# A container has a volume of 4 L and holds 2 mol of gas. If the container is expanded such that its new volume is 12 L, how many moles of gas must be injected into the container to maintain a constant temperature and pressure?

May 29, 2017

$4 \text{mol}$

#### Explanation:

We can solve this problem by using the quantity-volume relationship of gases, illustrated by Avogadro's law:

$\frac{{V}_{1}}{{n}_{1}} = \frac{{V}_{2}}{{n}_{2}}$

We need to find the new quantity of gas when the volume is increased from $4 \text{L}$ to $12 \text{L}$, with a starting quantity of $2 \text{mol}$. Let's plug in our known variables and rearrange the equation to solve for ${n}_{2}$:

${n}_{2} = \frac{{n}_{1} {V}_{2}}{{V}_{1}} = 2 \text{mol"((12cancel("L"))/(4cancel("L"))) = ul(6 "mol}$

This is the total number of moles that satisfies the equation; we're asked to find how many need to be injected. The number of moles that you need to add is simply the total final moles minus the initial moles:

6"mol" - 2"mol" = color(red)(4"mol")

Thus, you need to inject $4 \text{mol}$ of gas to maintain constant temperature and pressure.