A mineral of titanium (perovskite) is found to contain calcium ions at the corners, oxygen atoms at the face centres and titanium atoms at the centre of the cube. The oxidation state of titanium in the mineral is

Options

A. `+1`
B. `+3`
C. `+4`
D. `+2`

Explanation

To determine the oxidation state of titanium in the mineral perovskite, we can follow these steps:

### Step 1: Identify the positions of the ions in the unit cell
- The mineral contains:
- Calcium ions (Ca²⁺) at the corners of the cube
- Oxygen atoms (O²⁻) at the face centers
- Titanium atoms (Ti⁴⁺) at the center of the cube

### Step 2: Calculate the number of each type of atom in the unit cell
- **Calcium (Ca²⁺)**:
- There are 8 corners in a cube.
- Each corner contributes \( \frac{1}{8} \) of an atom.
- Total contribution from calcium:
\[ 8 \times \frac{1}{8} = 1 \text{ Ca atom} \]

- **Oxygen (O²⁻)**:
- There are 6 faces in a cube.
- Each face contributes \( \frac{1}{2} \) of an atom.
- Total contribution from oxygen:
\[ 6 \times \frac{1}{2} = 3 \text{ O atoms} \]

- **Titanium (Ti⁴⁺)**:
- There is 1 titanium atom at the center of the cube.
- Total contribution from titanium:
\[ 1 \text{ Ti atom} \]

### Step 3: Write the empirical formula based on the contributions
- The empirical formula for the mineral based on the contributions is:
\[ \text{Ca}_1\text{Ti}_1\text{O}_3 \]

### Step 4: Assign oxidation states to the ions
- **Calcium (Ca²⁺)**: +2
- **Oxygen (O²⁻)**: -2 (for 3 oxygen atoms, total = -6)
- **Titanium (Ti)**: Let its oxidation state be \( +X \)

### Step 5: Set up the charge balance equation
- The total positive charge must equal the total negative charge in the compound:
\[ \text{Total positive charge} = \text{Total negative charge} \]
\[ +2 + X + (-6) = 0 \]

### Step 6: Solve for \( X \)
- Rearranging the equation:
\[ X - 4 = 0 \]
\[ X = +4 \]

### Conclusion
- The oxidation state of titanium in the mineral perovskite is \( +4 \).

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