Achemist prepares a sample of helium gas at a certain pressure, temperature and volume and then removes all but a fourth of the gas molecules (only a fourth remain). how must the temperature be changed (as a multiple of t1) to keep the pressure and the volume the same?

The temperature must be changed to 4 times of the initial temperature so as to keep the pressure and the volume the same.

Explanation:

Pressure in the container is P and volume is V.

Temperature of the helium gas molecules =

Molecules helium gas = x

Moles of helium has =

PV = nRT (Ideal gas equation)

...[1]  

After removal of helium gas only a fourth of the gas molecules remains and pressure in the container and volume should remain same.

Molecules of helium left after removal =

Moles of helium has left after removal =

...[2]

The temperature must be changed to 4 times of the initial temperature so as to keep the pressure and the volume the same.