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 \(\boxed{2}\).
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As shown in the figures, a uniform rod $ OO' $ of length $ l $ is hinged at the point $ O $ and held in place vertically between two walls using two massless springs of the same spring constant. The springs are connected at the midpoint and at the top-end $ (O') $ of the rod, as shown in Fig. 1, and the rod is made to oscillate by a small angular displacement. The frequency of oscillation of the rod is $ f_1 $. On the other hand, if both the springs are connected at the midpoint of the rod, as shown in Fig. 2, and the rod is made to oscillate by a small angular displacement, then the frequency of oscillation is $ f_2 $. Ignoring gravity and assuming motion only in the plane of the diagram, the value of $\frac{f_1}{f_2}$ is:
The reaction sequence given below is carried out with 16 moles of X. The yield of the major product in each step is given below the product in parentheses. The amount (in grams) of S produced is ____. 
Use: Atomic mass (in amu): H = 1, C = 12, O = 16, Br = 80
Let $ a_0, a_1, ..., a_{23} $ be real numbers such that $$ \left(1 + \frac{2}{5}x \right)^{23} = \sum_{i=0}^{23} a_i x^i $$ for every real number $ x $. Let $ a_r $ be the largest among the numbers $ a_j $ for $ 0 \leq j \leq 23 $. Then the value of $ r $ is ________.
Let $ \mathbb{R} $ denote the set of all real numbers. Then the area of the region $$ \left\{ (x, y) \in \mathbb{R} \times \mathbb{R} : x > 0, y > \frac{1}{x},\ 5x - 4y - 1 > 0,\ 4x + 4y - 17 < 0 \right\} $$ is