The geometrical arrangement and shape of `I_3^-` are respectively

Options

A. Trigonal bipyramidal geometry , linear shape
B. Hexagonal geometry, T-shape
C. Triangular planar geometry , triangular shape
D. Tetrahedral geometry, pyramidal shape .

Answer

To determine the geometrical arrangement and shape of the ion \( I_3^- \), we can follow these steps:

### Step 1: Determine the Valence Electrons
Iodine (I) is in Group 17 of the periodic table, which means it has 7 valence electrons. Since we have three iodine atoms in \( I_3^- \), we will calculate the total number of valence electrons.

- Total valence electrons from three iodine atoms:
\[ 3 \times 7 = 21 \text{ electrons} \]

### Step 2: Account for the Negative Charge
The negative charge on \( I_3^- \) indicates that there is one extra electron. Therefore, we add this to the total number of valence electrons.

- Total valence electrons:
\[ 21 + 1 = 22 \text{ electrons} \]

### Step 3: Draw the Lewis Structure
In the Lewis structure, we will arrange the three iodine atoms and distribute the valence electrons.

- Place one iodine atom in the center and the other two iodine atoms on either side.
- Connect the outer iodine atoms to the central iodine with single bonds. This uses 4 electrons (2 for each bond).
- Remaining electrons:
\[ 22 - 4 = 18 \text{ electrons} \]
- Distribute the remaining electrons as lone pairs on the iodine atoms. Each iodine will have three lone pairs (6 electrons) and the central iodine will have one lone pair (2 electrons).

### Step 4: Calculate the Steric Number
The steric number is calculated by adding the number of sigma bonds and lone pairs around the central atom.

- Sigma bonds: 2 (from the two \( I-I \) bonds)
- Lone pairs: 3 (on the central iodine)

- Steric number:
\[ \text{Steric number} = 2 + 3 = 5 \]

### Step 5: Determine Hybridization
The steric number of 5 indicates that the hybridization of the central iodine atom is \( sp^3d \).

### Step 6: Determine Geometry and Shape
With \( sp^3d \) hybridization and a steric number of 5, the geometry is trigonal bipyramidal. However, since there are three lone pairs, the shape of the molecule will be linear.

### Conclusion
The geometrical arrangement of \( I_3^- \) is trigonal bipyramidal, and its shape is linear.

### Final Answer
- Geometrical Arrangement: Trigonal Bipyramidal
- Shape: Linear

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