$X$ is $Pd - C /$ quinoline / \(H _{2}\)
Calculate the potential for half-cell containing 0.01 M K\(_2\)Cr\(_2\)O\(_7\)(aq), 0.01 M Cr\(^{3+}\)(aq), and 1.0 x 10\(^{-4}\) M H\(^+\)(aq).
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 ____
Alcohols, phenols, and ethers are organic compounds that have distinct chemical properties.
Alcohols are characterized by the presence of the hydroxyl (-OH) functional group, which makes them polar and capable of forming hydrogen bonds. They are typically classified as primary, secondary, or tertiary, depending on the number of alkyl groups attached to the carbon atom bearing the hydroxyl group. Alcohols undergo various chemical reactions, including oxidation, dehydration, and esterification.
Phenols are organic compounds that contain an -OH group attached to an aromatic ring. They are weaker acids than carboxylic acids but stronger acids than alcohols due to the resonance stabilization of the phenoxide ion. Phenols undergo various chemical reactions, including electrophilic substitution and oxidation.
Read More: Classification of Alcohol, Phenols and Ethers
Ethers are organic compounds that contain an oxygen atom bonded to two alkyl or aryl groups. They are characterized by their low boiling points and are often used as solvents. Ethers undergo various chemical reactions, including cleavage of the C-O bond and oxidation.
In summary, alcohols, phenols, and ethers have distinct chemical properties due to the presence of the hydroxyl or ether functional group. Understanding these properties is important for understanding their reactivity and potential applications in various fields, including chemistry, biology, and industry.