\( (\text{CH}_3)_3\text{CH} \xrightarrow{\text{KMnO}_4} \text{X} \xrightarrow[\text{573K}]{\text{Cu}} \text{Y} \). The number of \( sp^3 \) and \( sp^2 \) carbons in Y are respectively
1. Oxidation with \( \text{KMnO}_4 \): Alkanes with a tertiary hydrogen atom (like isobutane) can be oxidized by strong oxidizing agents like \( \text{KMnO}_4 \) to corresponding tertiary alcohols.
\[ (\text{CH}_3)_3\text{CH} \xrightarrow{\text{KMnO}_4} (\text{CH}_3)_3\text{C-OH} \quad (\text{tert-Butyl alcohol, X}) \]
2. Dehydrogenation/Dehydration with Cu at 573 K:
Tertiary alcohols passed over heated Copper (Cu) at 573 K undergo dehydration (elimination of water) to form alkenes (not aldehydes/ketones like primary/secondary alcohols).
\[ (\text{CH}_3)_3\text{C-OH} \xrightarrow{\text{Cu}, 573\text{K}} \text{CH}_3-\text{C}(\text{CH}_3)=\text{CH}_2 + \text{H}_2\text{O} \]
Product Y is Isobutylene (2-methylpropene).
Step 2: Counting Hybridized Carbons in Y:
Structure of Y: \( \text{CH}_3-\text{C}(\text{CH}_3)=\text{CH}_2 \)
- Methyl carbons (\( \text{CH}_3 \)): Single bonds only \(\to\) \( sp^3 \). There are 2 methyl groups. Total = 2. Wait, let's recount.
Structure: One central Carbon double bonded to \( \text{CH}_2 \) and single bonded to two \( \text{CH}_3 \) groups.
Carbons:
1. Terminal \( =\text{CH}_2 \): Double bonded \(\to\) \( sp^2 \).
2. Central \( =\text{C}\textless \): Double bonded \(\to\) \( sp^2 \).
3. Two \( -\text{CH}_3 \) groups: Single bonded \(\to\) \( sp^3 \).
Total \( sp^2 \) carbons = 2.
Total \( sp^3 \) carbons = 2.
So answer should be (2, 2).
Let's check the Answer Key. The key marks Option 2 (1, 3)? Or Option 1?
Let's look at the crop image for Q156.
Green tick is on Option 1 (3, 1)?
Wait, let's re-evaluate Reaction 2.
Is it possible \( \text{KMnO}_4 \) oxidation of isobutane yields something else? No, t-butanol is standard.
Reaction of t-Butanol with Cu/573K: Tertiary alcohols undergo dehydration to alkenes.
Maybe Y is something else?
Could X be an aldehyde? No, alkane oxidation is specific.
What if \( \text{X} \) is not t-butanol?
Maybe the starting material is different? \( (\text{CH}_3)_3\text{CH} \) is Isobutane.
Maybe Y is an ether? No.
Let's re-read the green tick option.
Image 2 crop bottom part:
Q156. Options: 1. 3,1 (Red cross). 2. 1,3 (Red cross). 3. 2,2 (Green Tick). 4. 4,0.
Okay, the Correct Answer is (C) 2, 2.
My derivation (2 \( sp^3 \), 2 \( sp^2 \)) matches Option 3.
(Note: The text provided in the prompt "Correct Answer: 1 Wrong Marks: 0 ... Option 1 ... " might be misleading or I misread the provided text block order vs image. The image clearly shows the green check on Option 3.)
Step 4: Final Answer:
The number of \( sp^3 \) carbons is 2, and \( sp^2 \) carbons is 2. (Option 3).
