Step 1: Identify the products Y and Z. Cumene (isopropylbenzene) on oxidation forms cumene hydroperoxide (X). Upon acid-catalyzed cleavage, it yields phenol (Y) and acetone (Z).
Step 2: Count the \( sp^2 \) carbons. Phenol has four \( sp^2 \) carbons in the aromatic ring. Acetone, a ketone, features a carbonyl carbon that is also \( sp^2 \) hybridized. Thus, the total number of \( sp^2 \) carbons in Y (phenol) and Z (acetone) is 5 (from phenol) + 2 (from acetone) = 7.
Identify Z in the following reaction sequence.
What are the reagents X and Y respectively used in the following reaction sequence to convert a nitrile to a methyl group?
What are X, Y and Z in the given reaction sequence?
Given the function:
\[ f(x) = \begin{cases} \frac{(2x^2 - ax +1) - (ax^2 + 3bx + 2)}{x+1}, & \text{if } x \neq -1 \\ k, & \text{if } x = -1 \end{cases} \]
If \( a, b, k \in \mathbb{R} \) and \( f(x) \) is continuous for all \( x \), then the value of \( k \) is:
Given the function:
\[ f(x) = \begin{cases} \frac{2x e^{1/2x} - 3x e^{-1/2x}}{e^{1/2x} + 4e^{-1/2x}}, & \text{if } x \neq 0 \\ 0, & \text{if } x = 0 \end{cases} \]
Determine the differentiability of \( f(x) \) at \( x = 0 \).
A magnet suspended in a uniform magnetic field is heated so as to reduce its magnetic moment by 19%. By doing this, the time period of the magnet approximately
A Carnot heat engine has an efficiency of 10%. If the same engine is worked backward to obtain a refrigerator, then the coefficient of performance of the refrigerator is
Match the following physical quantities with their respective dimensional formulas.