Rate of effusion dependance on pressure

[jd12345]

In my class rate of effusion was told to be directly proportional to the mean speed of gas molecules which is intuitive and i understand. RMS speed of molecules is √3RT/M
So rate of effusion is inversely proportional to sqaure root of molar mass

But i don't understand how rate of effusion is directly proportional to pressure
RT = PV
So RMS speed = √PV/M so rate of effusion should be proportional to square root of pressure right? But apparently its not, please explain me why

Thank you!

 

[klimatos]

In my class rate of effusion was told to be directly proportional to the mean speed of gas molecules which is intuitive and i understand. RMS speed of molecules is √3RT/M
So rate of effusion is inversely proportional to sqaure root of molar mass

But i don't understand how rate of effusion is directly proportional to pressure
RT = PV
So RMS speed = √PV/M so rate of effusion should be proportional to square root of pressure right? But apparently its not, please explain me why

Thank you!

It makes more sense if you replace PV=RT with the statistical mechanical equation of state,
P = nkT. Then the number density (number of molecules per unit volume) is directly proportional to the pressure. The more molecules per unit volume, the greater the effusion through an opening.