# A container has a volume of 18 L and holds 7 mol of gas. If the container is compressed such that its new volume is 8 L, how many moles of gas must be released to maintain a constant temperature and pressure?

Jun 22, 2016

$3 \frac{8}{9} m o l$

#### Explanation:

Let n moles of gas to be released .

Given
${V}_{1} = \text{Initial volume of gas} = 18 L$

${V}_{2} = \text{Final volume of gas} = 8 L$

${n}_{1} = \text{Initial no mole of gas} = 7 m o l$

${n}_{2} = \text{Final no.of moles of gas} = 7 - n$

As the temerature and pressure of two gases are same their volume should be proportional to their respective no. Of moles as we know from Avogadro's law.

So

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

$\implies \frac{7 - n}{7} = \frac{8}{18}$

$\implies 7 - n = \frac{28}{9}$
$\implies n = 7 - \frac{28}{9} = \frac{35}{9} = 3 \frac{8}{9} m o l$