A container has a volume of #3 L# and holds #16 mol# of gas. If the container is expanded such that its new volume is #5 L#, how many moles of gas must be injected into the container to maintain a constant temperature and pressure?

1 Answer
Mar 11, 2018

Answer:

I get #10.7 \ "mol"#.

Explanation:

At a constant temperature and pressure, we can use Avogadro's law, which states that

#Vpropn#

or

#V_1/n_1=V_2/n_2#

where #V# is the volume of the substance, #n# is the number of moles of the substance.

Rearranging for #V_2#, we get

#n_2=n_1/V_1*V_2#

Plugging in the given values, we get

#n_2=(16 \ "mol")/(3 \ "L")*5 \ "L"#

#=(16 \ "mol")/(3color(red)cancelcolor(black)"L")*5color(red)cancelcolor(black)"L"#

#~~26.7 \ "mol"#

Since this is the new volume, and the question asks "how many moles should be injected", we need to subtract the new amount from the old amount, i.e. find #Deltan#.

We got:

#Deltan=n_2-n_1#

#=26.7 \ "mol"-16 \ "mol"#

#=10.7 \ "mol"#