A container has a volume of #4 L# and holds #2 mol# of gas. If the container is expanded such that its new volume is #12 L#, how many moles of gas must be injected into the container to maintain a constant temperature and pressure?

1 Answer
May 29, 2017

Answer:

#4 "mol"#

Explanation:

We can solve this problem by using the quantity-volume relationship of gases, illustrated by Avogadro's law:

#(V_1)/(n_1) = (V_2)/(n_2)#

We need to find the new quantity of gas when the volume is increased from #4"L"# to #12"L"#, with a starting quantity of #2 "mol"#. Let's plug in our known variables and rearrange the equation to solve for #n_2#:

#n_2 = (n_1V_2)/(V_1) = 2"mol"((12cancel("L"))/(4cancel("L"))) = ul(6 "mol"#

This is the total number of moles that satisfies the equation; we're asked to find how many need to be injected. The number of moles that you need to add is simply the total final moles minus the initial moles:

#6"mol" - 2"mol" = color(red)(4"mol")#

Thus, you need to inject #4"mol"# of gas to maintain constant temperature and pressure.