Problem 23 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

A bottle of dry ammonia and a bottle of dry hydrogen chloride connected through a long tube are opened simultaneously at both ends the white ammonium chloride ring first formed will be (a) at the centre of the tube. (b) near the hydrogen chloride bottle. (c) near the ammonia bottle. (d) throughout the length of the tube.

Step-by-Step Solution

Answer

(b) near the hydrogen chloride bottle.

Step 1: Understanding the Diffusion Concept

Diffusion is the process by which molecules spread from areas of high concentration to areas of low concentration. In a closed system, such as a tube connecting two bottles, gases will diffuse into each other until they reach equilibrium.

Step 2: Analyzing Molecular Weights

Compare the molar masses of ammonia (NH₃) and hydrogen chloride (HCl). The molar mass of NH₃ is approximately 17 g/mol, whereas the molar mass of HCl is approximately 36.5 g/mol. Since NH₃ has a lower molar mass, it diffuses faster than HCl.

Step 3: Applying Graham's Law of Effusion

According to Graham's Law, the rate of diffusion is inversely proportional to the square root of the molar mass. Therefore, \( \text{Rate}_{\text{NH}_3} > \text{Rate}_{\text{HCl}} \). This means NH₃ molecules will reach the region between the two gases faster than HCl molecules.

Step 4: Predicting the Location of NH₄Cl Ring Formation

Because NH₃ diffuses faster, the two gases will meet and react to form an ammonium chloride (NH₄Cl) ring closer to the hydrogen chloride bottle than to the ammonia bottle. This happens since HCl molecules, being heavier, travel more slowly than NH₃ molecules through the tube.

Key Concepts

Graham's Law

Graham's Law is a principle that describes the rate of diffusion or effusion of gases. It tells us how gases move through space or escape through tiny openings. According to Graham's Law, the rate at which a gas diffuses is inversely proportional to the square root of its molar mass. This means:

• Gases with lower molar mass diffuse faster.
• Gases with higher molar mass diffuse slower.

To apply Graham's Law, consider two gases, ammonia (NH₃) and hydrogen chloride (HCl). The ammonia molecules, being lighter, will diffuse faster than hydrogen chloride molecules. Mathematically, Graham's law is expressed as:\[ \frac{\text{Rate of diffusion of NH}_3}{\text{Rate of diffusion of HCl}} = \sqrt{\frac{\text{Molar mass of HCl}}{\text{Molar mass of NH}_3}} \]This principle is crucial for predicting the behavior of the two gases in a closed system, such as our experiment with ammonia and hydrogen chloride.

Molar Mass

Molar mass is an essential concept in chemistry that refers to the mass of one mole of a substance. For molecules, it’s the sum of the atomic masses of all atoms in a molecule, usually expressed in grams per mole (g/mol).

• The molar mass of ammonia (NH₃) is calculated as: 14 (Nitrogen) + 3×1 (Hydrogen) = 17 g/mol.
• For hydrogen chloride (HCl), it is calculated as: 1 (Hydrogen) + 35.5 (Chlorine) = 36.5 g/mol.

Knowing the molar masses allows us to determine how molecules of different gases will behave when they mix. In this particular case, ammonia has a significantly lower molar mass compared to hydrogen chloride, which directly affects its diffusion speed. Because of its lower molar mass, ammonia diffuses much faster, illustrating the effects of molar mass differences on gas behavior.

Ammonium Chloride Formation

Ammonium chloride is a compound that results from the chemical reaction between ammonia (NH₃) and hydrogen chloride (HCl). This reaction occurs when the two gases meet, and they react to form a white solid known as ammonium chloride (NH₄Cl). In the experiment, when bottles of dry ammonia and dry hydrogen chloride are interconnected and opened, the gases start to diffuse. Because ammonia travels faster due to its lower molar mass, it will reach the hydrogen chloride gas sooner. The reaction happens where the two gases meet, leading to the formation of ammonium chloride closer to the source of hydrogen chloride. This process can be summarized as: - NH₃(g) + HCl(g) → NH₄Cl(s) - The solid ammonium chloride forms a visible ring in the tube. - The location of the ring is influenced by the differing rates of diffusion of the gases. Understanding this process demonstrates how molecular interactions and physical differences between gases lead to observable outcomes in chemical reactions.