Question

A container has a volume of `18 L` and holds `6 mol` of gas. If the container is compressed such that its new volume is `3 L`, how many moles of gas must be released to maintain a constant temperature and pressure?

Answer 1

`5` moles

Explanation:

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

`Vpropn` or `V_1/n_1=V_2/n_2`

So, we need to find the new number of moles, and we can rearrange the equation into,

`n_2=n_1/V_1*V_2`

Now, we can substitute into the given values, and we get

`n_2=(6 \ "mol")/(18color(red)cancelcolor(black)"L")*3color(red)cancelcolor(black)"L"`

`=1 \ "mol"`

So, the new amount of moles will be `1 \ "mol"`.

In order to find the difference, `Deltan`, we use,

`Deltan=n_2-n_1`

`=1 \ "mol"-6 \ "mol"`

`=-5 \ "mol"`

So, five moles of the gas must be released.