# Given the following, how do you explain why these two gases do not share the same velocity speed under these conditions? What variable must change in order to increase the average velocity of the molecules in either cylinder?

## Suppose you have two identical 2.0 L cylinders. Both cylinders are kept at exactly 25°C. One cylinder contains 0.250 moles of helium, and the other contains 0.250 moles of krypton. The volumes of these cylinders can change. a.

Dec 31, 2016

Gases at the same temperature will possess the same average kinetic energy, but since this depends on mass, the average speed will differ for gases of differing mass.

#### Explanation:

Since kinetic energy is a matter of mass and velocity

$K = \frac{1}{2} m {v}^{2}$

So, even though the gases are at the same temperature, if the masses of the atoms differ (as they do in this case), the velocities will differ.

Helium has a relative mass of 4, while that of krypton is 83.8

Since the average kinetic energy is equal for the gases

$\frac{1}{2} {m}_{H e} {v}_{H e}^{2} = \frac{1}{2} {m}_{K r} {v}_{K r}^{2}$

Rearrange

${v}_{H e}^{2} / {v}_{K r}^{2} = {m}_{K r} / {m}_{H e}$

${v}_{H e} / {v}_{K r} = \sqrt{{m}_{K r} / {m}_{H e}} = \sqrt{\frac{83.8}{4}} = 4.58$

The helium atoms will, on average move at 4.58 times greater speed.

To increase the average velocity in either cylinder, one need only increase the temperature of the gas in that cylinder.