To solve this problem, we need to analyze the reaction and the hydrolysis of the given compound to determine the number of moles of HF produced.
1. Analyzing the Reaction:
From the reaction between \( \text{Xe} \) and \( \text{O}_2\text{F}_2 \), a xenon compound \( P \) is formed. The xenon compound formed is likely to be xenon tetrafluoride (XeF₄), as this is a common product in such reactions involving xenon and oxygen difluoride. The reaction can be represented as follows:
\[ \text{Xe} + \text{O}_2\text{F}_2 \rightarrow \text{XeF}_4 + \text{O}_2 \]
2. Hydrolysis of Xenon Tetrafluoride (XeF₄):
When xenon tetrafluoride (\( \text{XeF}_4 \)) undergoes complete hydrolysis, it reacts with water to produce xenon dioxide (XeO₂) and hydrofluoric acid (HF). The reaction for the hydrolysis of 1 mole of xenon tetrafluoride is:
\[ \text{XeF}_4 + 4\text{H}_2\text{O} \rightarrow \text{XeO}_2 + 4\text{HF} \]
3. Conclusion:
For each mole of xenon tetrafluoride (\( \text{XeF}_4 \)) hydrolyzed, 4 moles of hydrofluoric acid (HF) are produced.
Final Answer:
The number of moles of HF produced by the complete hydrolysis of 1 mole of \( P \) (which is \( \text{XeF}_4 \)) is 4.
\(\text{Xe} + 2\text{O}_2 + \text{F}_2 \rightarrow \text{XeF}_4 + 2\text{O}_2\)
\(3\text{XeF}_4 + 6\text{H}_2\text{O} \rightarrow 2\text{Xe} + \text{XeO}_3 + \frac{23}{2}\text{O}_2 + 12\text{HF}\)
∴ One mole of \(\text{XeF}_4\) gives 4 moles of HF on hydrolysis.
Given below are two statements.
In the light of the above statements, choose the correct answer from the options given below:
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 $ 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 ________.
The left and right compartments of a thermally isolated container of length $L$ are separated by a thermally conducting, movable piston of area $A$. The left and right compartments are filled with $\frac{3}{2}$ and 1 moles of an ideal gas, respectively. In the left compartment the piston is attached by a spring with spring constant $k$ and natural length $\frac{2L}{5}$. In thermodynamic equilibrium, the piston is at a distance $\frac{L}{2}$ from the left and right edges of the container as shown in the figure. Under the above conditions, if the pressure in the right compartment is $P = \frac{kL}{A} \alpha$, then the value of $\alpha$ is ____