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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?

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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.

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  • $\begingroup$ 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? $\endgroup$ – Xihai Luo Feb 20 '15 at 20:25
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Gases always occupy whole volume of the container, and it's not to going to change throughout.

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