# A container has a volume of 48 L and holds 12 mol of gas. If the container is compressed such that its new volume is 15 L, how many moles of gas must be released to maintain a constant temperature and pressure?

Nov 26, 2016

The amount of gas that must be released is $\text{8.2 mol}$.

#### Explanation:

This is an example of Avogadro's law, which states that when pressure and temperature are constant, the amount (moles) and volume of a gas are directly proportional, so that if moles increase, so does volume and vice versa.

Known
${V}_{1} = \text{48 L}$
${n}_{1} = \text{12 mol}$
${V}_{2} = \text{15 L}$

Unknown
${n}_{2}$

Solution
Rearrange the equation to isolate ${n}_{2}$. Substitute the known values into the equation and solve.

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

n_2=(15"L"*12"mol")/(48"L")="3.8 mol"

Determine how many moles must be removed from the container, subtract $\text{3.8 mol}$ from $\text{48 mol}$.

$\text{12 mol"-"3.8 mol"="8.2 mol}$