(a) When \(4.2 \mathrm{~g} \mathrm{NaHCO}_{3}\) is added to a solution \(\mathrm{of} \mathrm{CH}_{3} \mathrm{COOH}\) weighing \(10.0 \mathrm{~g}\), it is observed that \(2.2 \mathrm{~g} \mathrm{CO}_{2}\) is released into atmosphere. The residue is found to weigh \(12.0 \mathrm{~g}\). Show that these observations are in agreement with the low of conservation of weigh. (b) If \(6.3 \mathrm{~g}\) of \(\mathrm{NaHCO}_{3}\) are added to \(15.0 \mathrm{~g} \mathrm{CH}_{3} \mathrm{COOH}\) solution. The residue is found to weigh \(18.0 \mathrm{~g}\). What is the mass of \(\mathrm{CO}_{2}\) released in this reaction.

At the heart of chemistry lies the concept of chemical reactions, where substances, known as reactants, transform into new substances referred to as products. These reactions are guided by the rearrangement of atoms, involving breaking and forming bonds, and are depicted symbolically through balanced chemical equations.

A common example involves the reaction between sodium bicarbonate ((NaHCO_3)) and acetic acid ((CH_3COOH)) to produce carbon dioxide ((CO_2)), water, and sodium acetate. In educational scenarios, like IIT-JEE physical chemistry, understanding the profound implications of these interactions, along with their underlying principles such as conservation of mass, provides a fundamental basis for mastering the subject.

Students must learn to not only to write balanced chemical equations but to also interpret the physical changes they represent, such as gases being released into the atmosphere, which is apparent in the problem provided.

Stoichiometry is the quantitative aspect of chemistry that relates to the measurement and calculation of the products and reactants in a chemical reaction. It uses the concept of the mole and balanced equations to ensure the law of conservation of mass is observed. A balanced equation has equal numbers of each type of atom on both sides of the reaction.

In practice, stoichiometry involves calculations based on the molar ratios in a balanced chemical equation. For instance, if the initial and final mass in a chemical reaction involving (NaHCO_3) and (CH_3COOH) are measured, stoichiometry could be applied to predict the mass of (CO_2) released.

Understanding stoichiometry is critical for correctly interpreting the results of the textbook exercise. If one knows the molar mass of reactants and products, stoichiometry allows the prediction of masses involved before and after the reaction, verifying the conservation of mass.

IIT-JEE is one of the most challenging engineering entrance exams in India, and physical chemistry is a significant component of the chemistry syllabus. This branch of chemistry concerns itself with understanding the physical properties of molecules, the forces that act upon them, and their behavior in chemical reactions.

Within the IIT-JEE context, mastering the stoichiometry and the conservation of mass in chemical reactions is crucial. These principles not only form the core questions in the Physical Chemistry section but also are the foundational concepts that help students tackle more complex problems. The exercises involving the mass of (NaHCO_3) reacting with (CH_3COOH) and the resulting (CO_2) release illustrate the kind of practical, conceptual questions a student might encounter.

An in-depth comprehension of these concepts supports students in applying them to assorted scenarios, which is essential for excelling in the IIT-JEE physical chemistry examinations.