Which of the following is a decreasing order of oxidation states of the central atoms?

Options

A. (A) `PCl_(5), HIO_(4), Cl_(2)O_(7)^(2-), Cl_(2)O`
B. (B) `Cr_(2)O_(7)^(2-), Cl_(2)O, HIO_(4), PCl_(5)`
C. (C) `HIO_(4), Cr_(2)O_(7)^(2-), PCl_(5), Cl_(2)O`
D. (D) `Cr_(2)O_(7)^(2-), HIO_(4), Cl_(2)O, PCl_(5)`

Explanation

To determine the decreasing order of oxidation states of the central atoms in the given compounds, we will calculate the oxidation states for each central atom in the compounds provided.

### Step-by-Step Solution:

1. **Identify the Compounds and Central Atoms**:
- The compounds we need to analyze are:
- A: PCl₅ (Central atom: P)
- B: HIO₄ (Central atom: I)
- C: Cr₂O₇²⁻ (Central atom: Cr)
- D: Cl₂O (Central atom: Cl)

2. **Calculate the Oxidation State of Phosphorus in PCl₅**:
- The oxidation state of P (let's denote it as X) can be calculated using the formula:
\[ X + 5(-1) = 0 \]
\[ X - 5 = 0 \implies X = +5 \]

3. **Calculate the Oxidation State of Iodine in HIO₄**:
- The oxidation state of I (let's denote it as Y) can be calculated as follows:
\[ Y + 1(+1) + 4(-2) = 0 \]
\[ Y + 1 - 8 = 0 \implies Y = +7 \]

4. **Calculate the Oxidation State of Chromium in Cr₂O₇²⁻**:
- The oxidation state of Cr (let's denote it as Z) can be calculated using:
\[ 2Z + 7(-2) = -2 \]
\[ 2Z - 14 = -2 \implies 2Z = 12 \implies Z = +6 \]

5. **Calculate the Oxidation State of Chlorine in Cl₂O**:
- The oxidation state of Cl (let's denote it as W) can be calculated as:
\[ 2W + 1(-2) = 0 \]
\[ 2W - 2 = 0 \implies 2W = 2 \implies W = +1 \]

6. **Summary of Oxidation States**:
- P in PCl₅: +5
- I in HIO₄: +7
- Cr in Cr₂O₇²⁻: +6
- Cl in Cl₂O: +1

7. **Arrange the Oxidation States in Decreasing Order**:
- The decreasing order of oxidation states is:
- HIO₄ (I: +7)
- Cr₂O₇²⁻ (Cr: +6)
- PCl₅ (P: +5)
- Cl₂O (Cl: +1)

### Final Answer:
The decreasing order of oxidation states of the central atoms is:
**HIO₄ > Cr₂O₇²⁻ > PCl₅ > Cl₂O**