To solve the problem, we need to identify the species produced during the disproportionation of aqueous nitrous acid (HNO2) at room temperature.
1. Understanding Disproportionation of HNO2:
Disproportionation is a redox reaction where a single species undergoes both oxidation and reduction. In the case of nitrous acid (HNO2), it can disproportionate as:
\[ 3 \, \text{HNO}_2 \rightarrow \text{HNO}_3 + 2 \, \text{NO} + \text{H}_2\text{O} \]
This reaction produces nitric acid (HNO3), nitric oxide (NO), and water.
2. Ionic forms in aqueous medium:
- Nitric acid dissociates into hydronium ion (H3O+) and nitrate ion (NO3-).
- Nitric oxide (NO) remains as a gas.
3. Therefore, species formed are:
\[
\text{H}_3\text{O}^+, \quad \text{NO}_3^-, \quad \text{NO}
\]
Final Answer:
H3O+, NO3-, and NO.
Let $ S $ denote the locus of the point of intersection of the pair of lines $$ 4x - 3y = 12\alpha,\quad 4\alpha x + 3\alpha y = 12, $$ where $ \alpha $ varies over the set of non-zero real numbers. Let $ T $ be the tangent to $ S $ passing through the points $ (p, 0) $ and $ (0, q) $, $ q > 0 $, and parallel to the line $ 4x - \frac{3}{\sqrt{2}} y = 0 $.
Then the value of $ pq $ is
Let $ y(x) $ be the solution of the differential equation $$ x^2 \frac{dy}{dx} + xy = x^2 + y^2, \quad x > \frac{1}{e}, $$ satisfying $ y(1) = 0 $. Then the value of $ 2 \cdot \frac{(y(e))^2}{y(e^2)} $ is ________.