[Lussac13]

I have a fairly simple question about Avogadro's hypothesis:

Avogardro's hyp: "equal volumes of (ideal) gases at the same temperature and pressure contain the same number of molecules regardless of their chemical nature and physical properties."

Suppose you have 2 different gases (A and B) at equal temp (T) and volume (V). Because the temperatures are equal, the avg KE of the two gases must be equal. If mass(A) > mass(B), then velocity of A is less than velocity of B. Pressure is a measure of the average linear momentum of the moving molecules of a gas. One might say that, because A has a greater mass but lesser velocity, and B has a lesser mass but greater velocity, the momentum of the two gases would be the same and therefore the P of each gas is the same (as one would expect from Avogadro's hypothesis). But mathematically, I don't see how we the momentums of the 2 gases are equal. For example, if mass(A) is 4x that of mass(B), with the same KE, velocity(B) would be twice that of velocity(A). Therefore, momentum of the average particle A would be twice that of the average particle B, and gas A should have a larger P. This obviously is not the case. Can someone point out the error in the logic here?

Thanks.

[Borek]

Check the derivation here: https://en.wikipedia.org/wiki/Kinetic_theory_of_gases

[mjc123]

Strictly, the average momentum of the molecules is zero - there are as many moving in one direction as the opposite. The rms velocity of B is twice that of A, and the rms momentum of A is twice that of B. But since A molecules are slower than B, the rate of collisions with the wall is lower, therefore the rate of transfer of momentum works out the same.

[Lussac13]

Thank you. That makes sense.