# Why is the volume in this compress gas cylinder constant throughout?

I am stuck on this gas question and its really stressing me out.

A compressed cylinder of gas contains $2.25 \cdot 10^3~\mathrm{g}$ of $\ce{N2}$ gas at a pressure of $4.25 \cdot 10^7~\mathrm{Pa}$ and a temperature of $19.4~^\circ\mathrm{C}$. What volume of gas has been released into the atmosphere if the final pressure in the cylinder is $1.80 \cdot 10^5~\mathrm{Pa}$? Assume ideal behaviour and that the gas temperature remains unchanged.

I know I have to use the ideal gas law for this.
I've seen the solution for this problem, but something still doesn't make sense to me. In the solution they used $$\frac{nRT}{p} = \frac{n_\mathrm{f}RT}{p_\mathrm{f}},$$ to find the final amount of nitrogen gas in moles, $n_\mathrm{f}$, remaining in the gas cylinder. But why is the initial volume and final volume the same? Since gas is being released into the atmosphere, shouldn't the final volume change?

It is about the volume of the cylinder, which of course does not change. You do not also consider the volume of the escaped nitrogen gas.

• Why don't we consider the volume of the gas released? Isn't, V, the volume of gas there is in the container and since gas is being released, shouldn't there be a change in the final volume of gas? – Xihai Luo Feb 20 '15 at 20:25

Gases always occupy whole volume of the container, and it's not to going to change throughout.