Reaction Mechanisms

To solve the problem, we need to determine the structure of product $D$ by following the sequence of reactions step by step.

Step 1: Analyze the given reaction
The starting compound is:

$ $%5Ctext%7BCH%7D_3-%5Cunderset%7B%5Ctext%7BCH%7D_3%7D%7B%5Cunderbrace%7B%5Ctext%7BC%7D%7D%7D-%5Ctext%7BH%7D%20%2B%20%5Ctext%7BO%7D_2%20%5Crightarrow%20%5Ctext%7BProduct%20A%7D$ $This%20is%20a%20benzene%20ring%20with%20a%20methyl%20group%20and%20an%20ethyl%20group.%20The%20reaction%20involves%20oxidation%20of%20the%20alkyl%20side%20chain.%20Reaction%201%3A%20Oxidation%20of%20the%20Alkyl%20Side%20Chain**%20The%20alkyl%20side%20chain%20($ \text{CH}_3-\text{CH}_2- $)%20undergoes%20oxidation%20in%20the%20presence%20of%20oxygen%20($ \text{O}_2 $).%20The%20primary%20alcohol%20formed%20is%3A$ $%5Ctext%7BCH%7D_3-%5Cunderset%7B%5Ctext%7BCH%7D_3%7D%7B%5Cunderbrace%7B%5Ctext%7BC%7D%7D%7D(%5Ctext%7BOH%7D)-%5Ctext%7BH%7D$ $This%20is%20the%20product$ A $.%20Reaction%202%3A%20Acid-Catalyzed%20Dehydration%20The%20product$ A $(a%20primary%20alcohol)%20is%20treated%20with%20acid%20($ \text{H}^+ $)%20and%20water%20($ \text{H}_2\text{O} $)%20to%20form%20two%20products%2C$ A' $and$ B' $.%20This%20is%20an%20acid-catalyzed%20dehydration%20reaction%2C%20which%20eliminates%20a%20molecule%20of%20water%20to%20form%20an%20alkene%20and%20a%20carboxylic%20acid.%20The%20primary%20alcohol%20undergoes%20dehydration%20to%20form%3A%20-$ A' $%3A%20An%20alkene.%20-$ B' $%3A%20A%20carboxylic%20acid.%20The%20structure%20of$ A' $is%3A$ $%5Ctext%7BCH%7D_3-%5Cunderset%7B%5Ctext%7BCH%7D_3%7D%7B%5Cunderbrace%7B%5Ctext%7BC%7D%7D%7D%3D%5Ctext%7BCH%7D_2$ $This%20is%20a%20conjugated%20diene%20(4-methylpent-1%2C3-diene).%20The%20structure%20of$ B' $is%3A$ $%5Ctext%7BCH%7D_3-%5Ctext%7BCOOH%7D$ $This%20is%20acetic%20acid.%20Step%202%3A%20Identify%20Product$ A' $The%20problem%20states%20that%20product$ A' $gives%20a%20white%20precipitate%20when%20treated%20with%20bromine%20water.%20This%20indicates%20that$ A' $is%20an%20alkene%2C%20as%20alkenes%20react%20with%20bromine%20water%20to%20form%20addition%20products%2C%20which%20can%20sometimes%20appear%20as%20white%20precipitates%20due%20to%20the%20formation%20of%20insoluble%20bromides.%20Thus%2C$ A' $is%3A$ $%5Ctext%7BCH%7D_3-%5Cunderset%7B%5Ctext%7BCH%7D_3%7D%7B%5Cunderbrace%7B%5Ctext%7BC%7D%7D%7D%3D%5Ctext%7BCH%7D_2$ $Step%203%3A%20Identify%20Product$ B' $The%20problem%20states%20that%20product$ B' $is%20treated%20with%20barium%20hydroxide%20($ \text{Ba(OH)}_2 $)%20to%20form%20product$ C $.%20Acetic%20acid%20($ \text{CH}_3\text{COOH} $)%20reacts%20with%20barium%20hydroxide%20to%20form%20barium%20acetate%20($ \text{Ba(CH}_3\text{COO)}_2 $)%20and%20water%20($ \text{H}_2\text{O} $)%3A$ $%5Ctext%7BCH%7D_3%5Ctext%7BCOOH%7D%20%2B%20%5Ctext%7BBa(OH)%7D_2%20%5Crightarrow%20%5Ctext%7BBa(CH%7D_3%5Ctext%7BCOO)%7D_2%20%2B%202%5Ctext%7BH%7D_2%5Ctext%7BO%7D$ $Thus%2C%20product$ C $is%20barium%20acetate.%20Step%204%3A%20Identify%20Product$ D $The%20problem%20states%20that%20product$ C $(barium%20acetate)%20is%20heated%20strongly%20to%20form%20product$ D $.%20When%20barium%20acetate%20is%20heated%20strongly%2C%20it%20decomposes%20to%20form%20acetic%20acid%20($ \text{CH}_3\text{COOH} $)%20and%20barium%20oxide%20($ \text{BaO} $)%3A$ $%5Ctext%7BBa(CH%7D_3%5Ctext%7BCOO)%7D_2%20%5Cxrightarrow%7B%5Ctext%7BHeating%7D%7D%20%5Ctext%7BCH%7D_3%5Ctext%7BCOOH%7D%20%2B%20%5Ctext%7BBaO%7D$ $However%2C%20the%20problem%20asks%20for%20the%20final%20product$ D $%2C%20which%20is%20the%20result%20of%20the%20initial%20dehydration%20reaction.%20From%20the%20earlier%20steps%2C%20we%20know%20that%20the%20dehydration%20of%20the%20primary%20alcohol%20forms%20the%20alkene%3A$ $%5Ctext%7BCH%7D_3-%5Cunderset%7B%5Ctext%7BCH%7D_3%7D%7B%5Cunderbrace%7B%5Ctext%7BC%7D%7D%7D%3D%5Ctext%7BCH%7D_2$ $This%20is%204-methylpent-1%2C3-diene.%20Final%20Answer%3A%20The%20product$ D $is%3A$ $%5Cboxed%7B%5Ctext%7B(A)%204-Methylpent-3-en-2-one%7D%7D$ $

