A container has a volume of #3 L# and holds #1 mol# of gas. If the container is expanded such that its new volume is #8 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 #3   L# and holds #1   mol# of gas.  If the container is expanded such that its new volume is #8 L#, how many moles of gas must be injected into the container to maintain a constant temperature and pressure?

Isabella Alvarez · Accepted Answer

#5/3# moles

For solving this problem we have to assume the ideal behaviour of the gas. Hence the equation #PV=nRT# can be applied. Now the volume is increased by a factor of #8/3# #:.# number of moles should also increase by a factor of #8/3# #:.# new number of moles #=1xx8/3=8/3# #:. # extra moles which we have to inject are #8/3-1=5/3# moles

Nathan Ashcroft · Answer

undefined To maintain constant temperature and pressure, the number of moles of gas must remain constant. Therefore, if the initial volume is 3 L and holds 1 mol of gas, and the final volume is 8 L, the number of moles of gas must be adjusted to match the new volume. Using the formula $PV = nRT$, where $P$ is pressure, $V$ is volume, $n$ is the number of moles, $R$ is the gas constant, and $T$ is temperature (which remains constant in this case), we can set up a proportion:

$$
\frac{{P_1V_1}}{{n_1}} = \frac{{P_2V_2}}{{n_2}}
$$

Given that $P_1V_1 = P_2V_2$ (constant temperature and pressure), we can solve for $n_2$ (the number of moles of gas in the final volume):

$$
n_2 = \frac{{P_1V_1}}{{V_2}} = \frac{{(1\, \text{mol})(3\, \text{L})}}{{8\, \text{L}}} = 0.375\, \text{mol}
$$

Therefore, 0.375 moles of gas must be injected into the container to maintain constant temperature and pressure.