Order of `pK_(a)`

Options

A. `HOClgtHClO_(2)gtHClO_(3)gtHClO_(4)`
B. `HClO_(4)gtHClO_(3)gtHClO_(2)gtHOCl`
C. `HClO_(4)gtHClO_(3)gtHClO_(4)gtHOCl`
D. `HClO_(3)gtHClO_(2)gtHOClgtHClO_(4)`

Answer

To determine the order of pKa values for the given acids, we need to analyze the oxidation states of the central atom (chlorine in this case) in each acid and how they relate to acidic strength and pKa values.

### Step-by-Step Solution:

1. **Understanding the Relationship Between Acidic Strength and pKa:**
- Acidic strength is directly proportional to the oxidation state of the central atom.
- Higher oxidation states lead to stronger acids, which means lower pKa values.
- Conversely, lower oxidation states correspond to weaker acids, resulting in higher pKa values.

2. **Identify the Acids and Their Structures:**
- The acids in question are:
- HOCl (Hypochlorous acid)
- HClO2 (Chlorous acid)
- HClO3 (Chloric acid)
- HClO4 (Perchloric acid)

3. **Calculate the Oxidation States of Chlorine in Each Acid:**
- **For HOCl:**
- Oxidation state of H = +1
- Oxidation state of O = -2
- Let oxidation state of Cl = X
- Equation: \( +1 + X - 2 = 0 \) → \( X = +1 \)

- **For HClO2:**
- Oxidation state of H = +1
- Oxidation state of O = -2 (2 oxygen atoms contribute -4)
- Let oxidation state of Cl = X
- Equation: \( +1 + X - 4 = 0 \) → \( X = +3 \)

- **For HClO3:**
- Oxidation state of H = +1
- Oxidation state of O = -2 (3 oxygen atoms contribute -6)
- Let oxidation state of Cl = X
- Equation: \( +1 + X - 6 = 0 \) → \( X = +5 \)

- **For HClO4:**
- Oxidation state of H = +1
- Oxidation state of O = -2 (4 oxygen atoms contribute -8)
- Let oxidation state of Cl = X
- Equation: \( +1 + X - 8 = 0 \) → \( X = +7 \)

4. **Determine the Order of Acidic Strength Based on Oxidation States:**
- The oxidation states calculated are:
- HOCl: +1
- HClO2: +3
- HClO3: +5
- HClO4: +7
- As the oxidation state increases, the acidic strength increases:
- HOCl < HClO2 < HClO3 < HClO4

5. **Determine the Order of pKa Values:**
- Since higher acidic strength corresponds to lower pKa values:
- pKa order will be the reverse of the acidic strength order:
- pKa: HOCl > HClO2 > HClO3 > HClO4

6. **Final Answer:**
- The correct order of pKa values is:
- **HOCl > HClO2 > HClO3 > HClO4**