Key Structural Features: $$\begin{aligned} \text{H}_2\text{S}_2\text{O}_8 \text{ (Peroxodisulfuric Acid):} &\quad \text{Contains a Peroxy Linkage } (-\text{O-O}-) \\ \text{H}_2\text{S}_2\text{O}_7 \text{ (Pyrosulfuric Acid / Oleum):} &\quad \text{Contains a Sulfone Linkage } (-\text{S-O-S}-) \end{aligned}$$
Concept: These dimeric sulfur oxoacids are distinguished by their structural bridges; Marshall's acid features a peroxide bond where sulfur retains its high oxidation state without exceeding its coordination cap, while Oleum represents a dehydrated sulfuric acid dimer.
Notation:
- $$\text{H}_2\text{S}_2\text{O}_8$$ = Marshall's acid ($$\text{S}$$ in $$+6$$ state);
- $$\text{H}_2\text{S}_2\text{O}_7$$ = Oleum/Fuming sulfuric acid ($$\text{S}$$ in $$+6$$ state).