# A container has a volume of 18 L and holds 6 mol of gas. If the container is compressed such that its new volume is 3 L, how many moles of gas must be released to maintain a constant temperature and pressure?

Mar 21, 2018

$5$ moles

#### Explanation:

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

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

So, we need to find the new number of moles, and we can rearrange the equation into,

${n}_{2} = {n}_{1} / {V}_{1} \cdot {V}_{2}$

Now, we can substitute into the given values, and we get

n_2=(6 \ "mol")/(18color(red)cancelcolor(black)"L")*3color(red)cancelcolor(black)"L"

$= 1 \setminus \text{mol}$

So, the new amount of moles will be $1 \setminus \text{mol}$.

In order to find the difference, $\Delta n$, we use,

$\Delta n = {n}_{2} - {n}_{1}$

$= 1 \setminus \text{mol"-6 \ "mol}$

$= - 5 \setminus \text{mol}$

So, five moles of the gas must be released.