Does Avogadro's Law Account for Differences in Gas Density?

[tomlib]

TL;DR Summary

Does Avogadro's Law apply?

The law states that in the same volume at the same pressure, the number of any gas is the same. It seems to me that this law does not apply, since each molecule of a different gas must have a different size, and between the molecules there will also be different sizes of pressure force, density, etc. How can I clarify this idea?

 

[Ibix]

In a gas the typical space between molecules is much larger than the molecules, so how big they are is more or less irrelevant to how many of them are to be found in a given volume. It is true that no gases truly behave as ideal gases, but it's a very good approximation in many cases.

 

[Redbelly98]

You can google either real gas or van der Waals equation, and you'll find how the effects of particle size and interparticle forces can be accounted for.

 

[tomlib]

I'm sorry I don't have enough experience to counter but it seems to me from a layman's point of view that if a gas has a different density it can't have the same number of molecules and the distance between them can't always be the same. Apparently this is being tried with some reactions and a lot of products, but it would be very strange to me.
Unless, at the same pressure, the pressure in the mass would be different.

 

[Lord Jestocost]

One has to understand that Avogadro's law is an experimental gas law.

"These kinds of laws are first and foremost reliable regularities found in controlled experiments and which can be expressed as mathematical relations."
(Ismo T. Koponen, Experimental Laws and Measurements in Physics: The Legacy of 19th-Century Empiricism)

 

[jbriggs444]

I'm sorry I don't have enough experience to counter but it seems to me from a layman's point of view that if a gas has a different density it can't have the same number of molecules and the distance between them can't always be the same. Apparently this is being tried with some reactions and a lot of products, but it would be very strange to me.
Unless, at the same pressure, the pressure in the mass would be different.

Possibly you are failing to account for temperature.

Certainly you can imagine Nitrogen gas (molecular weight 28) being twice as dense at Hydrogen gas (molecular weight 2) if the intermolecular separation is the same. You would be right to think that if the molecules in both gasses were moving equally rapidly on average that the Nitrogen gas would have 14 times the pressure.

But if the two gasses are at the same temperature, the nitrogen molecules will be moving more slowly on average.

The temperature of an ideal gas corresponds to the average kinetic energy of its component molecules. Not to their average velocity. If you multiply the mass of the molecules by a factor of 14, you divide their velocity by a factor of $\sqrt{14}$. [At fixed temperature].

If you work out the pressure for particles with momentum multiplied by $\frac{14}{\sqrt{14}}$ striking the walls with frequency reduced by $\sqrt{14}$ you get that the pressure for a given temperature is unchanged. More massive molecules does not equate to higher pressure.

I do not know enough thermodynamics to justify why temperature corresponds to kinetic energy per molecule. It likely has to do with entropy and how a mixture of different ideal gasses in the particle model will equilibriate in a state where both component gasses in the mixture will end up with the same Maxwell-Boltzmann distribution of per particle energies. The thermodynamic definition of temperature has to do with the partial derivative of entropy with respect to energy in an equilibrium state, thus grounding that concept in a theoretical sense.

For dummies like us, the derivation or the confirming experimental evidence are both unimportant. Only the fact that temperature [in an ideal gas] correlates with per particle kinetic energy is relevant.

 

[nasu]

How do you get the factor of 2 for density (in the second paragraph)?

 

[jbriggs444]

How do you get the factor of 2 for density (in the second paragraph)?

Are you referring to Hydrogen at molecular weight 2 and Nitrogen at molecular weight 28? If so, the factor of two is because both are diatomic gasses.

Oh, drat. You are right. 14 times as dense, not twice.

 

[apostolosdt]

Under normal conditions, the average distance between two molecules is about 40 Angstroms. That gives the molecule a typical volume too large compared to the molecule’s volume (roughly 12,000 to 15,000 larger, even for polyatomic molecules). Add to that the statistical fluctuations and you can easily accept the experimental universality of the Law.

 

[phyzguy]

I'm sorry I don't have enough experience to counter but it seems to me from a layman's point of view that if a gas has a different density it can't have the same number of molecules and the distance between them can't always be the same. Apparently this is being tried with some reactions and a lot of products, but it would be very strange to me.
Unless, at the same pressure, the pressure in the mass would be different.

You need to accept that Avogadro's law is true to a pretty high degree of accuracy, and has been tested for over a hundred years. So if it is very strange to you, it can't be that the law is wrong. It must be that you are not understanding what it says. The law doesn't say anything about density. It just says that two gases with equal volumes, temperatures, and pressures have the same number of molecules. One gas might easily be heavier than the other.