Ideal gas law problems

Question

I got really confused about real gases volume and ideal gas volume. Ideal gas molecules take up no space, if we put gas into a 2.4L water bottle, we know that all the gas will expand all over the bottle and we say at this moment the gas has volume of 2.4L. So what is this volume?

Answer 1

That means the gas molecules are spread out in a 2.4L volume. There's nothing between the air molecules themselves.

Answer 2

Here is the definition of an ideal gas:

An ideal gas is defined as one in which all collisions between atoms or molecules are perfectly eleastic and in which there are no intermolecular attractive forces. One can visualize it as a collection of perfectly hard spheres which collide but which otherwise do not interact with each other. In such a gas, all the internal energy is in the form of kinetic energy and any change in internal energy is accompanied by a change in temperature.

So it is not true that

Ideal gas molecules take up no space,

they take the space of a molecule, have the mass of the molecule and kinetic energy and momentum.

if we put gas into a 2.4L water bottle, we know that all the gas will expand all over the bottle and we say at this moment the gas has volume of 2.4L. So what is this volume?

This volume is occupied by a huge number of molecules, order of 10^23 per mole, bouncing elastically against each other and displaying the ideal gas law:

P*V=nRT

where p is the pressure, V is the volume, n is the number of moles, T is the temperature and R is equal to 8.3145J/mol K .