Question

How many \(\beta\)-ketocarboxylic acids is possible to produce following product with evolution of 1 mole \(\mathrm{CO}_{2}\) on gentle heating: (A) 2 (B) 3 (C) 4 (D) 8

Short answer

The smallest number of β-ketocarboxylic acids that can release 1 mole of CO₂ upon gentle heating is 4. Therefore, the correct answer is (C) 4.

Step-by-step solution

Understand β-ketocarboxylic acid structure

A β-ketocarboxylic acid is a carboxylic acid that has a ketone functional group at the β position, which means it is two carbons away from the carboxylic acid group. The general structure of a β-ketocarboxylic acid is as follows: R – CH₂ – CO – CH₂ – COOH, where R is an alkyl group.

Decomposition of β-ketocarboxylic acids

Upon gentle heating, β-ketocarboxylic acids undergo a transformation known as decarboxylation, where they release CO₂ and form a new compound. The reaction can be represented by the following equation: β-Ketocarboxylic acid → Ketone + CO₂ We will use this principle to find the possible number of β-ketocarboxylic acids that can release 1 mole of CO₂ when heated gently.

Analyze the given options

Let's go through each of the provided options and analyze if they are possible β-ketocarboxylic acids that can release 1 mole of CO₂ upon gentle heating: Option (A): 2 If we consider two moles of the same β-ketocarboxylic acid or two different β-ketocarboxylic acids, only one of them will be involved in the decarboxylation reaction to form ketone and CO₂, meaning only 1 possible β-ketocarboxylic acid can release 1 mole of CO₂. Option (B): 3 It is not possible for three different β-ketocarboxylic acids to produce a single mole of CO₂ since each β-ketocarboxylic acid will lose one mole of CO₂ in the decarboxylation reaction. Therefore, this option is not feasible. Option (C): 4 If we have four moles of the same β-ketocarboxylic acid or a combination of four different β-ketocarboxylic acids, each of them can release one mole of CO₂ upon decarboxylation. This option works, as it is possible to produce four different β-ketocarboxylic acids that can release 1 mole of CO₂. Option (D): 8 With eight moles of β-ketocarboxylic acids involved, each will lose one mole of CO₂ upon decarboxylation. Although possible, it is not the smallest number of β-ketocarboxylic acids that can release 1 mole of CO₂ upon gentle heating, making this option not the most appropriate answer.

Identify the correct option

Since option (C) seems to be the most appropriate answer, as it's the smallest number of β-ketocarboxylic acids that can release 1 mole of CO₂ upon gentle heating, the answer is (C) 4.

Key concepts

Decarboxylation

Decarboxylation refers to a chemical reaction where a carboxyl group (–COOH) is removed from an organic molecule, typically releasing carbon dioxide (CO₂). This reaction is significant in organic chemistry, especially for biologically relevant transformations such as the conversion of amino acids during metabolism. In the context of β-ketocarboxylic acids, decarboxylation often leads to the formation of ketones. This process is particularly important as it simplifies molecules and can be used to deduce the structure of complex organic compounds.

In the exercise, understanding the decarboxylation mechanism is key to predicting the number of β-ketocarboxylic acids that could yield a single mole of CO₂ when heated gently. The reaction for β-ketocarboxylic acids is as follows: \
\( \text{β-Ketocarboxylic acid} \rightarrow \text{Ketone} + CO₂ \)
. The understanding of this reaction allows students to analyze options and determine the most plausible number of acids that fit the described transformation.

Organic Chemistry

Organic chemistry is the study of the structure, properties, composition, reactions, and synthesis of organic compounds, which contain carbon in covalent bonding. The study of organic reactions includes both their physical and chemical properties as well as molecular and electronic structures. Key to mastering organic chemistry is understanding functional groups, reaction mechanisms, and synthesis pathways.

β-ketocarboxylic acids are important organic compounds that contain both ketone (–CO–) and carboxyl (–COOH) functional groups. Their reactivity, particularly in decarboxylation reactions, is a critical concept for students. Grasping the arrangement of atoms in these compounds and the predictable patterns of their chemical behavior is essential. For the JEE Main and Advanced exams, a strong foundation in organic chemistry concepts like these is indispensable for success.

JEE Main and Advanced Preparation

Preparing for JEE Main and Advanced requires a strategic approach to mastering topics across Physics, Chemistry, and Mathematics. Aspiring students need to focus on conceptual clarity, problem-solving skills, and time management. For organic chemistry, understanding reaction mechanisms, including decarboxylation, is crucial.

Students should tackle a variety of problems, such as predicting the outcome of chemical reactions involving β-ketocarboxylic acids, to strengthen their grasp of the subject. Regular practice, combined with analysis of step-by-step solutions for textbook exercises, can help clarify doubts and solidify concepts.​​ Utilizing resources that explain the process and the rationale behind each step is beneficial to comprehend the depth of the subject matter. These practices will not only help students excel in competitive exams like the JEE but also lay a strong foundation for future studies in chemistry.