The order of acidity of oxides of chlorine .
`{:(Cl_(2) O ,, Cl_(2) O_(3) ,, Cl_(2) O_(5) ,, Cl_(2)O_(7)), (I ,, II ,, III ,, IV):}` is

Options

A. `I lt II lt III lt IV `
B. `I gt II gt III gt IV`
C. `I gt III gt II gt IV`
D. `IV gt I gt II gt III`

Answer

To determine the order of acidity of the oxides of chlorine, we need to analyze the oxidation states of chlorine in each oxide. The general rule is that the higher the oxidation state of the central atom (in this case, chlorine), the higher the acidity of the oxide.

Let's calculate the oxidation states of chlorine in each oxide:

1. **Cl₂O**:
- Let the oxidation state of Cl be \( x \).
- The equation for the compound is:
\[ 2x + (-2) = 0 \]
- Solving for \( x \):
\[ 2x = 2 \implies x = 1 \]
- Therefore, the oxidation state of chlorine in Cl₂O is +1.

2. **Cl₂O₃**:
- Let the oxidation state of Cl be \( x \).
- The equation for the compound is:
\[ 2x + 3(-2) = 0 \]
- Solving for \( x \):
\[ 2x - 6 = 0 \implies 2x = 6 \implies x = 3 \]
- Therefore, the oxidation state of chlorine in Cl₂O₃ is +3.

3. **Cl₂O₅**:
- Let the oxidation state of Cl be \( x \).
- The equation for the compound is:
\[ 2x + 5(-2) = 0 \]
- Solving for \( x \):
\[ 2x - 10 = 0 \implies 2x = 10 \implies x = 5 \]
- Therefore, the oxidation state of chlorine in Cl₂O₅ is +5.

4. **Cl₂O₇**:
- Let the oxidation state of Cl be \( x \).
- The equation for the compound is:
\[ 2x + 7(-2) = 0 \]
- Solving for \( x \):
\[ 2x - 14 = 0 \implies 2x = 14 \implies x = 7 \]
- Therefore, the oxidation state of chlorine in Cl₂O₇ is +7.

Now we have the oxidation states:
- Cl₂O: +1
- Cl₂O₃: +3
- Cl₂O₅: +5
- Cl₂O₇: +7

Based on the oxidation states, we can determine the order of acidity:
- Higher oxidation state corresponds to higher acidity.
- Therefore, the order of acidity from least acidic to most acidic is:
\[ \text{Cl}_2\text{O} < \text{Cl}_2\text{O}_3 < \text{Cl}_2\text{O}_5 < \text{Cl}_2\text{O}_7 \]

Thus, the final answer is:
\[ \text{I} < \text{II} < \text{III} < \text{IV} \]