Which one of the following orders correctly represents the increasing acid strengths of the given acids:

Options

A. `HOClO_(3) lt HOClO_(2) lt HOClO lt HOCl`
B. `HOCl lt HOClO lt HOClO_(2) lt HOClO_(3) `
C. `HOClO lt HOCl lt HOClO_(3) lt HOClO_(2)`
D. `HOClO_(2) lt HOClO_(3) lt HOClO lt HOCl`

Answer

To determine the increasing acid strengths of the given oxoacids (HOCl, HClO2, HClO3, HClO4), we need to analyze the oxidation states of chlorine in each acid and how they relate to acid strength.

### Step-by-Step Solution:

1. **Identify the Oxoacids**: The oxoacids we are comparing are:
- HOCl (Hypochlorous acid)
- HClO2 (Chlorous acid)
- HClO3 (Chloric acid)
- HClO4 (Perchloric acid)

2. **Calculate the Oxidation State of Chlorine in Each Acid**:
- For **HOCl**:
- Let the oxidation state of Cl be \( x \).
- The equation is: \( 1 + x - 2 = 0 \) (where +1 is for H and -2 is for O).
- Solving gives \( x = +1 \).

- For **HClO2**:
- The equation is: \( 1 + x - 2 \times 2 = 0 \).
- Solving gives \( x + 1 - 4 = 0 \) or \( x = +3 \).

- For **HClO3**:
- The equation is: \( 1 + x - 3 \times 2 = 0 \).
- Solving gives \( x + 1 - 6 = 0 \) or \( x = +5 \).

- For **HClO4**:
- The equation is: \( 1 + x - 4 \times 2 = 0 \).
- Solving gives \( x + 1 - 8 = 0 \) or \( x = +7 \).

3. **Determine the Acid Strength Based on Oxidation States**:
- The acid strength of oxoacids generally increases with the increase in the oxidation state of the central atom (chlorine in this case). This is because a higher oxidation state leads to a stronger pull on the O-H bond, making it easier to release H⁺ ions.
- The oxidation states we calculated are:
- HOCl: +1
- HClO2: +3
- HClO3: +5
- HClO4: +7

4. **Order the Acids by Increasing Strength**:
- Based on the oxidation states, the order of increasing acid strength is:
- HOCl (least acidic, +1)
- HClO2 (+3)
- HClO3 (+5)
- HClO4 (most acidic, +7)

5. **Final Answer**:
- The correct order representing the increasing acid strengths of the given acids is:
- HOCl < HClO2 < HClO3 < HClO4