# A container has a volume of 12 L and holds 15 mol of gas. If the container is expanded such that its new volume is 27 L, how many moles of gas must be injected into the container to maintain a constant temperature and pressure?

Aug 13, 2017

$34$ moles of gas must be injected into the container.

#### Explanation:

Avogadro's law states that, "equal volumes of all gases, at the same temperature and pressure, have the same number of molecules".

This law describes how, under the same condition of temperature and pressure, equal volumes of all gases contain the same number of molecules. For comparing the same substance under two different sets of conditions, the law can be usefully expressed as follows:

${V}_{1} / {n}_{1} = {V}_{2} / {n}_{2}$,

where:

$$V is the volume of the gas
n is the amount of substance of the gas (measured in moles).


Organize the data:

Known

${V}_{1} = \text{12 L}$

${n}_{1} = \text{15 mol}$

${V}_{2} = \text{27 L}$

Unknown

${n}_{2}$

Solution

Rearrange the equation to isolate ${n}_{2}$. Insert the data and solve.

${n}_{2} = \frac{{V}_{2} \times {n}_{1}}{V} _ 1$

n_2=(27color(red)cancel(color(black)("L"))xx15"mol")/(12color(red)cancel(color(black)("L")))="34 mol" (rounded to two significant figures)