Distribution of Molecular Velocities

Not all molecules in a gas have the same velocity. The probability distribution for the molecular velocities tells us the likelihood of any individual velocity.

[@ericlol1337]

wow this is high key the best video and derivation example of this i have seen. also your off the cuff drawing of the gaussian hill is so good, i really appreciate that you didnt go "oh im not an artist so bear with me" and just put in the bare minimum. weird compliment but ykwim

[@reza_aliasgari]

Sir, your work is outstanding, thank you very much!

[@PhysicalChemistry]

You're welcome, and thanks for your comment

[@mortezakhoshbin]

outstanding.thank you

[@PhysicalChemistry]

thanks so much

[@user-kr5mg6sf6n]

but sir we already derived the partition function for ideal gas then why are we not using it....or why are we not using the 3d particle in a box energy levels what difference will it cause

[@PhysicalChemistry]

Great question, very observant. There is a key difference. The partition function here is for the *classical* ideal gas. (Notice that we use an integral instead of a sum in this video; any energy is allowed.) The partition function for a 3d particle in a box is for a *quantum mechanical* ideal gas. (Notice the presence of h, Planck's constant, in that partition function, while it is absent in this one.)

[@user-kr5mg6sf6n]

so does this mean that since earlier we derived/established that in the classical limit we can ignore quantum mechanics' energy quantization and because gases in a container of finite volume also have many many energy levels closely spaced, so we can assume gases' energy levels to be continous

[@PhysicalChemistry]

@@user-kr5mg6sf6n Yes, that's right. That's exactly what we are doing in this video. Once we assume the energy levels are continuous, we can evaluate the partition function with an integral instead of a sum.