# Solving: Kinetic Theory of Gases

Hi, I need some assistance with the following problems:

1. If the translational rms speed of the water vapor molecules (H2O) in air is 664 m/s, what is the translational rms speed of the carbon dioxide molecules (CO2) in the same air? Both gases are at the same temperature.

2. Near the surface of Venus, the rms speed of carbon dioxide molecules (CO2) is 715 m/s. What is the temperature (in kelvins) of the atmosphere at that point?

3. Two gas cylinders are identical. One contains the monatomic gas neon (Ne), and the other contains an equal mass of the monatomic gas radon (Rn). The pressures in the cylinders are the same, but the temperatures are different. Determine the ratio KEAvg,radon/KEAvg,neon of the average kinetic energy of a radon atom to the average kinetic energy of a neon atom.

4. Initially, the translational rms speed of a molecule of an ideal gas is 583 m/s. The pressure and volume of this gas are kept constant, while the number of molecules are doubled. What is the final translational rms speed of the molecules?

5. The temperature near the surface of the earth is 295 K. An argon atom (atomic mass = 39.948 u) has a kinetic energy equal to the average translational kinetic energy and is moving straight up. If the atom does not collide with any other atoms or molecules, how high up would it go before coming to rest? Assume that the acceleration due to gravity is constant throughout the ascent.

#### Solution Preview

1. The root mean square speed is given by SQRT(3 pressure/density gas). The density of a gas is given by the number of moles x the molecular weight divided by the volume of gas. The pressure and volume for these molecules is the same. The parameter that is changing is the molecular weight of the gas in question.

We obtain finally the equation Vrms(1)/Vrms(2)=SQRT(M2/M1) - 1 is for gas 1 and 2 is for gas 2.

So if you let 2 be water vapor and 1 be CO2, at the same temperature you obtain

Vrms(1) = 664 m/s SQRT((12 ...

#### Solution Summary

This solution is comprised of a detailed response which addresses each of these physics-based questions. The equations and variables needed are provided. This is all completed in about 420 words.