Why is Avogadro's law always true? How and why do equal volumes of gases at equal pressure and temperature contain equal number of molecules? I know it is a fundamental principle in chemistry but I wonder how it works.
Answer
I'll attempt an explanation without any equations.
In kinetic theory, the pressure exerted by an ideal gas (point-like, non-interacting particles, elastic collisions) depends on the rate at which momentum is exchanged with the walls of any container as the molecules bounce off them.
The momentum is of course proportional to the molecule's speed and mass, but the rate at which molecules hit a wall additionally depends on how fast they are going and how many molecules there are in the volume of gas.
If you put that together you find that pressure depends on the number of molecules in a volume of gas and how much kinetic energy each molecule has.
The final step is to understand that the (average) kinetic energy of molecules in an (ideal) gas depends only on their temperature.
Thus a gas of a given temperature and number of molecules per unit volume will always exert the same pressure (in ideal circumstances). Or to turn this around, a gas of a given pressure and temperature will contain the same number of molecules per unit volume.
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