Identification of Oxoacids of Sulfur Containing Peroxide Linkage

To determine which of the given oxoacids of sulfur contain a peroxide linkage ($-\text{O}-\text{O}-$), we examine the oxidation state of sulfur and the chemical structures of each compound.

Sulfur belongs to Group 16 and has 6 valence electrons; hence, its maximum possible oxidation state is $+6$. If the calculated average oxidation state of sulfur (assuming all oxygen atoms have an oxidation state of $-2$) exceeds $+6$, it indicates the presence of a peroxide linkage where the oxygen atoms involved have an oxidation state of $-1$.

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1. Option (A): $\text{H}_2\text{S}_2\text{O}_7$ (Pyrosulfuric acid / Oleum)

• Calculated oxidation state of $\text{S}$: $2(+1) + 2(x) + 7(-2) = 0 \implies 2x = 12 \implies x = +6$
• Since $x = +6$, which is equal to the maximum oxidation state of sulfur, there is no peroxide linkage.
• Structural arrangement: It contains an $\text{S}-\text{O}-\text{S}$ bridge: $\text{HO}-\text{SO}_2-\text{O}-\text{SO}_2-\text{OH}$

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2. Option (B): $\text{H}_2\text{S}_2\text{O}_8$ (Peroxydisulfuric acid / Marshall's acid)

• Calculated oxidation state of $\text{S}$: $2(+1) + 2(x) + 8(-2) = 0 \implies 2x = 14 \implies x = +7$
• Since $+7 > +6$, a peroxide linkage must be present to reduce the oxidation state of sulfur to its maximum of $+6$.
• Structural arrangement: It contains one peroxide linkage ($-\text{O}-\text{O}-$): $\text{HO}-\text{SO}_2-\text{O}-\text{O}-\text{SO}_2-\text{OH}$
• Actual oxidation states: The two peroxide oxygens have an oxidation state of $-1$, while the remaining six oxygens have $-2$, yielding $x = +6$ for sulfur.

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3. Option (C): $\text{H}_2\text{S}_2\text{O}_5$ (Pyrosulfurous acid)

• Calculated oxidation state of $\text{S}$: $2(+1) + 2(x) + 5(-2) = 0 \implies 2x = 8 \implies x = +4$
• Since $+4 < +6$, no peroxide linkage is present.
• Structural arrangement: It contains a direct $\text{S}-\text{S}$ single bond: $\text{HO}-\text{S}(=\text{O})-\text{SO}_2-\text{OH}$

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4. Option (D): $\text{H}_2\text{SO}_5$ (Peroxymonosulfuric acid / Caro's acid)

• Calculated oxidation state of $\text{S}$: $2(+1) + x + 5(-2) = 0 \implies x = +8$
• Since $+8 > +6$, a peroxide linkage must be present.
• Structural arrangement: It contains one hydroperoxide group ($-\text{O}-\text{O}-\text{H}$): $\text{HO}-\text{O}-\text{SO}_2-\text{OH}$
• Actual oxidation states: Two oxygens are part of the peroxide group (oxidation state $-1$), and the other three oxygens have $-2$, giving sulfur an oxidation state of $+6$.

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Conclusion:

The compounds that possess a peroxide linkage are $\text{H}_2\text{S}_2\text{O}_8$ and $\text{H}_2\text{SO}_5$.

Correct Options: (B) and (D)