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Chapter 17: Problem 5

Two different gases are at the same temperature, and both have low enough densities that they behave like ideal gases. Do their molecules have the same thermal speeds? Explain.

Short Answer

Expert verified
No, the molecules of two different gases, even at the same temperature and behave as ideal gases, do not necessarily have the same thermal speeds. This difference is due to different molecular masses of the gases.

Step by step solution

01

Understand the Question

Knowing that both gases are at the same temperature and behave as ideal gases, you need to determine whether their molecules would have the same thermal speeds.
02

Recall the Ideal Gas Assumption

In ideal gases, the kinetic energy at a static temperature is the same for all molecules (KE = 1 / 2 mv虏). This form directly implies that the velocity (or thermal speed) of a gas particle is related to both its kinetic energy and its mass.
03

Factor in Different Masses

Even if the kinetic energy is the same for all particles in an ideal gas at the same temperature, it does not necessarily mean that their thermal speeds are the same. This is because different gases have different molar masses, and thus different molecular masses.
04

Conclusion

This means that, despite the same kinetic energy due to the same temperature, the different gas molecules will not necessarily have the same thermal speeds. For instance, lighter molecules in a gas will probably move faster (larger thermal speed) while heavier ones will move slower (smaller thermal speed).

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