Why is volume an extensive property but molar volume an intensive one? If we take volume of a system, then it's often defined as volume of container and is an extensive property but it's often said that molar volume is an intensive property.  How exactly does dividing the volume by number of moles turn an extensive property into an intensive one?
reference: 21:36 of this of this video
 A: The number of moles is proportional to the number of atoms/molecules in the system.
Suppose you bring another identical copy of the system, and consider the two copies as a whole.
The number of atoms/molecules will double, so will the number of moles.
For usual solids and liquids, the volume will double (assuming external conditions like pressure, temperature remains the same).
For gases, the volume does not depend on the mass (it will consume the whole volume of the container). However, if another identical container (having the same mass of gas, and same $P$, $T$) is brought, the volume of the whole system will double. So, both these are extensive properties.
However, the ratio $\frac{\text{volume}}{\text{no of moles}}$ will remain the same. So it is an intensive property.
A: The ratio of an extensive property to another extensive property is an intensive property. $$\frac{extensive \;property}{another \;extensive\; property}={\text extensive\, property\, per \,unit \,}$$
The extensive properties depend on amount and the amount is fixed by the property taken in denominator.
Molar volume =$\frac{volume\, of\, gas}{no.\, of\, moles}$
In the case of molar volume , dividing by no of moles fixes the amount to 1 mole.Thus molar volume is the volume of 1 mole of gas , a property which doesn't depend on the amount under observation.
A: The ratio of two extensive properties of the same system is an intensive property. Mass, volume, and moles are extensive properties. Mass divided by volume (density) and volume divided by moles (molar volume) are intensive properties.
An extensive property depends on the amount of stuff, an intensive property doesn’t. Take a room full of gas. It has volume, mass, pressure and temperature. If you divide the room in half each half has only half the original volume and mass of gas. But each half has the same density, pressure, molar volume and temperature as the original room full of gas.
Hope this helps
