# A container has a volume of 14 L and holds 9 mol of gas. If the container is compressed such that its new volume is 4 L, how many moles of gas must be released from the container to maintain a constant temperature and pressure?

Jul 4, 2016

$P V = n R T$

Rewriting, we can say

$\setminus \frac{n}{V} = \setminus \frac{P}{R T}$

According to your problem, the right side is constant, since the temperature and pressure - both remain constant during the entire process. This means that $\frac{n}{V}$ is constant during the whole process. Again, this means

$\setminus \frac{{n}_{i n i t i a l}}{{V}_{i n i t i a l}} = \setminus \frac{{n}_{f i n a l}}{{V}_{f i n a l}}$

$\setminus R i g h t a r r o w {n}_{f i n a l} = \setminus \frac{{V}_{f i n a l}}{{V}_{i n i t i a l}} {n}_{i n i t i a l} = \setminus \frac{18}{7} \setminus \textrm{m o l}$

The number of moles that have escaped is given by ${n}_{f i n a l} - {n}_{i n i t i a l} = \setminus \frac{45}{7} \setminus \textrm{m o l}$.