Question

A chemist 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?

Answer 1

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

Step-by-step explanation:

Pressure in the container is P and volume is V.

Temperature of the helium gas molecules =
`T_1`

Molecules helium gas = x

Moles of helium has =
`n_1= (x)/(N_A)`

PV = nRT (Ideal gas equation)

`PV=n_1RT_1`...[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 =
`(x)/(4)`

Moles of helium has left after removal =
`n_2= (x)/(4* N_A)`

`PV=n_2RT_2`...[2]

`n_1RT_1=n_2RT_2`

`(x)/(N_A)* T_1=(x)/(4* N_A)* T_2`

`T_1=(T_2)/(4)`

`T_2=4T_1`

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