.
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[PtI₄]²⁻ complex: In this part of the complex, the platinum (Pt) is coordinated to four iodide (I⁻) ions. Similarly, each I⁻ is also a monodentate ligand and binds through a single donor atom (iodine). Thus, the coordination number of Pt in this complex is also 4.
In summary, both platinum centers in the complex have a coordination number of 4. Therefore, the coordination number for the entire complex \([Pt(NH_3)_4][PtI_4]\) reflects that both platinum centers contribute a coordination number of 4 for their respective ligands.