Step 1: Understanding the Question:
The question asks for the rate of a first-order reaction at a specific concentration (

0.01%20%5Ctext%7B%20M%7D

). To find this, we first need to determine the rate constant (

k

) using the time taken for a given change in concentration.
Step 2: Key Formula or Approach:
For a first-order reaction:
1. Integrated rate law:

k%20%3D%20%5Cfrac%7B2.303%7D%7Bt%7D%20%5Clog%5Cleft(%5Cfrac%7B%5BR%5D_0%7D%7B%5BR%5D_t%7D%5Cright)

2. Rate law:

%5Ctext%7BRate%7D%20%3D%20k%5BR%5D

3. Relation between

k

and half-life

t_%7B1%2F2%7D

k%20%3D%20%5Cfrac%7B0.693%7D%7Bt_%7B1%2F2%7D%7D

Step 3: Detailed Explanation:
1. Finding the Rate Constant ( $k$ ):
Initial concentration,

%5BR%5D_0%20%3D%200.1%20%5Ctext%7B%20M%7D

.
Final concentration after 40 min,

%5BR%5D_t%20%3D%200.025%20%5Ctext%7B%20M%7D

.
Notice that

%5Cfrac%7B%5BR%5D_t%7D%7B%5BR%5D_0%7D%20%3D%20%5Cfrac%7B0.025%7D%7B0.1%7D%20%3D%20%5Cfrac%7B1%7D%7B4%7D

.
Since the concentration becomes one-fourth, two half-lives have passed in 40 minutes (

0.1%20%5Crightarrow%200.05%20%5Crightarrow%200.025

).
Therefore,

2%20%5Ctimes%20t_%7B1%2F2%7D%20%3D%2040%20%5Ctext%7B%20min%7D%20%5Cimplies%20t_%7B1%2F2%7D%20%3D%2020%20%5Ctext%7B%20min%7D

.
Now, calculate the rate constant

k

k%20%3D%20%5Cfrac%7B0.693%7D%7Bt_%7B1%2F2%7D%7D%20%3D%20%5Cfrac%7B0.693%7D%7B20%20%5Ctext%7B%20min%7D%7D%20%3D%200.03465%20%5Ctext%7B%20min%7D%5E%7B-1%7D

2. Calculating the Rate of Reaction:
We need the rate when

%5BR%5D%20%3D%200.01%20%5Ctext%7B%20M%7D

%5Ctext%7BRate%7D%20%3D%20k%20%5Ctimes%20%5BR%5D

%5Ctext%7BRate%7D%20%3D%200.03465%20%5Ctext%7B%20min%7D%5E%7B-1%7D%20%5Ctimes%200.01%20%5Ctext%7B%20M%7D

%5Ctext%7BRate%7D%20%3D%200.0003465%20%5Ctext%7B%20M%20min%7D%5E%7B-1%7D%20%3D%203.465%20%5Ctimes%2010%5E%7B-4%7D%20%5Ctext%7B%20M%20min%7D%5E%7B-1%7D

Rounding to three significant figures, we get

3.47%20%5Ctimes%2010%5E%7B-4%7D%20%5Ctext%7B%20M%20min%7D%5E%7B-1%7D

.
Step 4: Final Answer:
The rate is

3.47%20%5Ctimes%2010%5E%7B-4%7D%20%5Ctext%7B%20M%20min%7D%5E%7B-1%7D

, which corresponds to option (B).

High-Yield Trend

Chapter Questions
2 MCQs

Official Solution

Official Solution

Reaction Mechanisms

High-Yield Trend

Chapter Questions 2 MCQs

Official Solution

Official Solution

Chapter Questions
2 MCQs