# A container has a volume of 21 L and holds 24 mol of gas. If the container is compressed such that its new volume is 12 L, how many moles of gas must be released from the container to maintain a constant temperature and pressure?

Oct 25, 2016

The amount of gas that needs to be released to maintain constant pressure and temperature is $\text{10 mol}$.

#### Explanation:

This is an example of Avogadro's law, which states that the volume of a gas is directly proportional to the amount in moles (n), as long as the pressure and temperature are kept constant. The proportion $\frac{V}{n} = C$ (a constant) means that ${V}_{1} / {n}_{1} = {V}_{2} / {n}_{2} = {V}_{3} / {n}_{3}$, etc... .

Since there are only two sets of data, the equation to use is ${V}_{1} / {n}_{1} = {V}_{2} / {n}_{2}$, where ${V}_{1}$ is the initial volume, ${n}_{1}$ is the original amount in moles, ${V}_{2}$ is the final volume, and ${n}_{2}$ is the final amount in moles.

Given
${V}_{1} = \text{21 L}$
${n}_{1} = \text{24 mol}$
${V}_{2} = \text{12 L}$

Unknown
${n}_{2}$

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

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

n_2=(12"L"xx24"mol")/(21"L")="14 mol"

The amount of gas that must be released to maintain constant pressure and temperature is ${n}_{1} - {n}_{2}$.

$\text{24 mol"-"14 mol"="10 mol}$