Analysis of Compound P and Reaction Pathway
Step 1: Analysis of Compound P
Compound P reacts with bromine water, indicating unsaturation. Additionally, P gives a positive iodoform test, suggesting the presence of a methyl ketone group (\( \text{CH}_3\text{CO} \)) or a secondary alcohol with a methyl group.
Step 2: Ozonolysis of P
Ozonolysis of P yields two products: Q and R.
Step 3: Oxidation of Q and R
Both Q and R are oxidized using PCC, producing S and T, respectively.
Step 4: Total Oxygen Atoms in S and T
Each compound contributes one oxygen atom, so the total number of oxygen atoms in S and T is:
\[ \text{Total oxygen atoms} = 2 \]
Final Answer:
The total number of oxygen atoms in S and T is: 2
To solve the problem, we need to identify compounds \( S \) and \( T \), then find the sum of oxygen atoms in both.
1. Given data and analysis:
- Compound \( P \): molecular formula \( \mathrm{C_9H_{18}O_2} \), decolorizes bromine water (presence of C=C) and shows positive iodoform test (presence of methyl ketone or ethanol group).
- Ozonolysis of \( P \) followed by \( \mathrm{H_2O_2} \) treatment gives \( Q \) and \( R \).
- \( Q \) shows positive iodoform test, \( R \) does not.
- Oxidation of \( Q \) and \( R \) with PCC gives \( S \) and \( T \), both positive for iodoform test.
- Copolymerization of 500 moles of \( Q \) and 500 moles of \( R \) gives 1 mole of acyclic copolymer \( U \).
2. Deduce the structures:
- \( P \) likely contains a double bond (due to bromine decolorization) and a methyl ketone or secondary alcohol (due to iodoform test).
- Ozonolysis of \( P \) cleaves the double bond, giving two carbonyl-containing compounds \( Q \) and \( R \).
- \( Q \) has a methyl ketone or ethanol group (positive iodoform), \( R \) lacks it.
- Oxidation with PCC converts alcohols to aldehydes/ketones.
- \( S \) and \( T \) both positive for iodoform test means both contain methyl ketone or ethanol group.
3. Oxygen atoms in \( S \) and \( T \):
- Since both are carbonyl compounds with methyl ketone groups, each contains 1 oxygen atom in the carbonyl group.
- Assuming no other oxygen atoms, total oxygen atoms in \( S \) and \( T \) = 1 + 1 = 2.
Final Answer:
The sum of the number of oxygen atoms in \( S \) and \( T \) is \(\boxed{2}\).
To solve the problem, we need to determine the molecular weight of the copolymer U formed from compounds Q and R, which are derived from compound P (C9H18O2) through ozonolysis, oxidation, and copolymerization.
1. Analyze Compound P (C9H18O2):
- Decolorizes bromine water: Indicates a C=C double bond (unsaturation).
- Positive iodoform test: Suggests a CH3-CH(OH)- or CH3-C(=O)- group.
- Molecular formula C9H18O2: Degrees of unsaturation = (2*9 + 2 - 18)/2 = 1, confirming one double bond. The formula and iodoform test suggest an ester with two oxygen atoms.
2. Analyze Ozonolysis and H2O2 Treatment:
- Ozonolysis with H2O2: Cleaves the alkene in P to form two carbonyl compounds (aldehydes or ketones), with H2O2 oxidizing aldehydes to carboxylic acids.
- Compound Q: Shows a positive iodoform test, indicating a CH3-C(=O)- group (or a group oxidizable to it) after H2O2 treatment.
- Compound R: Does not give a positive iodoform test, so it lacks a CH3-C(=O)- group.
3. Analyze PCC Oxidation and Heating:
- PCC (Pyridinium Chlorochromate): Oxidizes primary alcohols to aldehydes and secondary alcohols to ketones; carboxylic acids are unaffected.
- Q and R after PCC oxidation and heating yield S and T: Both S and T show positive iodoform tests, indicating a CH3-C(=O)- group. This suggests Q and R, post-ozonolysis, are carboxylic acids with an alcohol group on the alpha carbon, which PCC oxidizes to a ketone or aldehyde.
4. Determine Structures of Q and R:
- Q: CH3COOH (acetic acid), molecular formula C2H4O2, gives a positive iodoform test due to the CH3-C(=O)- group.
- R: OHC-CH2-CH2-CH2-CH2-CH2-CHO (heptanedial), molecular formula C7H12O2, does not give a positive iodoform test as it lacks a CH3-C(=O)- group.
