Question

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?

Answer 1

I get `10.7 \ "mol"`.

Explanation:

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

`Vpropn`

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*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"`

`~~26.7 \ "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 `Deltan`.

We got:

`Deltan=n_2-n_1`

`=26.7 \ "mol"-16 \ "mol"`

`=10.7 \ "mol"`