Perovskite is a mineral composed of `Ca, Ti` and oxygen, cations of titanium lie at the centre, oxides ions at the face centres and calcium ions lie at corners. In this compound the oxidation number of Titanium is `+x`. Find the value of x?

Answer

To find the oxidation number of Titanium (Ti) in the perovskite mineral composed of Calcium (Ca), Titanium (Ti), and Oxygen (O), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Composition of Perovskite**:
- The formula for perovskite is generally represented as \( CaTiO_3 \). Here, Calcium (Ca) is at the corners, Titanium (Ti) is at the center, and Oxygen (O) is at the face centers.

2. **Determine the Contributions of Each Ion**:
- **Calcium (Ca)**: There are 8 corner positions, and each corner contributes \( \frac{1}{8} \) of a Ca ion. Therefore, the total contribution from Calcium is:
\[ 8 \times \frac{1}{8} = 1 \text{ Ca ion} \]
- **Titanium (Ti)**: There is 1 Ti ion at the body center.
- **Oxygen (O)**: There are 6 face centers, and each face center contributes \( \frac{1}{2} \) of an O ion. Therefore, the total contribution from Oxygen is:
\[ 6 \times \frac{1}{2} = 3 \text{ O ions} \]

3. **Write the Oxidation State Equation**:
- The overall charge of the compound must be neutral (0). The oxidation states can be represented as:
\[ \text{Oxidation state of Ca} + \text{Oxidation state of Ti} + \text{Oxidation state of O} = 0 \]
- Assign the oxidation states:
- Oxidation state of Ca = +2 (since it is a group 2 element)
- Oxidation state of Ti = \( +x \) (what we need to find)
- Oxidation state of O = -2 (common oxidation state for oxygen)

4. **Set Up the Equation**:
- Substituting the oxidation states into the equation gives:
\[ +2 + x + 3(-2) = 0 \]

5. **Simplify the Equation**:
- This simplifies to:
\[ +2 + x - 6 = 0 \]
- Rearranging gives:
\[ x - 4 = 0 \]

6. **Solve for x**:
- Therefore, \( x = +4 \).

### Conclusion:
The oxidation number of Titanium (Ti) in the perovskite mineral \( CaTiO_3 \) is \( +4 \).