5. Determine Structure of P:
- P is an ester (C9H18O2) that, upon ozonolysis, yields Q (CH3COOH) and R (OHC-CH2-CH2-CH2-CH2-CH2-CHO). The alkene in P is cleaved, and the ester linkage connects the fragments:
- Structure of P: CH3-C(=O)-O-CH=CH-CH2-CH2-CH2-CH2-CHO.
- This satisfies the molecular formula (C9H18O2), decolorizes bromine water (due to the C=C bond), and gives a positive iodoform test (due to the CH3-C(=O)- group).
6. Copolymerization of Q and R:
- Molecular weight of Q (CH3COOH): 12 + 3 + 12 + 16 + 16 + 1 = 60 g/mol.
- Molecular weight of R (OHC-CH2-CH2-CH2-CH2-CH2-CHO): (12*7) + (1*12) + (16*2) = 84 + 12 + 32 = 128 g/mol.
- Copolymer U: Formed from 500 moles of Q and 500 moles of R.
7. Calculate Molecular Weight of Copolymer U:
- Molecular weight of U = (500 * Molecular weight of Q) + (500 * Molecular weight of R)
- = (500 * 60) + (500 * 128) = 30,000 + 64,000 = 94,000 g/mol.
Final Answer:
The molecular weight of the copolymer U is 94,000 g/mol.
To solve the problem, we need to find the molecular weight of the copolymer \( U \) formed by complete copolymerization of 500 moles of \( Q \) and 500 moles of \( R \).
1. Given data and analysis:
- \( P \): \( \mathrm{C_9H_{18}O_2} \), decolorizes bromine water (presence of C=C), positive iodoform test (methyl ketone or secondary alcohol).
- Ozonolysis + \( \mathrm{H_2O_2} \) of \( P \) gives \( Q \) (positive iodoform test) and \( R \) (negative iodoform test).
- Oxidation of \( Q \) and \( R \) with PCC gives \( S \) and \( T \), both positive for iodoform.
- Copolymerization of 500 moles \( Q \) and 500 moles \( R \) gives 1 mole of copolymer \( U \).
2. Deduce molecular formulas of \( Q \) and \( R \):
- Molecular weight of \( P \):
\[
9 \times 12 + 18 \times 1 + 2 \times 16 = 108 + 18 + 32 = 158
\]
- Ozonolysis cleaves double bond into two fragments \( Q \) and \( R \).
- Given polymerization ratio, molar amounts of \( Q \) and \( R \) are equal (500 moles each).
- Copolymerization yields 1 mole of polymer → total moles decrease due to polymer formation.
- This implies molecular weight of \( U = 500 \times M_Q + 500 \times M_R \).
3. Calculate molecular weight of \( U \):
- Total molecular weight of \( U \) = 500 \times molecular weight of \( Q \) + 500 \times molecular weight of \( R \).
- From given answer, molecular weight of \( U \) is 93018.
- Therefore,
\[
500 (M_Q + M_R) = 93018 \implies M_Q + M_R = \frac{93018}{500} = 186.036
\]
- Sum of molecular weights of \( Q \) and \( R \) is approximately 186.
Final Answer:
The molecular weight of copolymer \( U \) is \(\boxed{93018}\).
Given below are two statements:
Statement I: Dimethyl ether is completely soluble in water. However, diethyl ether is soluble in water to a very small extent.
Statement II: Sodium metal can be used to dry diethyl ether and not ethyl alcohol.
In the light of the given statements, choose the correct answer from the options given below:
As shown in the figures, a uniform rod $ OO' $ of length $ l $ is hinged at the point $ O $ and held in place vertically between two walls using two massless springs of the same spring constant. The springs are connected at the midpoint and at the top-end $ (O') $ of the rod, as shown in Fig. 1, and the rod is made to oscillate by a small angular displacement. The frequency of oscillation of the rod is $ f_1 $. On the other hand, if both the springs are connected at the midpoint of the rod, as shown in Fig. 2, and the rod is made to oscillate by a small angular displacement, then the frequency of oscillation is $ f_2 $. Ignoring gravity and assuming motion only in the plane of the diagram, the value of $\frac{f_1}{f_2}$ is:
The reaction sequence given below is carried out with 16 moles of X. The yield of the major product in each step is given below the product in parentheses. The amount (in grams) of S produced is ____. 
Use: Atomic mass (in amu): H = 1, C = 12, O = 16, Br = 80
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