# A container has a volume of 9 L and holds 5 mol of gas. If the container is compressed such that its new volume is 12 L, how many moles of gas must be released to maintain a constant temperature and pressure?

Mar 16, 2017

The number of moles is $= 1.67 m o l$

#### Explanation:

The Ideal Gas Law is

$P V = n R T$

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

$\frac{V}{n} = k$

Where $k =$constant

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

${V}_{1} = 9 L$

${n}_{1} = 5 m o l$

${V}_{2} = 12 L$

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

$= \frac{12}{9} \cdot 5 = 6.67 m o l$

We must inject $6.67 - 5 = 1.67 m o l$