Compound of a metal A is `M_2O_3` , the formula of its halide is

Options

A. `M_3X`
B. MX
C. `MX_3`
D. `M_3X_2`

Answer

To find the formula of the halide of the metal A, we start with the information given in the question:

1. **Identify the metal and its oxide**: The compound of metal A is given as \( M_2O_3 \). This indicates that metal A has a valency of 3 (since there are 2 metal atoms for every 3 oxygen atoms).

2. **Determine the valency of the metal**: From the formula \( M_2O_3 \), we can deduce that the valency of metal A (M) is 3. This is because the oxide ion (O) has a valency of 2, and the crisscross method shows that the metal must have a valency of 3 to balance the charges.

3. **Identify the halogen**: Halogens typically have a valency of 1. This is because they need one additional electron to achieve a stable noble gas configuration.

4. **Combine the valencies to find the halide formula**: To find the formula of the halide, we use the valencies of metal A and the halogen. The valency of metal A is 3 and the valency of the halogen is 1. Using the crisscross method, we write the formula as follows:
- The metal (M) with a valency of 3 will be combined with the halogen (X) with a valency of 1.
- Therefore, the formula will be \( MX_3 \).

5. **Conclusion**: The formula of the halide of metal A is \( MX_3 \).

### Summary of Steps:
1. Identify the metal and its oxide: \( M_2O_3 \).
2. Determine the valency of the metal: 3.
3. Identify the halogen's valency: 1.
4. Combine the valencies to find the halide formula: \( MX_3 \).
5. Conclude that the formula of the halide is \( MX_3 \).