Question

A container has a volume of `2 L` and holds `12 mol` of gas. If the container is compressed such that its new volume is `14 L`, how many moles of gas must be injected into the container to maintain a constant temperature and pressure?

Answer 1

84 moles of gas must be injected into the container.

Explanation:

The answer can be determined by using Avogadro's law:

`v_1/n_1 = v_2/n_2`

The number 1 represents the initial conditions and the number 2 represents the final conditions.

Identify your known and unknown variables:

`color(gold)("Knowns:"`
`v_1`= 2 L
`v_2`= 14 L
`n_1`= 12 mol

`color(tan) ("Unknowns:"`
`n_2`

Rearrange the equation to solve for the final number of moles:

`n_2=(v_2xxn_1)/v_1`

Plug in your given values to obtain the final number of moles:

`n_2=(14 cancelLxx12mol)/(2\cancel"L")` = `84mol`