The compound(s) having peroxide linkage is(are)

The correct compounds having a peroxide linkage are H₂S₂O₈ and H₂SO₅.

1. Understanding Peroxide Linkage:
A peroxide linkage is a single covalent bond between two oxygen atoms ($-O-O-$), where each oxygen atom has an oxidation state of -1.
Sulfur belongs to Group 16 and has 6 valence electrons, meaning its maximum possible oxidation state is +6. If a simple chemical calculation of the oxidation state of sulfur yields a value greater than +6, it strongly indicates the presence of a peroxide linkage (where some oxygen atoms are in the -1 oxidation state instead of -2).

2. Analyzing H₂S₂O₈ (Peroxodisulfuric acid / Marshall's acid):
Let the oxidation state of sulfur be $x$. Assuming all oxygen atoms have a standard oxidation state of -2:
$2(+1)+2\left(x\right)+8(-2)=0$
$2+2x-16=0$
$2x=14$
$x=+7$
Since the calculated oxidation state (+7) exceeds the maximum limit of +6, a peroxide bond must be present. The actual structure contains two sulfur atoms linked via a peroxide bridge: $O_{3}S-O-O-S{O}_3$ with two acidic hydrogen atoms attached, giving each sulfur an actual oxidation state of +6.

3. Analyzing H₂SO₅ (Peroxomonosulfuric acid / Caro's acid):
Let the oxidation state of sulfur be $x$. Assuming all oxygen atoms are -2:
$2(+1)+x+5(-2)=0$
$2+x-10=0$
$x=+8$
Since the calculated oxidation state (+8) is greater than +6, a peroxide linkage is present. The structure consists of a central sulfur atom bonded to one peroxo group ($-O-O-H$), leaving the actual oxidation state of sulfur at +6.

4. Analyzing other options:
- H₂S₂O₇ (Pyrosulfuric acid): The calculated oxidation state of sulfur is +6, which is equal to its maximum oxidation state. It has a $S-O-S$ linkage but no peroxide linkage.
- H₂S₂O₅ (Thiosulfurous/Pyrosulfurous acid): The calculated oxidation state of sulfur is +4, which is below the maximum limit, showing no peroxide linkage.