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

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Discussion Overview

The discussion centers on the question of why equal volumes of different gases contain the same number of molecules at standard temperature and pressure (STP). Participants explore this concept through theoretical and empirical lenses, referencing both Avogadro's law and the kinetic theory of gases.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions the logic behind equal volumes of different gases containing the same number of molecules, using an analogy of different-sized balls in containers.
  • Another participant clarifies that the concept applies to ideal gases and emphasizes that the actual volume occupied by gas molecules is negligible compared to the empty space in a gas.
  • It is noted that Avogadro's law states that one mole of any gas contains the same number of molecules, regardless of the gas type, and this is supported by the ideal gas equation PV = nRT.
  • A participant mentions that the ideal gas law holds true under specific conditions, such as low pressure and high temperature.
  • Further contributions explain that while Avogadro's law is empirical, the kinetic theory provides a framework for understanding the relationship between pressure, volume, and the number of molecules.
  • Some participants discuss the implications of temperature on the average kinetic energy of molecules and how this relates to pressure, suggesting that pressure remains consistent across different gases at the same volume and temperature.
  • There is a mention that modifications to the kinetic theory may be necessary at high pressures and low temperatures to align with experimental observations.

Areas of Agreement / Disagreement

Participants generally agree on the validity of Avogadro's law and the ideal gas equation, but there are nuances regarding the applicability of these concepts under different conditions. The discussion remains unresolved regarding the implications of molecular size and the limits of the ideal gas law.

Contextual Notes

Some limitations are noted, such as the dependence on ideal gas behavior and the conditions under which the ideal gas law is applicable. There is also an acknowledgment that the kinetic theory may require adjustments at certain pressures and temperatures.

Rashik
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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
 
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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.
 
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gleem said:
shown experimentally that PV =nRT
... technically "in the limit of zero pressure and infinite temperature."
 
Thanks Gleem and Bystander.
I got the point.

Regards,
Rashik
 
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
 
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Thanks Lychette.
Nice explanation. I got the point...
 
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.
 
Khashishi said:
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.
 

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