Question

A sample of Helium has a volume of 2 Liters when the pressure is 250 torr, What volume does the gas occupy at 100 torr?

Answer 1

At constant temperature, the volume $V$ of an ideal gas is inversely proportional to its pressure $p$:

$V\propto\frac{1}{p}$ , or $p_1V_1 = p_2V_2$

where $p_1$ and $V_1$ are pressure and volume in the initial state , respectively, and $p_2$ and $V_2$ are pressure and volume in the final state , respectively.

In the initial state, the system has pressure $p_1$ of 250 torr and its volume $V_1$ is 2 L. In the final state, the pressure $p_2$ is 100 torr. Using the relation above, we get the volume in the final state:

$V_2 = \frac{p_1V_1}{p_2} = \frac{250\text{ torr}\cdot2\text{ L}}{100\text{ torr}} = 5$ L.

Answer: the helium sample occupies 5 L at 100 torr.