Which statements about a sample of gas containing molecules of different masses are true?

Check all that apply.

__ The rms speed depends only on temperature, and so all types of particles in the sample have the same rms speed.

__ More-massive gas molecules in the sample have lower rms speed than less-massive ones.

__ More-massive gas molecules in the sample have higher rms speed than less-massive ones.

The kinetic molecular theory of gases explains how gas molecules behave in terms of motion, speed, and energy.

One important aspect of this theory deals with the relationship between temperature and the average speed of the gas molecules. Increasing the temperature of a gas sample increases the average kinetic energy of the molecules. The kinetic energy of a molecule determines its speed. It is important to realize that not all molecules in a sample will have the same kinetic energy, which is why we refer to the average kinetic energy and the average speed. The speed of a particle with average kinetic energy is called the *root mean square* (rms) speed, *v*_{rms}.

The rms speed may be expressed by the following equation:

${\mathbf{v}}_{\mathbf{rms}}\mathbf{=}\sqrt{\frac{\mathbf{3}\mathbf{RT}}{\mathbf{M}}}$

where *R* is the ideal gas constant, *T* is the absolute temperature, and *M* is the molar mass of the substance in kilograms per mole.

The constant motion of gas molecules causes diffusion and effusion. Diffusion is the gradual mixing of two substances resulting from the movement of their particles. Effusion is the gradual escape of gas molecules through microscopic holes in their container.

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Root Mean Square Speed concept. You can view video lessons to learn Root Mean Square Speed. Or if you need more Root Mean Square Speed practice, you can also practice Root Mean Square Speed practice problems.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Davis' class at UCF.