The correct option is (C): \(Cl _2 O _6\)
When chloric acid (\(HClO_3\)) reacts with hydrochloric acid (\(HCl\)), it forms chlorine dioxide (\(ClO_2\)), which is a paramagnetic gas. The balanced reaction is:
\[ HClO_3 + HCl \rightarrow ClO_2 + Cl_2 + H_2O \]
Chlorine dioxide (\(ClO_2\)) can react further with ozone (\(O_3\)). The reaction of \(ClO_2\) with \(O_3\) can produce dichlorine hexoxide (\(Cl_2O_6\)).
The balanced chemical equation for the reaction of chlorine dioxide with ozone is:
\[ 2ClO_2 + 2O_3 \rightarrow Cl_2O_6 + 2O_2 \]
So, the paramagnetic gas \(ClO_2\) reacts with ozone to produce dichlorine hexoxide (\(Cl_2O_6\)).
The correct Answer is option is (C):\(Cl_2O_6\)
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 ____