Increasing order of bond angle of `(Cl_(2)O, ClO_(2), Cl_(2)O_(7), I_(3)^(ɵ))` is

Options

A. `Cl_(2)O lt ClO_(2) lt Cl_(2)O_(7) lt I_(3)^(ɵ)`
B. `Cl_(2)O lt ClO_(2) lt I_(3)^(ɵ) lt Cl_(2)O_(7)`
C. `I_(3)^(ɵ) lt Cl_(2)O_(7) lt ClO_(2) lt Cl_(2)O`
D. `Cl_(2)O lt Cl_(2)O_(7) lt ClO_(2) lt I_(3)^(ɵ)`

Answer

To determine the increasing order of bond angles for the compounds \(Cl_2O\), \(ClO_2\), \(Cl_2O_7\), and \(I_3^{\circ}\), we need to analyze the molecular geometry and the presence of lone pairs of electrons around the central atoms in each compound.

### Step-by-Step Solution:

1. **Identify the Central Atom and Its Valence Electrons**:
- For \(Cl_2O\): The central atom is \(O\) (oxygen) which has 6 valence electrons.
- For \(ClO_2\): The central atom is \(Cl\) (chlorine) which has 7 valence electrons.
- For \(Cl_2O_7\): The central atom is again \(Cl\) (chlorine) which has 7 valence electrons.
- For \(I_3^{\circ}\): The central atom is \(I\) (iodine) which has 7 valence electrons.

2. **Determine the Molecular Geometry**:
- **\(Cl_2O\)**: Oxygen forms two single bonds with chlorine and has two lone pairs. The geometry is bent, leading to a bond angle of approximately \(110.8^\circ\).
- **\(ClO_2\)**: Chlorine forms two double bonds with oxygen and has one lone pair. The geometry is also bent, leading to a bond angle of approximately \(117^\circ\).
- **\(Cl_2O_7\)**: Chlorine forms multiple bonds with oxygen (7 bonds total) and has two lone pairs. The bond angles are approximately \(119^\circ\).
- **\(I_3^{\circ}\)**: The structure is linear due to the three iodine atoms arranged around a central iodine atom with three lone pairs. The bond angle is \(180^\circ\).

3. **Compare the Bond Angles**:
- \(Cl_2O\) has a bond angle of \(110.8^\circ\).
- \(ClO_2\) has a bond angle of \(117^\circ\).
- \(Cl_2O_7\) has a bond angle of \(119^\circ\).
- \(I_3^{\circ}\) has a bond angle of \(180^\circ\).

4. **Establish the Increasing Order**:
- From the bond angles calculated, we can establish the increasing order:
- \(Cl_2O < ClO_2 < Cl_2O_7 < I_3^{\circ}\)

### Final Answer:
The increasing order of bond angles is:
\[ Cl_2O < ClO_2 < Cl_2O_7 < I_3^{\circ} \]