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. `[TiBr_(6)]^(3-)`
B. `[Ti(H_(2)O)_(6)Br_(4)`
C. `[TiBr_(6)]^(2-)`
D. `Ti(H_(2)O)_(4)Br_(2)]`

Answer

To solve the problem regarding the aqueous solution of titanium bromide that shows zero magnetic moment, we will follow these steps:

### Step 1: Understand the Magnetic Moment
The magnetic moment (μ) is calculated using the formula:
\[ \mu = \sqrt{n(n + 2)} \]
where \(n\) is the number of unpaired electrons. For a magnetic moment to be zero, \(n\) must be zero, meaning there are no unpaired electrons.

### Step 2: Identify the Oxidation State of Titanium
Given that titanium bromide is in an aqueous solution and shows zero magnetic moment, we need to determine the oxidation state of titanium in the complex.

Assuming the complex is octahedral, we can represent it as \([Ti(H_2O)_6]^{x}\) with bromide ions \(Br^-\) balancing the charge.

### Step 3: Write the Charge Balance Equation
Let’s consider the complex as \([Ti(H_2O)_6]^{4+}\) and the bromide ions as \(Br^-\). The overall charge of the complex must equal the charge contributed by the bromide ions.

If we assume the complex has a total charge of +4, the equation can be set up as:
\[ x + 6(-1) = -3 \quad \text{(for 3 bromide ions)} \]
This gives us:
\[ x - 6 = -3 \implies x = +3 \]

### Step 4: Determine the Electron Configuration
Titanium (Ti) has an atomic number of 22. The ground state electron configuration is:
\[ [Ar] 4s^2 3d^2 \]
When titanium is in the +3 oxidation state, it loses three electrons (two from 4s and one from 3d):
\[ \text{For } Ti^{3+}: [Ar] 4s^0 3d^1 \]
This means there is **1 unpaired electron** in the \(3d\) orbital.

### Step 5: Check Other Possible Oxidation States
Next, we check for the +4 oxidation state:
Assuming the complex is \([Ti(H_2O)_6]^{4+}\):
\[ x + 6(0) = +4 \quad \text{(for neutral water)} \]
This gives us:
\[ x = +4 \]
The electron configuration for \(Ti^{4+}\) would be:
\[ [Ar] 4s^0 3d^0 \]
This means there are **0 unpaired electrons**.

### Step 6: Conclusion
Since we need a complex that shows zero magnetic moment, the correct oxidation state is +4, which corresponds to the configuration \( [Ar] 4s^0 3d^0 \). Therefore, the formula of the complex is:
\[ [Ti(H_2O)_6]^{4+} \]

### Final Answer
The formula of the complex is \([Ti(H_2O)_6]^{4+}\).

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