Rate of effusion dependance on pressure

In summary, the rate of effusion is directly proportional to the mean speed of gas molecules and inversely proportional to the square root of molar mass. However, it is not directly proportional to pressure because the number density of molecules is directly proportional to pressure, leading to a higher rate of effusion through an opening.
  • #1
jd12345
256
2
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!
 
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  • #2
jd12345 said:
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.
 

1. How does pressure affect the rate of effusion?

The rate of effusion is directly proportional to the pressure. This means that as the pressure increases, the rate of effusion also increases. This is because higher pressure causes more gas molecules to collide with the opening and escape, resulting in a faster effusion rate.

2. Is there a limit to how much pressure can affect the rate of effusion?

Yes, there is a limit. As the pressure increases, the gas molecules become more densely packed and the space between them decreases. This reduces the number of collisions and can eventually lead to a plateau in the rate of effusion, where further increases in pressure do not significantly affect the rate.

3. Can the rate of effusion be affected by changes in temperature?

Yes, the rate of effusion is also dependent on temperature. As temperature increases, the gas molecules gain more kinetic energy and move faster, resulting in a higher rate of effusion. This is why gas molecules tend to effuse faster at higher temperatures.

4. How does the size of the gas molecule affect the rate of effusion at different pressures?

The rate of effusion is inversely proportional to the square root of the molar mass of the gas molecule. This means that smaller gas molecules will effuse faster than larger ones at the same pressure. This is because smaller molecules have higher average speeds and are able to escape through the opening more easily.

5. Can the rate of effusion be affected by the size or shape of the opening?

Yes, the size and shape of the opening can affect the rate of effusion. A smaller opening will result in a slower rate of effusion because fewer gas molecules can escape at once. Similarly, a longer and narrower opening will also slow down the rate of effusion compared to a shorter and wider opening.

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