Question

A container has a volume of `24 L` and holds `9 mol` of gas. If the container is expanded such that its new volume is `36 L`, how many moles of gas must be injected into the container to maintain a constant temperature and pressure?

Answer 1

`Deltan = 4.5` `"mol"`

Explanation:

We're asked to find the number of moles that need to be added to a container so that the temperature and pressure remain constant.

To do this, we can use the quantity-volume relationship of gases, illustrated by Avogadro's law:

`(n_1)/(V_1) = (n_2)/(V_2)color(white)(al)` (constant temperature and pressure)

Our quantities:

• `n_1 = 9` `"mol"`

• `V_1 = 24` `"L"`

• `n_2 = ?`

• `V_2 = 36` `"L"`

Plugging in known values, and solving for the final quantity (`n_2`), we have

`n_2 = (n_1V_2)/(V_1) = ((9color(white)(l)"mol")(36cancel("L")))/(24cancel("L")) = color(red)(13.5` `color(red)("mol"`

This represents the final quantity of moles of gas; to find the amount that needs added, we subtract the initial value from the final value:

`Deltan = n_2 - n_1 = color(red)(13.5color(white)(l)"mol") - 9color(white)(l)"mol" = color(blue)(ul(4.5color(white)(l)"mol"`