# A container has a volume of 48 L and holds 6 mol of gas. If the container is compressed such that its new volume is 36 L, how many moles of gas must be released to maintain a constant temperature and pressure?

Aug 24, 2016

$4.5 \text{moles}$ 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.

Identify your known and unknown variables:

color(teal)("Knowns:"
${v}_{1}$= 48 L
${v}_{2}$= 36 L
${n}_{1}$= 6 mol

color(orange) ("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:

${n}_{2} = \frac{36 \cancel{L} \times 6 m o l}{48 \cancel{\text{L}}}$ = $4.5 m o l$