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 determine the formula of the halide for the metal A, given that its oxide is \( M_2O_3 \), we can follow these steps:

### Step 1: Determine the oxidation state of metal A
The formula \( M_2O_3 \) indicates that there are 2 moles of metal A (M) for every 3 moles of oxygen (O). Oxygen typically has an oxidation state of -2. Therefore, the total oxidation state contributed by oxygen in \( M_2O_3 \) is:
\[ 3 \times (-2) = -6 \]
To balance this, the total oxidation state contributed by the metal A must be +6. Since there are 2 moles of metal A, we can find the oxidation state of one metal A atom:
\[ \text{Oxidation state of } M = \frac{+6}{2} = +3 \]

### Step 2: Determine the formula of the halide
Halides are typically formed from metals and halogens. The halogens (like Cl, Br, I) usually have an oxidation state of -1. Since the oxidation state of metal A is +3, we need three halide ions to balance the charge of one metal ion.

Thus, the formula for the halide will be:
\[ M^{3+} + 3X^{-} \rightarrow MX_3 \]
where \( X \) represents the halogen.

### Step 3: Write the final formula
Since we have established that the metal A has a +3 oxidation state and requires three halide ions, the formula of the halide for metal A is:
\[ MX_3 \]

### Conclusion
The formula of the halide for the metal A, given that its oxide is \( M_2O_3 \), is \( MX_3 \).

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