At high pressure and regulated supply of air, methane is heated with catalyst ‘X’ to give methanol and with catalyst ‘Y’ to give methanal. \( X \) and \( Y \) respectively are:
\( KMnO_4, Cr_2O_3 \)
Step 1: Understanding the Oxidation of Methane
Methane (\( CH_4 \)) can be oxidized under controlled conditions to form methanol (\( CH_3OH \)) and methanal (\( HCHO \)). The choice of catalyst determines the specific oxidation product.
Step 2: Identifying the Catalysts
1. Formation of Methanol (\( CH_3OH \)):
- Methane is converted to methanol using copper (\( Cu \)) as a catalyst under high pressure. \[ CH_4 + \frac{1}{2} O_2 \xrightarrow{\text{Cu}} CH_3OH \] 2. Formation of Methanal (\( HCHO \)):
- Methane is converted to methanal using molybdenum oxide (\( Mo_2O_3 \)) as a catalyst. \[ CH_4 + O_2 \xrightarrow{Mo_2O_3} HCHO + H_2O \] Step 3: Evaluating the Given Options
- Option (1): Incorrect, as it swaps the catalysts.
- Option (2): Correct, as \( Cu \) is used for methanol and \( Mo_2O_3 \) for methanal.
- Option (3): Incorrect, as \( V_2O_5 \) and \( KMnO_4 \) are not the catalysts used in this reaction.
- Option (4): Incorrect, as \( KMnO_4 \) and \( Cr_2O_3 \) are not the correct catalysts.
Thus, the correct answer is
Option (2).
The products formed in the following reaction, A and B, are:
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 \( 3^a + b^2 \)?