# A container has a volume of 5 L and holds 18 mol of gas. If the container is expanded such that its new volume is 46 L, how many moles of gas must be injected into the container to maintain a constant temperature and pressure?

Dec 16, 2017

$165.6 \text{ moles}$

#### Explanation:

This is a variation on the usual use of the Ideal Gas Laws.
$\frac{{P}_{1} \times {V}_{1}}{T} _ 1 = \frac{{P}_{2} \times {V}_{2}}{T} _ 2 = n \times R$
At constant temperature the ratio of moles $n$ to volume is:
${V}_{2} / {V}_{1} = {M}_{2} / {M}_{1}$

$\frac{46}{5} = {\text{moles}}_{2} / 18$

$\text{moles"_2 = (18 xx 46)/5 = 165.6" moles}$