Question

A container has a volume of `48 L` and holds `12 mol` of gas. If the container is compressed such that its new volume is `15 L`, how many moles of gas must be released to maintain a constant temperature and pressure?

Answer 1

The amount of gas that must be released is `"8.2 mol"`.

Explanation:

This is an example of Avogadro's law, which states that when pressure and temperature are constant, the amount (moles) and volume of a gas are directly proportional, so that if moles increase, so does volume and vice versa.

Known
`V_1="48 L"`
`n_1="12 mol"`
`V_2="15 L"`

Unknown
`n_2`

Solution
Rearrange the equation to isolate `n_2`. Substitute the known values into the equation and solve.

`n_2=(V_2*n_1)/V_1`

`n_2=(15"L"*12"mol")/(48"L")="3.8 mol"`

Determine how many moles must be removed from the container, subtract `"3.8 mol"` from `"48 mol"`.

`"12 mol"-"3.8 mol"="8.2 mol"`