Gases Question

[letmein1992]

Equal volumes of H2 gas and O2 gas exist at the same temperature. Which of the following statements must be true of these two samples?

A. The number of molecules in each gas must be same.
B. The pressure of the two gases must be the same.
C. The speed of any H2 gas molecules will be greater than the speed of any O2 molecule.
D. The molecules of H2 gas will have the same kinetic energy as the molecules of O2 gas.

I don't understand is why D is the correct choice. When it said KE, I automatically thought KE=1/2mv^2. Since H2 is lighter than O2, these two gases should have different kinetic energies.

Can someone please explain why these two gases would have the same kinetic energy?

Thanks!

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[basophilic]

D should probably say average KE. Average KE of ANY population of particles is proportional to temperature according to equipartition theorem. Hence, if two gases are at the same temperature, they will have the same average KE (regardless of the identity of the gases)
KE = 1/2mv2 applies only to a single particle, not to a POPULATION as is mentioned in question stem.
A and B should be eliminated because you need the RATIO of pressure to # moles to be constant. C should be eliminated because the question deals with a population of gases, whose speeds are distributed in a distribution (Boltzmann distribution, which is pretty similar to the statistical bell curve); hence, you should have some O2 molecules being faster than H2 molecules and vice versa.

 

[letmein1992]

E = 1/2mv2 applies only to a single particle, not to a POPULATION

clarified everything. Thank you!