# 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 4 L, how many moles of gas must be released from the container to maintain a constant temperature and pressure?

Aug 2, 2018

The number of moles to be released is $= 5.33 m o l$

#### Explanation:

$\text{Volume"/"Number of moles"= " Constant}$

At constant temperature and pressure

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

The initial volume is $= 12 L$

The initial number of moles is ${n}_{1} = 8 m o l$

The final volume is ${V}_{2} = 4 L$

The final number of moles is

${n}_{2} = {V}_{2} / {V}_{1} \cdot {n}_{1} = \frac{4}{12} \cdot 8 = \frac{8}{3} m o l$

The number of moles to be released is

$= {n}_{2} - {n}_{1} = 8 - \frac{8}{3} = \frac{16}{3} = 5.33 m o l$