# 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 27 L, how many moles of gas must be injected into the container to maintain a constant temperature and pressure?

Oct 8, 2016

${n}_{a \mathrm{dd} e d} = 416 m o l$

#### Explanation:

Using the Ideal Gas Law:

$P {V}_{1} = {n}_{1} r T$ [1]

and

$P {V}_{2} = {n}_{2} r T$ [2]

Dividing [2] by [1]

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

${n}_{2} = \frac{27 L}{1 L} \left(16 m o l\right)$

${n}_{2} = 432 m o l$

Subtract 16 to find the amount that you must add:

${n}_{a \mathrm{dd} e d} = 416 m o l$