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?a. T2=1/16T1b. T2=2T1c. T2=16T1d. T2= 1/2T1e. T2=4T1f. None of theseg. T2=1/4T1

Answer 1

Answer:

e. T₂= 4T₁

Explanation:

Initially, we have a number of moles (n₁) a gas sample at a certain pressure (P), temperature (T₁) and volume (V). We can relate these variables through the ideal gas equation.

P . V = n₁ . R . T₁

where,

R is the ideal gas constant

We can rearrange this equation like:

$T_{1}=\frac{P.V}{n_{1}.R}$

If only one fourth of the initial molecules remain n₂ = 1/4 n₁. The new temperature (T₂) assuming pressure and temperature remain constant is:

$P.V=n_{2}.R.T_{2}=\frac{1}{4} n_{1}.R.T_{2}\\\frac{P.V}{n_{1}.R} =\frac{1}{4} T_{2}\\T_{1}=\frac{1}{4} T_{2}\\T_{2}=4.T_{1}$