1. Oxidation and Reduction Reactions:
We are given the following overall reaction for the electrochemical process:
$ \text{N}_2\text{H}_4 + \text{O}_2 \longrightarrow \text{N}_2 + \text{H}_2\text{O}^{2-} $
2. At the Anode (Oxidation):
The oxidation reaction at the anode is:
$ \text{N}_2\text{H}_4 + 4 \text{OH}^- \longrightarrow \text{N}_2 + 4 \text{H}_2\text{O} + 4 e^- $
3. At the Cathode (Reduction):
The reduction reaction at the cathode is:
$ \text{O}_2 + 2 \text{H}_2\text{O} + 4 e^- \longrightarrow 4 \text{OH}^- $
4. Complete Reaction:
The complete reaction combining both oxidation and reduction is:
$ \text{N}_2\text{H}_4 + \text{O}_2 \longrightarrow \text{N}_2 + 2 \text{H}_2\text{O} $
5. Conclusion:
The correct statements are (A) and (C).
To solve the problem, analyze the electrochemical oxidation of hydrazine (\(N_2H_4\)) by oxygen, focusing on reactions at the anode and cathode and products formed.
1. Anode reaction:
In alkaline medium, hydrazine is oxidized at the anode:
\[
N_2H_4 + 4OH^- \rightarrow N_2(g) + 4H_2O + 4e^-
\]
Hydroxide ions react with hydrazine to form nitrogen gas, water, and release electrons.
Option 1 is correct.
2. Cathode reaction:
Oxygen is reduced at the cathode:
\[
O_2 + 2H_2O + 4e^- \rightarrow 4OH^-
\]
Molecular oxygen gets converted to hydroxide ions.
Option 3 is correct.
3. Option 2 analysis:
Hydrazine does not undergo reduction at the cathode in this process; instead, oxygen is reduced. Nascent hydrogen is not formed.
Option 2 is incorrect.
4. By-products:
Electrochemical oxidation of hydrazine mainly produces nitrogen and water; oxides of nitrogen are not major by-products.
Option 4 is incorrect.
Final Answer:
Options 1 and 3 are correct.


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?