Step 1: Understanding the Concept:
The oxidation state (or oxidation number) represents the degree of oxidation of an atom in a chemical compound. It is a formal charge assigned to an atom assuming that all bonds to different elements are 100% ionic. However, in complex oxyacids like Marshall's acid (peroxodisulfuric acid), relying solely on the formula H\(_{2}\)S\(_{2}\)O\(_{8}\) and general rules (H=+1, O=-2) can lead to erroneous results. This is because standard rules fail to account for special bonding environments such as peroxide linkages (\(-O-O-\)). In a peroxide bond, the oxygen atoms are bonded to each other, and each oxygen is assigned an oxidation state of -1 instead of the usual -2. Sulfur, being a Group 16 element, has 6 valence electrons, meaning its maximum possible oxidation state is +6. Any calculation yielding a value higher than +6 indicates a structural anomaly like a peroxide bond.
Step 2: Key Formula or Approach:
The chemical structure of Marshall's acid is \(HO-SO_{2}-O-O-SO_{2}-OH\).
From this structure, we can categorize the atoms:
- 2 Hydrogen atoms (each is +1).
- 2 Sulfur atoms (let their oxidation state be \(x\)).
- 6 "Normal" Oxygen atoms (bonded to S or H, each is -2).
- 2 "Peroxide" Oxygen atoms (forming the bridge between Sulfurs, each is -1).
The sum of all oxidation states in a neutral molecule is equal to zero.
Step 3: Detailed Explanation:
Let's set up the algebraic equation based on the structural breakdown:
\[ 2(\text{H}) + 2(\text{S}) + 6(\text{O}_{\text{oxide}}) + 2(\text{O}_{\text{peroxide}}) = 0 \]
Substituting the known values into the equation:
\[ 2(+1) + 2(x) + 6(-2) + 2(-1) = 0 \]
Simplifying the terms:
\[ 2 + 2x - 12 - 2 = 0 \]
The +2 and -2 cancel out, leaving:
\[ 2x - 12 = 0 \]
\[ 2x = 12 \]
\[ x = +6 \]
If we had ignored the peroxide bridge and used the standard formula method:
\[ 2(+1) + 2(x) + 8(-2) = 0 \Rightarrow 2 + 2x - 16 = 0 \Rightarrow 2x = 14 \Rightarrow x = +7 \]
Since Sulfur cannot have an oxidation state of +7 (as it only has 6 valence electrons to lose/share), the result of +7 is chemically impossible. This serves as a "red flag" that peroxide bonds exist in the molecule. Structure-based calculation correctly shows that each sulfur atom maintains its maximum stable oxidation state of +6 by sharing its valence electrons with the surrounding oxygens.
Step 4: Final Answer:
The oxidation state of sulfur in Marshall's acid (H\(_{2}\)S\(_{2}\)O\(_{8}\)) is +6.
Therefore, the correct answer is option (3).