In which of the following pairs is there the greatest difference in the oxidation numbers of the underlined elements?

Options

A. `ul(N)O_(2)` and `ul(N_(2))O_(4)`
B. `ul(S)O_(3)^(2)` and `ul(S)O_(4)^(2-)`
C. `ul(S)^(2-)` and `ul(S)O_(3)^(2-)`
D. `ul(S)^(2-)` and `ul(S)O_(4)^(2-)`

Explanation

To determine the greatest difference in oxidation numbers of the underlined elements in the given pairs, we will calculate the oxidation numbers for each element in the pairs and find the difference. Here’s how to approach the problem step by step:

### Step 1: Identify the pairs and the underlined elements.
Assume the pairs are:
1. Pair 1: N in N2 and N in some compound (let's say NO2)
2. Pair 2: S in SO2 and S in SO4^2-
3. Pair 3: S in S^2- and S in SO3^2-
4. Pair 4: S in S^2- and S in SO4^2-

### Step 2: Calculate the oxidation numbers for each underlined element.

1. **For Pair 1 (N in N2 and NO2)**:
- In N2, the oxidation number of nitrogen (N) = 0 (elemental form).
- In NO2, the oxidation number of nitrogen (N) can be calculated as follows:
- Let the oxidation number of N be x.
- For NO2: x + 2(-2) = 0 → x - 4 = 0 → x = +4.
- Difference in oxidation number = |0 - 4| = 4.

2. **For Pair 2 (S in SO2 and SO4^2-)**:
- In SO2, the oxidation number of sulfur (S):
- Let the oxidation number of S be y.
- For SO2: y + 2(-2) = 0 → y - 4 = 0 → y = +4.
- In SO4^2-, the oxidation number of sulfur (S):
- Let the oxidation number of S be z.
- For SO4^2-: z + 4(-2) = -2 → z - 8 = -2 → z = +6.
- Difference in oxidation number = |4 - 6| = 2.

3. **For Pair 3 (S in S^2- and SO3^2-)**:
- In S^2-, the oxidation number of sulfur (S) = -2.
- In SO3^2-, the oxidation number of sulfur (S):
- Let the oxidation number of S be w.
- For SO3^2-: w + 3(-2) = -2 → w - 6 = -2 → w = +4.
- Difference in oxidation number = |-2 - 4| = 6.

4. **For Pair 4 (S in S^2- and SO4^2-)**:
- In S^2-, the oxidation number of sulfur (S) = -2.
- In SO4^2-, we already calculated that the oxidation number of sulfur (S) = +6.
- Difference in oxidation number = |-2 - 6| = 8.

### Step 3: Compare the differences calculated.
- Pair 1: Difference = 4
- Pair 2: Difference = 2
- Pair 3: Difference = 6
- Pair 4: Difference = 8

### Conclusion:
The greatest difference in oxidation numbers is found in Pair 4, which is 8.

### Final Answer:
The correct option is **Pair 4 (S in S^2- and SO4^2-)** with a difference of 8.

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