Question

that equal volumes of gas under the same conditions have equal numbers of molecules. This concept is a very important one, as it will be used often in future studies.

Answer 1

This one is easy. It's the Avogadros' Hypothesis or Avogadros' Law, where the equal volumes of gases in SAME conditions have an equal amount of molecules!

Answer 2

Avagadro’s law states at constant temperature and pressure, volume is directly proportional to the number of molecules of the gas.

For example

At STP that is standard temperature and pressure at which T = 273K and P = 1 atm

Volume occupied by 1 mole (
`6.022* 10^(23)` gas molecules) of any gas is equal to 22.4L

That is

1 mole = 22.4L

2 mole = 44.8 L

3 mole = 67.2 L

So 1 mole of
`CO_2` gas =22.4L (
`6.022* 10^(23)` gas molecules)

1 mole of
`H_2` gas =22.4L (
`6.022* 10^(23)` gas molecules)

1 mole of
`Cl_2` gas =22.4L (
`6.022* 10^(23)` gas molecules)