A container has a volume of #24 L# and holds #9 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?

1 Answer
Jul 31, 2017

Answer:

#Deltan = 4.5# #"mol"#

Explanation:

We're asked to find the number of moles that need to be added to a container so that the temperature and pressure remain constant.

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

#(n_1)/(V_1) = (n_2)/(V_2)color(white)(al)# (constant temperature and pressure)

Our quantities:

  • #n_1 = 9# #"mol"#

  • #V_1 = 24# #"L"#

  • #n_2 = ?#

  • #V_2 = 36# #"L"#

Plugging in known values, and solving for the final quantity (#n_2#), we have

#n_2 = (n_1V_2)/(V_1) = ((9color(white)(l)"mol")(36cancel("L")))/(24cancel("L")) = color(red)(13.5# #color(red)("mol"#

This represents the final quantity of moles of gas; to find the amount that needs added, we subtract the initial value from the final value:

#Deltan = n_2 - n_1 = color(red)(13.5color(white)(l)"mol") - 9color(white)(l)"mol" = color(blue)(ul(4.5color(white)(l)"mol"#