Question

A container has a volume of `21 L` and holds `24 mol` of gas. If the container is compressed such that its new volume is `12 L`, how many moles of gas must be released from the container to maintain a constant temperature and pressure?

Answer 1

The amount of gas that needs to be released to maintain constant pressure and temperature is `"10 mol"`.

Explanation:

This is an example of Avogadro's law, which states that the volume of a gas is directly proportional to the amount in moles (n), as long as the pressure and temperature are kept constant. The proportion `V/n=C` (a constant) means that `V_1/n_1=V_2/n_2=V_3/n_3`, etc... .

Since there are only two sets of data, the equation to use is `V_1/n_1=V_2/n_2`, where `V_1` is the initial volume, `n_1` is the original amount in moles, `V_2` is the final volume, and `n_2` is the final amount in moles.

Given
`V_1="21 L"`
`n_1="24 mol"`
`V_2="12 L"`

Unknown
`n_2`

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

`n_2=(V_2xxn_1)/(V_1)`

`n_2=(12"L"xx24"mol")/(21"L")="14 mol"`

The amount of gas that must be released to maintain constant pressure and temperature is `n_1-n_2`.

`"24 mol"-"14 mol"="10 mol"`