Question

If Kinetic Energy is directly proportional to mass, than the gas with the larger mass would have the larger kinetic energy, right? But what if the two separate gases are in two non-rigid containers of equal volume (1 Liter), and at the same temperature (25 celsius). The two gases are Carbon monoxide and carbon dioxide. There are 2 atm of carbon monoxide, and 1 atm of carbon dioxide. I used PV=nRT to find the moles of CO and CO2 using these conditions and concluded that there is more of Carbon monoxide than there is Carbon dioxide. Shouldn't this mean that it has more kinetic energy than carbon dioxide? Still, I also know that temperature is indicative of average kinetic energy, and so if they are both the same temperature than they should have the same kinetic energy. So I guess I was confused about which was right.

Answer 1

Question #83336

If Kinetic Energy is directly proportional to mass, than the gas with the larger mass would have the larger kinetic energy, right? But what if the two separate gases are in two non-rigid containers of equal volume (1 Liter), and at the same temperature (25 celsius). The two gases are Carbon monoxide and carbon dioxide. There are 2 atm of carbon monoxide, and 1 atm of carbon dioxide. I used PV=nRT to find the moles of CO and CO2 using these conditions and concluded that there is more of Carbon monoxide than there is Carbon dioxide. Shouldn't this mean that it has more kinetic energy than carbon dioxide? Still, I also know that temperature is indicative of average kinetic energy, and so if they are both the same temperature than they should have the same kinetic energy. So I guess I was confused about which was right.

Answer:

Your first statement is correct, while the second one is not. The reason, why the second statement is wrong, is that the average kinetic energy of two gases at the same temperature is the same only in case if their number of moles is also the same:

"The average molecular kinetic energy is proportional to the ideal gas law's absolute temperature.

$$PV = \frac{2}{3} K$$

Thus, the product of pressure and volume per mole is proportional to the average (translational) molecular kinetic energy. [1]"

As there is 0.0409 mol of CO₂ and 0.0818 mol of CO, the average kinetic energy is not the same.

Reference:

[1] https://en.wikipedia.org/wiki/Kinetic_theory_of_gases

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