The rms speed of an ideal gas is $v_{\text{rms}}$ = $\sqrt{\frac{3RT}{M} }$ and the kinetic energy is $E_\text{k} = \frac32RT$. From this, it is concluded that the speed is mass dependent, while the kinetic energy isn't.
This doesn't make sense to me. I know the speed and kinetic energy for things other than ideal gases are surely mass dependent. The heavier an object is, the slower it is and will have a bigger kinetic energy. Why isn't this true for ideal gases?
As the mass increases, the velocity decreases, yes that is true. But how does the kinetic energy remain the same?
The increment in the mass is balanced by the decrement in the velocity. In other words, the velocity changes as the mass changes in such a manner that the kinetic energy of the molecules of the gas will remain to be same no matter what. It's something like the multiplication of two variables always giving the same constant value. Keeping in mind that this is true in an ideal environment.
We start with two samples of pure gas, one containing molecules of A (the larger molecule) and one containing molecules of B (the smaller molecule) with the same average speed (it will turn out that gas A has the higher temperature). If you mix these samples, their kinetic energy (per degree of translation freedom) will be different at first. However, they will quickly achieve thermal equilibrium. This means that the energy transfer in collisions between molecules of A and molecules of B average out. In a collision between a bat (molecule A) and a baseball (molecule B) coming at each other at the same speed, there is a kinetic energy transfer from bat to ball (the bat slows own a bit, the ball speeds up - if we assume an elastic collision).
Here is a simulation that shows one diatomic molecule and many monoatomic molecules. The diatomic is a bit slower on average.
The answer can be $$Speed \propto1/√m$$ And$$ K.E. = 1/2mv^2$$. Finally m will cut, and therefore K.E. does not depend on mass.
