A container has a volume of #12 L# and holds #15 mol# of gas. If the container is expanded such that its new volume is #27 L#, how many moles of gas must be injected into the container to maintain a constant temperature and pressure?

Question

A container has a volume of #12   L# and holds #15   mol# of gas.  If the container is expanded such that its new volume is #27 L#, how many moles of gas must be injected into the container to maintain a constant temperature and pressure?

Olivia Askew · Accepted Answer

#34# moles of gas must be injected into the container.

Avogadro's law states that, "equal volumes of all gases, at the same temperature and pressure, have the same number of molecules". This law describes how, under the same condition of temperature and pressure, equal volumes of all gases contain the same number of molecules. For comparing the same substance under two different sets of conditions, the law can be usefully expressed as follows: #V_1/n_1=V_2/n_2#, where: https://tutor.hix.ai Organize the data: Known #V_1="12 L"# #n_1="15 mol"# #V_2="27 L"# Unknown #n_2# Solution Rearrange the equation to isolate #n_2#. Insert the data and solve. #n_2=(V_2xxn_1)/V_1# #n_2=(27color(red)cancel(color(black)("L"))xx15"mol")/(12color(red)cancel(color(black)("L")))="34 mol"# (rounded to two significant figures)

Olivia Askew · Answer

undefined To maintain constant temperature and pressure during expansion, 22 moles of gas must be injected into the container.