# A container has a volume of 18 L and holds 18 mol of gas. If the container is expanded such that its new volume is 54 L, how many moles of gas must be injected into the container to maintain a constant temperature and pressure?

Nov 14, 2016

$54 \text{moles}$ of gas

#### 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(red)("Knowns:"
${v}_{1}$= 18 L
${v}_{2}$= 54 L
${n}_{1}$= 18 mol

color(pink) ("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:

${n}_{2} = \frac{54 \cancel{L} \times 18 m o l}{18 \setminus \cancel{\text{L}}}$ = $54 m o l$