The shape of `[Co(NH_(3))_(6)]^(3+)` is

Options

A. Tetrahedral
B. Trigonal bipyramidal
C. Octahedral
D. Square planar

Explanation

To determine the shape of the complex ion \([Co(NH_3)_6]^{3+}\), we can follow these steps:

### Step 1: Identify the Central Metal Ion and Its Oxidation State
The central metal ion in this complex is cobalt (Co). The overall charge of the complex is \(3+\). Since ammonia (NH₃) is a neutral ligand, the oxidation state of cobalt must be \(+3\).

**Hint:** Remember that the oxidation state of the metal ion can be determined by considering the charges of the ligands attached to it.

### Step 2: Determine the Electron Configuration of Cobalt in the \(+3\) State
Cobalt has an atomic number of 27, and its electron configuration in the neutral state is \([Ar] 4s^2 3d^7\). When cobalt is in the \(+3\) oxidation state, it loses 3 electrons, typically from the 4s and 3d orbitals. Therefore, the electron configuration for \(Co^{3+}\) is \([Ar] 3d^6\).

**Hint:** The oxidation state affects the electron configuration, particularly which orbitals lose electrons.

### Step 3: Identify the Ligands and Their Nature
The complex contains six ammonia (NH₃) ligands. Ammonia is a weak field ligand, which means it does not cause significant pairing of electrons in the d-orbitals.

**Hint:** The nature of the ligands (weak or strong field) influences the arrangement of electrons in the d-orbitals.

### Step 4: Determine the Hybridization
In this case, with six ligands surrounding the cobalt ion, we can predict the hybridization. The coordination number is 6, which typically leads to an octahedral geometry. The hybridization for an octahedral complex is \(d^2sp^3\).

**Hint:** The hybridization can be determined by the number of ligands and the coordination number.

### Step 5: Conclude the Geometry of the Complex
Given that the hybridization is \(d^2sp^3\) and the coordination number is 6, the geometry of the complex \([Co(NH_3)_6]^{3+}\) is octahedral.

**Hint:** The geometry of a complex can often be inferred from the hybridization and coordination number.

### Final Answer
The shape of the complex \([Co(NH_3)_6]^{3+}\) is **octahedral**.