# A container has a volume of 18 L and holds 9 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?

Aug 14, 2016

color(blue)(" 6 moles of gas must be released."

#### Explanation:

${v}_{1} / {n}_{1} = {v}_{2} / {n}_{2}$

The number 1 represents the initial conditions and the number 2 represents the final conditions.

Let's identify our known and unknown variables.

color(magenta)("Knowns:"
${V}_{1}$= 18 L
${V}_{2}$= 12 L
${n}_{1}$= 9 mol

color(blue)("Unknowns:"
${n}_{2}$

Rearrange the equation to solve for the final number of moles:

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

Plug in your given values to obtain the final number of moles:

${n}_{2} = \frac{12 \cancel{L} \times 9 m o l}{18 \setminus \cancel{\text{L}}}$ = $6 m o l$