# A container has a volume of 42 L and holds 12 mol of gas. If the container is compressed such that its new volume is 14 L, how many moles of gas must be released to maintain a constant temperature and pressure?

Jun 8, 2018

$8$ moles of gas must be released.

#### Explanation:

For constant temperature and pressure, we can use Avogadro's law, which states that,

$n \propto V$ or ${n}_{1} / {V}_{1} = {n}_{2} / {V}_{2}$

$\therefore \left(12 \setminus \text{mol")/(42 \ "L")=n_2/(14 \ "L}\right)$

n_2=(12 \ "mol")/(42color(red)cancelcolor(black)"L")*14color(red)cancelcolor(black)"L"

$= 4 \setminus \text{mol}$

So, the number of moles that have to be released is:

$\Delta n = 12 \setminus \text{mol"-4 \ "mol}$

$= 8 \setminus \text{mol}$