What are X and Y respectively in the following reactions?
Step 1: Understanding the Reaction Sequence
1. Hofmann Bromamide Reaction (Formation of X) - The reaction of amide with bromine (\( Br_2 \)) and sodium hydroxide (\( NaOH \)) is known as the Hofmann Bromamide Reaction. - This reaction leads to converting an amide into an amine with one fewer carbon atoms. \[ \text{CONH}_2 \xrightarrow{NaOH + Br_2} \text{NH}_2 \] - Here, compound Y (amide) undergoes Hofmann bromamide reaction to form compound X (amine). 2. Reduction of Amide to Amine (Formation of Y) - The amide (\( CONH_2 \)) can be formed from the corresponding acid or acid derivative. - The amide reduction using lithium aluminum hydride (\( LiAlH_4 \)) gives an amine. \[ \text{COOH} \xrightarrow{LiAlH_4 + H_2O} \text{CONH}_2 \] - This reduction step forms Y (amide).
Step 2: Evaluating the Given Options
- Option (1): Incorrect, as it misplaces the Hofmann bromamide reaction step. - Option (2): Correct, as Hofmann bromamide reaction forms X and LiAlH\(_4\) reduces to Y. - Option (3): Incorrect, as NaBH\(_4\) is not strong enough to reduce amides. - Option (4): Incorrect, as the order of reactions is incorrect. Thus, the correct answer is
Option (2).
Ethanal to But-2-enal
In Bohr model of hydrogen atom, if the difference between the radii of \( n^{th} \) and\( (n+1)^{th} \)orbits is equal to the radius of the \( (n-1)^{th} \) orbit, then the value of \( n \) is:
Given the function:
\[ f(x) = \frac{2x - 3}{3x - 2} \]
and if \( f_n(x) = (f \circ f \circ \ldots \circ f)(x) \) is applied \( n \) times, find \( f_{32}(x) \).
For \( n \in \mathbb{N} \), the largest positive integer that divides \( 81^n + 20n - 1 \) is \( k \). If \( S \) is the sum of all positive divisors of \( k \), then find \( S - k \).
If the real-valued function
\[ f(x) = \sin^{-1}(x^2 - 1) - 3\log_3(3^x - 2) \]is not defined for all \( x \in (-\infty, a] \cup (b, \infty) \), then what is \( 3^a + b^2 \)?