# A container has a volume of 12 L and holds 8 mol of gas. If the container is compressed such that its new volume is 5 L, how many moles of gas must be released from the container to maintain a constant temperature and pressure?

Mar 5, 2018

4.67 mol

#### Explanation:

$P V = n R T$

T is constant. P is constant. R is constant.

$\frac{{n}_{1}}{{V}_{1}} = \frac{R T}{P}$

$\frac{{n}_{2}}{{V}_{2}} = \frac{R T}{P}$

Hence:
$\frac{{n}_{1}}{{V}_{1}} = \frac{{n}_{2}}{{V}_{2}}$

$\frac{8}{12} = {n}_{2} / 5$

$12 {n}_{2} = 40$

${n}_{2} = \frac{40}{12} = \frac{10}{3}$ mol

If we had 8 mol and now we have 3.33 mol, then 4.67 mol were released.