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 1: Determine the formula of the compound
In perovskite, the arrangement of ions is as follows:
- Calcium ions (Ca²⁺) are located at the corners of the cube.
- Titanium ions (Ti⁴⁺) are located at the center of the cube.
- Oxygen ions (O²⁻) are located at the face centers.

### Step 2: Calculate the number of each type of ion
- **Calcium (Ca)**: There are 8 corners in a cube, and each corner contributes 1/8 of a Ca atom. Therefore, the total contribution from calcium is:
\[ 8 \times \frac{1}{8} = 1 \text{ Ca atom} \]

- **Oxygen (O)**: There are 6 faces on a cube, and each face contributes 1/2 of an O atom. Therefore, the total contribution from oxygen is:
\[ 6 \times \frac{1}{2} = 3 \text{ O atoms} \]

- **Titanium (Ti)**: There is 1 titanium atom located at the center of the cube, contributing:
\[ 1 \text{ Ti atom} \]

### Step 3: Write the empirical formula
From the contributions calculated, the empirical formula of perovskite can be written as:
\[ \text{CaTiO}_3 \]

### Step 4: Assign oxidation states
Let the oxidation state of titanium be \( +x \). The oxidation states of the other elements are:
- Calcium (Ca) has an oxidation state of \( +2 \).
- Oxygen (O) has an oxidation state of \( -2 \).

### Step 5: Set up the equation based on the overall charge
The sum of the oxidation states in a neutral compound must equal zero. Therefore, we can set up the equation:
\[ (+2) + (x) + 3 \times (-2) = 0 \]

### Step 6: Simplify the equation
This simplifies to:
\[ 2 + x - 6 = 0 \]
\[ x - 4 = 0 \]

### Step 7: Solve for \( x \)
Solving for \( x \) gives:
\[ x = 4 \]

### Conclusion
The oxidation number of titanium in perovskite is \( +4 \).

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