To solve the problem step by step, we will analyze the information provided and derive the structure of alcohol (A).
### Step 1: Calculate the moles of methane produced
Given that 560 mL of methane (CH₄) is liberated at STP (Standard Temperature and Pressure), we can calculate the number of moles of methane produced using the formula:
\[
\text{Number of moles} = \frac{\text{Volume at STP}}{22.4 \, \text{L/mol}}
\]
Converting 560 mL to liters:
\[
560 \, \text{mL} = 0.560 \, \text{L}
\]
Now, calculating the moles:
\[
\text{Number of moles of CH₄} = \frac{0.560 \, \text{L}}{22.4 \, \text{L/mol}} = 0.025 \, \text{mol}
\]
### Step 2: Relate moles of alcohol to moles of methane
From the reaction of alcohol (A) with Grignard reagent (CH₃MgI), we know that:
\[
1 \, \text{mol of alcohol (A)} \rightarrow 1 \, \text{mol of CH₄}
\]
Thus, the moles of alcohol (A) used will also be 0.025 mol.
### Step 3: Calculate the molar mass of alcohol (A)
Given that the mass of alcohol (A) is 2.2 g, we can find the molar mass using the formula:
\[
\text{Molar mass} = \frac{\text{mass}}{\text{moles}} = \frac{2.2 \, \text{g}}{0.025 \, \text{mol}} = 88 \, \text{g/mol}
\]
### Step 4: Determine the molecular formula of alcohol (A)
The general formula for alcohols is \(C_nH_{2n+1}OH\). The molar mass can be expressed as:
\[
\text{Molar mass} = 12n + (2n + 1) + 16
\]
Setting this equal to the molar mass we calculated:
\[
12n + 2n + 1 + 16 = 88
\]
Simplifying:
\[
14n + 17 = 88
\]
\[
14n = 71
\]
\[
n = 5.07 \approx 5
\]
Thus, the molecular formula of alcohol (A) is \(C_5H_{11}OH\).
### Step 5: Identify the structure of alcohol (A)
Given that the molecular formula is \(C_5H_{11}OH\), we can deduce that alcohol (A) could be 2-pentanol or 3-pentanol, as both can undergo dehydration to form alkenes.
### Step 6: Analyze the dehydration and ozonolysis products
Alcohol (A) on dehydration will form an alkene, which upon ozonolysis will yield a ketone (B) and another compound (C).
### Step 7: Determine the nitrogen percentage in oxime of ketone (B)
The oxime of ketone (B) contains 19.17% nitrogen. The molecular formula of an oxime is \(C_nH_{2n}N\).
### Step 8: Find ketone (D) from oxidation of alcohol (A)
Alcohol (A) on oxidation gives ketone (D) with the same number of carbon atoms, confirming that the structure of alcohol (A) is consistent with the information provided.
### Conclusion
Based on the calculations and deductions, the structure of alcohol (A) is:
**Structure of (A): 2-Pentanol or 3-Pentanol (C5H12O)**
