# A container has a volume of 3 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?

Mar 11, 2018

I get $10.7 \setminus \text{mol}$.

#### Explanation:

At a constant temperature and pressure, we can use Avogadro's law, which states that

$V \propto n$

or

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

where $V$ is the volume of the substance, $n$ is the number of moles of the substance.

Rearranging for ${V}_{2}$, we get

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

Plugging in the given values, we get

n_2=(16 \ "mol")/(3 \ "L")*5 \ "L"

=(16 \ "mol")/(3color(red)cancelcolor(black)"L")*5color(red)cancelcolor(black)"L"

$\approx 26.7 \setminus \text{mol}$

Since this is the new volume, and the question asks "how many moles should be injected", we need to subtract the new amount from the old amount, i.e. find $\Delta n$.

We got:

$\Delta n = {n}_{2} - {n}_{1}$

$= 26.7 \setminus \text{mol"-16 \ "mol}$

$= 10.7 \setminus \text{mol}$