Why equal volumes of diferent gases have the same number of molecules @ STP?

[Rashik]

Hi,
A silly techiniacal, very basic but logical question. Trying to understand since long but unable to justify myself. Can u help?

Deferent gases have deferent molecular size, then how is it possible that equal volume of deferent gases have same numbers of volume at standard temperature & pressure?

We can analyze it by saying that in two different but same size container say 1 m3 (1mx1mx1m)(each), if filled with Tennis balls and filled with foot balls will be equal in numbers? Which looks bit illogical but is widely accepted in chemistry. Why?

Regards
Rashidk

 

[gleem]

Keep in mind this is for an ideal gas and applies to most gases at low pressures. The football/tennis ball analogy for different molecules is misleading. The actual space taken up by any molecule is minuscule and most of the volume is empty space. The actual volumes of the molecules are not radically different. for example the radius of Xe is 140 pm and that of N₂ is 200 pm even though Xe is about 4.5 time more massive than N₂.

It has been shown experimentally that PV =nRT where n is the number of moles. One mole of any gas contains the same number of molecules (Avogadro's Number), The kinetic theory shows that the product PV is proportional to the number of molecules with no reference to size.

 

[Bystander]

shown experimentally that PV =nRT

... technically "in the limit of zero pressure and infinite temperature."

 

[Rashik]

Thanks Gleem and Bystander.
I got the point.

Regards,
Rashik

 

[lychette]

this relationship is known as Avagadros law and came about (1811)before the development of the Kinetic theory .
The ideal gas equation is PV = nRT. Imagine 2 gases 1 and 2
for gas 1... P₁V₁ = n₁RT₁
for gas 2 ...P₂V₂ = n₂RT₂
For equal volumes at the same pressure P₁V₁ = P₂V₂
If they are at the same temperature the T₁ = T₂
therefore n₁ must equal n₂

 

[Rashik]

Thanks Lychette.
Nice explanation. I got the point...

 

[Khashishi]

Avagadro's law is empirical, but kinetic theory provides an explanation for it.
Temperature tells you something about the average kinetic energy of each molecule. So you can calculate the force of each molecule hitting the wall of a chamber. Multiply this by the particle flux and you have the pressure.
Verify that you get the same pressure for equal volumes and temperature independent of the mass.

 

[lychette]

Avagadro's law is empirical, but kinetic theory provides an explanation for it.
Temperature tells you something about the average kinetic energy of each molecule. So you can calculate the force of each molecule hitting the wall of a chamber. Multiply this by the particle flux and you have the pressure.
Verify that you get the same pressure for equal volumes and temperature independent of the mass.

over a very wide range of temperature and pressure the Kinetic Theory agrees with experimental observations. At high pressure and low temperature modifications need to be made to the theory to confer with experimental observations.