Question

Which of the following is not correct? (a) Diffusion of gases occurs more rapidly at higher temperatures. (b) Effusion of \(\mathrm{H}_{2}\) is faster than effusion of He (assume similar conditions and a rate expressed in units of mol/h). (c) Diffusion will occur faster at low pressure than at high pressure. (d) The rate of effusion of a gas (mol/h) is directly proportional to molar mass.

Short answer

Option (d) is not correct; effusion rate is inversely proportional to molar mass.

Step-by-step solution

Understanding the Concept of Gas Diffusion and Effusion

Diffusion refers to the process where particles spread from an area of high concentration to low concentration, while effusion involves the passage of gas through a tiny hole. Both processes are influenced by temperature, molecular mass, and pressure.

Assessing Option (a) - Temperature and Diffusion Rate

Statement (a) suggests that diffusion of gases occurs more rapidly at higher temperatures. This is true because higher temperatures increase the kinetic energy of particles, making them move faster and thus leading to a higher rate of diffusion.

Assessing Option (b) - Effusion of Hydrogen vs Helium

According to Graham's Law, the rate of effusion of a gas is inversely proportional to the square root of its molar mass. Hydrogen ( H_{2} ) has a lower molar mass than Helium (He), therefore it effuses faster, making statement (b) correct.

Assessing Option (c) - Pressure and Diffusion Rate

Lower pressure means fewer gas particles to collide with each other, enabling them to diffuse more freely. This makes diffusion occur faster at low pressure than at high pressure, supporting statement (c) as accurate.

Assessing Option (d) - Rate of Effusion and Molar Mass

Statement (d) claims that the rate of effusion is directly proportional to molar mass. However, Graham's Law states that effusion rate is inversely proportional to the square root of molar mass, making this statement incorrect.

Key concepts

Diffusion

Diffusion is all about the movement of gas particles from areas where they are crowded to areas where they are less dense. Imagine having a drop of perfume released in one corner of a room. The fragrance spreads throughout the room as the perfume molecules move from high concentration areas (near the drop) to areas of lower concentration (rest of the room). This process occurs naturally and is influenced by several factors.

Key factors affecting diffusion include:

• Temperature: Higher temperatures give gas particles more kinetic energy, making them move faster and diffuse quicker.
• Pressure: Lower pressure allows particles more space to move, increasing diffusion rate.
• Molecular Mass: Lighter molecules diffuse faster than heavier ones.

By understanding these influences, we can predict how quickly a gas will spread in various environments.

Effusion

Effusion refers to the process where gas particles escape through a tiny hole into a vacuum or another separate area. Think of a balloon with a microscopic hole; the gas slowly leaks out due to effusion. Key to understanding effusion is realizing that it is not just about the size of the opening but also how fast the particles are moving.

Factors influencing the rate of effusion include:

• Molar Mass: According to Graham's Law, lighter gas molecules effuse faster than heavier ones.
• Temperature: Similar to diffusion, higher temperatures mean greater kinetic energy, thus faster effusion.

Effusion is important in various scientific applications, such as separating isotopes or studying gas properties.

Graham's Law

Graham's Law is a crucial principle that relates to both diffusion and effusion. It states that the rate of effusion (and similarly, diffusion under constant conditions) is inversely proportional to the square root of the gas’s molar mass. Mathematically, it is represented as:\[\text{Rate of effusion of gas 1} / \text{Rate of effusion of gas 2} = \sqrt{M_2 / M_1}\]Where \(M_1\) and \(M_2\) are the molar masses of the two gases. This law explains why lighter gases like hydrogen effuse and diffuse more rapidly than heavier gases like helium.

In practical terms, knowing Graham's Law helps us:

• Predict how quickly a gas will spread or escape.
• Understand the behavior of gases in different environments.
• Design systems where gas separation is needed.

Kinetic Theory of Gases

The kinetic theory of gases provides a framework for understanding how gases behave. It describes gases as a large number of small particles, all of which are in constant, random motion. This theory helps explain the properties of gases, such as pressure, volume, and temperature, and is fundamental to the understanding of gas laws.

Key concepts of this theory include:

• Particle Motion: Gas particles move in straight lines until they collide with another particle or the container's wall.
• Collisions: The collisions between gas particles and the walls of the container create pressure.
• Energy and Temperature: The average kinetic energy of gas particles is proportional to the gas's temperature in Kelvin.
• Volume and Pressure Relationship: At constant temperature, increasing the volume decreases the pressure and vice versa.

Understanding these concepts is crucial for explaining why gases behave the way they do under different conditions.