Question

A container has a volume of `8 L` and holds `1 mol` of gas. If the container is expanded such that its new volume is `9 L`, how many moles of gas must be injected into the container to maintain a constant temperature and pressure?

Answer 1

`1.125` mol.

Explanation:

The law of the perfect gasses says:

`PV=nRT`

where `P` is the pressure, `V` is the volume, `n` is the number of mol `R` is the constant of the perfect gas and `T` is the temperature.

At the beginning `V_i=8` L and `n_i=1` mol while at the end `V_f=9` L. We want that all the quantities except `n` stay constant. So we can write the two equations such as

`PV_i=n_iRT`
`PV_f=n_fRT`

and we can divide the first for the second:

`\frac{PV_i}{PV_f}=\frac{n_iRT}{n_fRT}`

Only the quantities with index `i` or `f` changes, the other are constant, so we can cancel them

`V_i/V_f=n_i/n_f` and substituting the numbers

`8/9=1/n_f` and then

`n_f=9/8=1.125` mol.