# A container has a volume of 1 L and holds 16 mol of gas. If the container is expanded such that its new volume is 5 L, how many moles of gas must be injected into the container to maintain a constant temperature and pressure?

Feb 28, 2017

The number of moles of gas to be injected is $= 64 m o l$

#### Explanation:

We apply the gas equation

$P V = n R T$

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

Therefore,

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

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

${n}_{1} = 16 m o l$

${V}_{2} = 5 L$

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

$= \frac{5}{1} \cdot 16 = 80 m o l$

We have to inject

$= 80 - 16 = 64 m o l$