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 #9 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 #4   L# and holds #3   mol# of gas.  If the container is expanded such that its new volume is #9 L#, how many moles of gas must be injected into the container to maintain a constant temperature and pressure?

Charlotte Aaron · Accepted Answer

#3.75# #"mol"#

To solve this problem, we can use the volume-quantity relationship of gases, illustrated by Avogadro's law:

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

where

#n_1# and #n_2# are the initial and final quantities, in #"mol"#, of the gas, and

#V_1# and #V_2# are the initial and final volumes of the gas, usually in #"L"#

Since we're trying to find how many moles of gas are needed to inject, we'll rearrange the equation to solve for #n_2#:

#n_2 = (n_1V_2)/(V_1)#

Our known quantities are

#n_1 = 3# #"mol"#

#V_1 = 4# #"L"#

#V_2 = 9# #"L"#

Plugging these values into the equation, we have

#n_2 = (n_1V_2)/(V_1) = ((3"mol")(9cancel("L")))/(4cancel("L")) = 6.75# #"mol"#

This is the total final volume; we were asked to find how many moles needed to be injected. To find this, we simply subtract the initial value from the final value:

#n_"need" = 6.75# #"mol" - 3# #"mol" = color(red)(3.75# #color(red)("mol"#

Thus, to maintain a constant temperature and pressure, you must inject #color(red)(3.75# moles of gas into the container.

If you follow the rules for significant figures, the answer is technically #4# moles, but questions like this with one significant figure are universally disliked... one significant figure is too uncertain for most people :)

Adam Arnold · Answer

undefined 5 moles of gas.