Ch.5 - Gases

Tro - Chemistry: A Molecular Approach 4th Edition

Tro4th EditionChemistry: A Molecular ApproachISBN: 9780134112831Not the one you use?Change textbook

Tro 4th Edition

Ch.5 - Gases

Problem 82c

Chapter 5, Problem 82c

A flask at room temperature contains exactly equal amounts (in moles) of nitrogen and xenon. c. The molecules of which gas have the greater average kinetic energy?

Verified step by step guidance

insert step 1> Understand that the average kinetic energy of gas molecules is related to temperature.

insert step 2> Recall that according to the kinetic molecular theory, the average kinetic energy of gas molecules is given by the equation: \( KE_{avg} = \frac{3}{2}kT \), where \( k \) is the Boltzmann constant and \( T \) is the temperature in Kelvin.

insert step 3> Note that the average kinetic energy of gas molecules depends only on the temperature of the gas, not on the type of gas or its molar mass.

insert step 4> Since both nitrogen and xenon are at the same temperature (room temperature), their molecules have the same average kinetic energy.

insert step 5> Conclude that the molecules of nitrogen and xenon have equal average kinetic energy at the same temperature.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Kinetic Molecular Theory

The Kinetic Molecular Theory explains the behavior of gases in terms of particles in constant motion. It states that the average kinetic energy of gas molecules is directly proportional to the temperature of the gas in Kelvin. This means that at the same temperature, all gases have the same average kinetic energy, regardless of their molecular mass.

Temperature and Kinetic Energy

Temperature is a measure of the average kinetic energy of the particles in a substance. In the context of gases, if two gases are at the same temperature, their average kinetic energies will be equal. Therefore, the average kinetic energy of nitrogen and xenon in the flask will be the same since they are both at room temperature.

Molecular Mass and Speed

While the average kinetic energy of gas molecules is the same at a given temperature, the speed of the molecules varies with their mass. Lighter molecules, like nitrogen (N2), move faster than heavier molecules, like xenon (Xe). This difference in speed does not affect the average kinetic energy but is important for understanding the behavior of gases in terms of diffusion and effusion.

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