# Avogadro's law states that the volume of a gas is directly proportional to the number of particles. My teacher, after saying this, says an equal volume of all gases contains an equal number of...

Avogadro's law states that the volume of a gas is directly proportional to the number of particles. My teacher, after saying this, says an equal volume of all gases contains an equal number of particles. How?

*print*Print*list*Cite

This law bothered me for a long time. I knew the law and could use it, but it just didn't make sense how a liter of hydrogen and a liter of neon could have the same number of particles. The thing about gasses though is that they are a little odd. They have no definite shape, and volume is just the tip of the story.

Important to Avogadro's Law is pressure. And gasses exert pressure evenly in all directions. It's why bubbles are round. That pressure is caused by the particles whacking into the sides of a container. Now here's the important part. That pressure is affected by a few things. More particles means more pressure because more collisions are occurring. The speed of the particles is also a factor. Fast particles have more kinetic energy, which means they hit harder than slow particles. Changes in temperature cause changes in particle speed. Hot = faster.

Avogadro's Law says gasses at equal volume, temperature, and pressure have the same number of particles.

The best way for me to explain how that's possible is to talk about momentum of particles. Hydrogen has low mass particles, but they move fast. So at a given temperature and volume, it's pressure is "x." Neon has higher mass particles than hydrogen, but they move slower than hydrogen. So at that same temperature and volume, the pressure is still "x." Both gasses have the same temp, volume, pressure, AND number of particles.

See, as per Avagadro's Law:- " Equal volumes of gases (at same temperature & pressure), contains equal moles"

Now, Number of particles = number of moles*Avagadro's Number

Avagadro's Number = 6.022*10^23

To prove this, Let there be 3 gases having volume 'v' litres at temperature 'T' Kelvin and Pressure 'P' atm

Now, As per Ideal gas eqaution i.e p*v = n*R*T; where p = pressure of the gas in atm v = volume of the gas in litres , n = moles of the gas , R = universal gas constant = 0.0821 atm-L/mole/K & T = temperature in Kelvin,

number of moles of gas 1, n(1) = (R*T)/(P*V)...........(1)

number of moles of gas 2, n(2) = (R*T)/(P*V)...........(2)

number of moles of gas 3, n(3) = (R*T)/(P*V)...........(3)

Since, (1) = (2) = (3) , hence the law is proved.