Structures of Sulfuric Acid Derivatives
1. Structure of \( \text{H}_2\text{S}_2\text{O}_7 \) (Pyrosulfuric Acid):
No peroxide linkage present.
2. Structure of \( \text{H}_2\text{S}_2\text{O}_8 \) (Peroxydisulfuric Acid):
Contains an \( -\text{O-O}- \) (peroxide) linkage.
3. Structure of \( \text{H}_2\text{S}_2\text{O}_5 \) (Pyro Sulfurous Acid):
No peroxide linkage present.
4. Structure of \( \text{H}_2\text{SO}_5 \) (Peroxomonosulfuric Acid):
Contains an \( -\text{O-O}- \) (peroxide) linkage.
To solve the problem, identify which compound(s) contain a peroxide (–O–O–) linkage.
Analysis of compounds:
Final Answer:
Compounds with peroxide linkage are:
\[
\boxed{\text{H}_2\text{S}_2\text{O}_8 \text{ and } \text{H}_2\text{SO}_5}
\]
Let $ P(x_1, y_1) $ and $ Q(x_2, y_2) $ be two distinct points on the ellipse $$ \frac{x^2}{9} + \frac{y^2}{4} = 1 $$ such that $ y_1 > 0 $, and $ y_2 > 0 $. Let $ C $ denote the circle $ x^2 + y^2 = 9 $, and $ M $ be the point $ (3, 0) $. Suppose the line $ x = x_1 $ intersects $ C $ at $ R $, and the line $ x = x_2 $ intersects $ C $ at $ S $, such that the $ y $-coordinates of $ R $ and $ S $ are positive. Let $ \angle ROM = \frac{\pi}{6} $ and $ \angle SOM = \frac{\pi}{3} $, where $ O $ denotes the origin $ (0, 0) $. Let $ |XY| $ denote the length of the line segment $ XY $. Then which of the following statements is (are) TRUE?