Predict the dipole moment of :
(i) a molecule of the type `AX_(4)` having square planar geometry
(ii) a molecule of type `AX_(5)`having trigonal bipyramidal geometry
(iii) a molecule of the type `AX_(6)` having octahedral geometry.

Answer

To predict the dipole moments for the given molecular geometries, we will analyze each case step by step.

### Step 1: Molecule of type `AX4` with Square Planar Geometry
1. **Understand the Geometry**: The square planar geometry consists of four atoms (X) arranged at the corners of a square, with the central atom (A) at the center.
2. **Draw the Structure**: Visualize or draw the square planar structure:
```
X
/ \
X X
\ /
A
```
3. **Consider Electronegativity**: Assume that the electronegativity of atom X is greater than that of atom A. This means each bond will have a dipole moment pointing towards atom X.
4. **Analyze the Dipoles**: The dipoles from each bond will be equal in magnitude but opposite in direction:
- The dipoles from the top and bottom X atoms will cancel each other.
- The dipoles from the left and right X atoms will also cancel each other.
5. **Resultant Dipole Moment**: Since all dipoles cancel out, the resultant dipole moment for `AX4` in square planar geometry is **zero**.

### Step 2: Molecule of type `AX5` with Trigonal Bipyramidal Geometry
1. **Understand the Geometry**: The trigonal bipyramidal geometry consists of five atoms (X) with three in a plane (equatorial) and two above and below (axial).
2. **Draw the Structure**: Visualize or draw the trigonal bipyramidal structure:
```
X
|
X-A-X
|
X
```
3. **Consider Electronegativity**: Again, assume that the electronegativity of atom X is greater than that of atom A.
4. **Analyze the Dipoles**: The dipoles will point from A towards each X atom:
- The two axial dipoles will cancel each other.
- The three equatorial dipoles will also cancel each other due to symmetry.
5. **Resultant Dipole Moment**: Since all dipoles cancel out, the resultant dipole moment for `AX5` in trigonal bipyramidal geometry is **zero**.

### Step 3: Molecule of type `AX6` with Octahedral Geometry
1. **Understand the Geometry**: The octahedral geometry consists of six atoms (X) arranged around the central atom (A) at the vertices of an octahedron.
2. **Draw the Structure**: Visualize or draw the octahedral structure:
```
X
|
X-A-X
|
X
```
3. **Consider Electronegativity**: Assume that the electronegativity of atom X is greater than that of atom A.
4. **Analyze the Dipoles**: Each bond will have a dipole moment pointing towards atom X:
- The dipoles from opposite sides will cancel each other out.
5. **Resultant Dipole Moment**: Since all dipoles cancel out, the resultant dipole moment for `AX6` in octahedral geometry is **zero**.

### Final Conclusion
For all three types of molecules (`AX4`, `AX5`, and `AX6`), the resultant dipole moment is **zero** due to the symmetrical arrangement of the bond dipoles which cancel each other out.