A container has a volume of #2 L# and holds #24 mol# of gas. If the container is expanded such that its new volume is #4 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 #2   L# and holds #24   mol# of gas.  If the container is expanded such that its new volume is #4 L#, how many moles of gas must be injected into the container to maintain a constant temperature and pressure?

Charlotte Aaron · Accepted Answer

The number of moles to be injected is #=24mol#

The Ideal Gas Law is

#PV=nRT#

#V/n=RT/P#

#V/n=k#

Where #k=#constant

#V_1/n_1=V_2/n_2#

#V_1=2L#

#n_1=24mol#

#V_2=4L#

#n_2=V_2/V_1*n_1#

#=4/2*24=48mol#

We must inject #48-24=24mol#

Nicholas Agrusa · Answer

undefined Using the ideal gas law equation $PV = nRT$, where $P$ is pressure, $V$ is volume, $n$ is the number of moles of gas, $R$ is the ideal gas constant, and $T$ is temperature, and assuming constant temperature and pressure:

$PV = nRT$

$n = \frac{{PV}}{{RT}}$

Since the temperature and pressure are constant, $RT$ remains constant. So, for the initial state:

$n_1V_1 = n_2V_2$

Given $V_1 = 2$ L, $V_2 = 4$ L, and $n_1 = 24$ mol:

$n_2 = \frac{{n_1V_1}}{{V_2}} = \frac{{24 \times 2}}{{4}}$

$n_2 = 12$ mol

To find how many moles of gas must be injected into the container:

$n_{\text{injected}} = n_2 - n_1 = 12 - 24$

$n_{\text{injected}} = -12$ mol

Since $n_{\text{injected}}$ cannot be negative, it means that gas must be removed from the container to maintain a constant temperature and pressure.