A container has a volume of 4 L and holds 3 mol of gas. If the container is expanded such that its new volume is 36 L, how many moles of gas must be injected into the container to maintain a constant temperature and pressure?

Sep 15, 2016

$27$ moles

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:"
${v}_{1}$= 4 L
${v}_{2}$= 3L
${n}_{1}$= 36 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:

${n}_{2} = \frac{36 \cancel{L} \times 3 m o l}{4 \setminus \cancel{\text{L}}}$ = $27 m o l$