Textbook Question
(c) Calculate the most probable speed of an ozone molecule in the stratosphere, where the temperature is 270 K.
Ch.10 - Gases
Chapter 10, Problem 83
Which one or more of the following statements are true? (a) O2 will effuse faster than Cl2. (b) Effusion and diffusion are different names for the same process. (c) Perfume molecules travel to your nose by the process of effusion. (d) The higher the density of a gas, the shorter the mean free path.
Verified step by step guidance1
Identify the concept of effusion and diffusion: Effusion is the process by which gas molecules escape through a tiny hole into a vacuum, while diffusion is the spreading of gas molecules throughout a container or space.
Apply Graham's Law of Effusion to statement (a): According to Graham's Law, the rate of effusion of a gas is inversely proportional to the square root of its molar mass. Compare the molar masses of O2 and Cl2 to determine which effuses faster.
Evaluate statement (b) by clarifying the difference between effusion and diffusion: Effusion involves gas molecules passing through a small opening, while diffusion involves the mixing of gases in a space.
Consider statement (c) by understanding how perfume molecules travel: Perfume molecules spread through the air by diffusion, not effusion, as they mix with air molecules and travel to your nose.
Analyze statement (d) by considering the relationship between gas density and mean free path: The mean free path is the average distance a molecule travels before colliding with another molecule. Higher density means more molecules in a given volume, leading to a shorter mean free path.
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
4mWas this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Graham's Law of Effusion
Graham's Law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. This means lighter gases effuse faster than heavier gases. For example, O2 (molar mass ~32 g/mol) will effuse faster than Cl2 (molar mass ~71 g/mol) because it is lighter.
Recommended video:
Guided course
01:14
Graham's Law of Effusion
Diffusion vs. Effusion
Diffusion is the process by which gas molecules spread out to occupy a space uniformly, while effusion is the escape of gas molecules through a tiny opening into a vacuum. Although both processes involve the movement of gas particles, they are distinct in their mechanisms and conditions.
Recommended video:
Guided course
01:31Effusion vs Diffusion
Mean Free Path
The mean free path is the average distance a gas molecule travels between collisions with other molecules. It is inversely related to the density of the gas; as density increases, the mean free path decreases due to more frequent collisions. Thus, higher density gases have shorter mean free paths.
Recommended video:
Guided course
01:05Root Mean Square Speed Formula
Related Practice
Textbook Question
(c) Calculate the most probable speeds of CO molecules at 300 K.
Textbook Question
(c) Calculate the most probable speeds of Cl2 molecules at 300 K.
Textbook Question
At constant pressure, the mean free path 1l2 of a gas molecule is directly proportional to temperature. At constant temperature, l is inversely proportional to pressure. If you compare two different gas molecules at the same temperature and pressure, l is inversely proportional to the square of the diameter of the gas molecules. Put these facts together to create a formula for the mean free path of a gas molecule with a proportionality constant (call it Rmfp, like the ideal-gas constant) and define units for Rmfp.
Textbook Question
Hydrogen has two naturally occurring isotopes, 1H and 2H. Chlorine also has two naturally occurring isotopes, 35Cl and 37Cl. Thus, hydrogen chloride gas consists of four distinct types of molecules: 1H35Cl, 1H37Cl, 2H35Cl, and 2H37Cl. Place these four molecules in order of increasing rate of effusion.