# 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?

Jul 31, 2017

$\Delta n = 4.5$ $\text{mol}$

#### 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:

$\frac{{n}_{1}}{{V}_{1}} = \frac{{n}_{2}}{{V}_{2}} \textcolor{w h i t e}{a l}$ (constant temperature and pressure)

Our quantities:

• ${n}_{1} = 9$ $\text{mol}$

• ${V}_{1} = 24$ $\text{L}$

• n_2 = ?

• ${V}_{2} = 36$ $\text{L}$

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"