Question

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?

Answer 1

`4 "mol"`

Explanation:

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

`(V_1)/(n_1) = (V_2)/(n_2)`

We need to find the new quantity of gas when the volume is increased from `4"L"` to `12"L"`, with a starting quantity of `2 "mol"`. Let's plug in our known variables and rearrange the equation to solve for `n_2`:

`n_2 = (n_1V_2)/(V_1) = 2"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"mol"` of gas to maintain constant temperature and pressure.