An aqueous solution of titanium bromide shows zero magnetic moment. Assuming the complex as octahedral in aqueous solution, the formula of the complex is .

Options

A. `[Ti(H_(2)O)_(6)]Cl_(2)`
B. `[Ti(H_(2)O)_(6)]Cl_(4)`
C. `[TiCl_(3)(H_(2)O)_(3)]`
D. `[TiCl_(2)(H_(2)O)_(4)]`

Explanation

To solve the problem, we need to determine the formula of the titanium bromide complex that shows zero magnetic moment in an aqueous solution, assuming it has an octahedral geometry. Here’s a step-by-step breakdown of the solution:

### Step 1: Identify the oxidation states of titanium in the complex
1. **Understanding the charge of titanium bromide**: Titanium (Ti) can exist in multiple oxidation states, commonly +2, +3, and +4.
2. **Assuming the complex is octahedral**: In an octahedral complex, the coordination number is 6. The complex can be represented as Ti(H2O)6^x, where x is the oxidation state of titanium.
3. **Considering the bromide ions**: Since bromide (Br) is a monovalent anion (charge -1), the overall charge of the complex will depend on the number of bromide ions present.

### Step 2: Determine the possible complexes
1. **Possible complexes**:
- TiBr2(H2O)4
- TiBr3(H2O)3
- TiBr4(H2O)2
- TiBr5(H2O)1

2. **Calculate oxidation states**:
- For TiBr2(H2O)4:
- Charge = 2(-1) + x + 0 = 0 → x = +2
- For TiBr3(H2O)3:
- Charge = 3(-1) + x + 0 = 0 → x = +3
- For TiBr4(H2O)2:
- Charge = 4(-1) + x + 0 = 0 → x = +4
- For TiBr5(H2O)1:
- Charge = 5(-1) + x + 0 = 0 → x = +5 (not possible for Ti)

### Step 3: Analyze the magnetic properties
1. **Understanding magnetic moment**: A zero magnetic moment indicates that the complex is diamagnetic, meaning it has no unpaired electrons.
2. **Electronic configuration of titanium**:
- Ti (atomic number 22) has the electronic configuration: [Ar] 4s² 3d².
- For Ti²⁺: [Ar] 3d² (2 unpaired electrons) - paramagnetic.
- For Ti³⁺: [Ar] 3d¹ (1 unpaired electron) - paramagnetic.
- For Ti⁴⁺: [Ar] 3d⁰ (no unpaired electrons) - diamagnetic.

### Step 4: Conclusion
- The complex that shows zero magnetic moment must have titanium in the +4 oxidation state (Ti⁴⁺) since it is diamagnetic.
- The formula of the complex is **TiBr4(H2O)2** because it contains 4 bromide ions and 2 water molecules, leading to a +4 oxidation state for titanium.

### Final Answer
The formula of the complex is **TiBr4(H2O)2**.

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