Reaction and Mole Calculation
Step 1: Reaction Equation
The balanced chemical reaction is:
\[ 2 \text{KI} + 2 \text{K}_3[\text{Fe(CN)}_6] \xrightarrow{\text{H}^+} \text{I}_2 + 2 \text{K}_4[\text{Fe(CN)}_6] \]
Step 2: Mole Calculation
From the reaction, 2 moles of KI react with 2 moles of \( \text{K}_3[\text{Fe(CN)}_6] \) to produce 1 mole of \( \text{I}_2 \) and 2 moles of \( \text{K}_4[\text{Fe(CN)}_6] \).
The stoichiometric ratio between KI and \( \text{K}_3[\text{Fe(CN)}_6] \) is 1:1.
If 2 moles of \( \text{K}_3[\text{Fe(CN)}_6] \) are used, 2 moles of KI are required.
To solve the problem, we need to determine the number of moles of potassium iodide required to produce 2 moles of complex \( P \) when potassium iodide reacts with potassium ferricyanide.
1. Reaction and complex formation:
- Potassium ferricyanide: \( \mathrm{K_3[Fe(CN)_6]} \)
- Potassium iodide: \( \mathrm{KI} \)
- Reaction forms complex \( P \) reversibly.
- In strong acidic medium, equilibrium shifts completely towards \( P \).
2. Stoichiometry:
- The complex \( P \) is formed by the reaction of potassium ferricyanide with potassium iodide.
- Each mole of potassium ferricyanide requires 1 mole of potassium iodide to form 1 mole of complex \( P \) (typical for such redox/complex formation reactions).
- To form 2 moles of \( P \), 2 moles of potassium iodide are required.
Final Answer:
The number of moles of potassium iodide required to produce 2 moles of \( P \) is \(\boxed{2}\).
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?