Why Do Elements Behave Differently as Gas or Liquid?”

[scientifico]

Hello, why the same quantity of different elements behave in the same way (take about 22,4 L) when they are gas and they don't when they are liquid ?

 

[Philip Wood]

6.02 x 10²³ molecules of any gas at standard pressure and temperature occupy 22.4 litre. This is a special case of Avogadro's law: equal numbers of molecules of any gas occupy the same volume if they are at the same temperature and pressure. This can be deduced from the kinetic theory formula for gas pressure, plus the principle that the mean translational kinetic energy of gas molecules, even of different gases, is the same at the same temperature. I explained this in more detail on the thread "Explaining Avogadro's Law using kinetic theory" (September 4th 2012). I don't think there's a much simpler way to arrive convincingly at Avogadro's law, but I'd like to be shown otherwise.

 

[Nugatory]

Hello, why the same quantity of different elements behave in the same way (take about 22,4 L) when they are gas and they don't when they are liquid ?

Hand-waving answer, qualitatively good enough but not scientifically rigorous:

In a gas, the molecules are bouncing around independently so they can spread out to fill a large volume - the number of molecules per unit volume just goes down, and with it the pressure. The type of the molecules is somewhat unimportant, what matters is the number of molecules per unit volume.

In a liquid, the molecules want to cling to one another instead of spreading out to fill the available space. The volume will be more or less constant and depends on how tightly the molecules are attracted to one another.

 

[haruspex]

Suppose you have a container of gas at a given temperature and pressure, and by some magic you get to double the mass of every molecule without altering the velocities. This doubles the KE of each molecule, which means both temperature and pressure double. Now you allow the gas to cool back to its original temperature. The average speed of the molecules drops until the KE per molecule is as before. This, it turns out, means the pressure is also restored to its original. It follows that for a given temperature and pressure, the relationship between volume and number of molecules is independent of the molecular mass. So it comes down to the relationship between pressure and KE per molecule.
In liquids and solids, the molecules are bound together by forces which depend on their chemophysical natures. This is like springs with different moduli.

 

[scientifico]

The type of the molecules is somewhat unimportant, what matters is the number of molecules per unit volume.

But if a molecule is smaller won't them be more in the same volume like in this picture ?

 

[nasu]

But if a molecule is smaller won't them be more in the same volume like in this picture ?

If the two boxes are at the same temperature, the second one will have a larger pressure. You have to compare them in the same conditions of pressure and temperature. The molar volume (the 22.4 L) is defined in normal conditions (room temperature and atmospheric pressure). If the conditions are different the volume will be different.

 

[Philip Wood]

Scientifico You might indeed think that more would fit if the molecules were smaller. That's why Avogadro's Law is not trivial or obvious. It might help to consider two points:

(1) The molecules have big empty spaces between them: the molecules aren't elbowing each other apart, as in a solid or liquid.

(2) Note the very specific conditions under which there are equal numbers of different kinds of molecules in the same volume: equal pressure and temperature. It is only by considering in detail what each of these conditions implies (in terms of molecules) that we can really understand how Avogadro's law arises. Again I refer you to the thread "Explaining Avogadro's Law using kinetic theory" (September 4th 2012).

 

[Nugatory]

But if a molecule is smaller won't them be more in the same volume like in this picture ?

You'd think so... Until you look at the numbers. The size of a gas molecule is something like 10^-8 cm (an oxygen or nitrogen molecule is about half that size). So if you have 6x10²³ of them, that's a total volume of less than one cubic centimeter. Spread that through 22.4 liters (22,400 cubic centimeters) and you'll see that it's nearly all empty space and the molecules can be thought of as point particles.

 

[nasu]

You'd think so... Until you look at the numbers. The size of a gas molecule is something like 10^-8 cm (an oxygen or nitrogen molecule is about half that size).

This does not invalidate your point but the size of oxygen and nitrogen molecules is around 3 Angstroms (or 3 x 10^(-8)cm) and not half an Angstom.

 

[scientifico]

has Avogadro discovered his law making gasous hydrogen and oxygen reacting to obtain H2O ?

 

[Philip Wood]

I think so. Avogadro built on the discovery of Gay-Lussac that when gases reacted, the gas volumes involved (at the same temperature and pressure) were in simple ratios. Avogadro hypothesised that this was because equal volumes of gases (at the same temperature and pressure) contained equal numbers of molecules. These would naturally react in simple ratios. Part of the brilliance of Avogadro was to realize that even for a single element in a gaseous state the molecules weren't necessarily atoms but could be pairs or triplets of atoms.