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

Answer:

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 =$T_1$

Molecules helium gas = x

Moles of helium has = $n_1= \frac{x}{N_A}$

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 = $\frac{x}{4}$

Moles of helium has left after removal = $n_2= \frac{x}{4\times N_A}$

$PV=n_2RT_2$...[2]

$n_1RT_1=n_2RT_2$

$\frac{x}{N_A}\times T_1=\frac{x}{4\times N_A}\times T_2$

$T_1=\frac{T_2}{4}$

$T_2=4T_1$

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