A container has a volume of #21 L# and holds #27 mol# of gas. If the container is compressed such that its new volume is #18 L#, how many moles of gas must be released from the container to maintain a constant temperature and pressure?

Question

A container has a volume of #21   L# and holds #27   mol# of gas.  If the container is compressed such that its new volume is #18 L#, how many moles of gas must be released from the container to maintain a constant temperature and pressure?

Layla Ahmed · Accepted Answer

#24.1# mol

Applying Avogadro's law here: #v_1/n_1 = v_2/n_2# The initial conditions are denoted by the number 1, and the final conditions are represented by the number 2. • Determine the variables you know and don't know: #color(brown)("Knowns:"# #v_1#= 21L #v_2#= 18 L #n_1#= 27 mol #color(blue) ("Unknowns:"# #n_2# • Rewrite the equation to find the total number of moles in the end: #n_2=(v_2xxn_1)/v_1# • Enter the provided values to determine the total number of moles: #n_2=(18cancelLxx27mol)/(21\cancel"L")# = # 24.1 mol#

Amelia Adams · Answer

undefined Use the ideal gas law equation to solve for the number of moles of gas released:

$$ PV = nRT $$

Where:
$ P $ = pressure (constant)
$ V $ = volume
$ n $ = number of moles of gas
$ R $ = ideal gas constant
$ T $ = temperature (constant)

Since pressure and temperature are constant, the equation can be simplified to:

$$ \frac{V_1}{n_1} = \frac{V_2}{n_2} $$

Where:
$ V_1 = 21 $ L
$ n_1 = 27 $ mol
$ V_2 = 18 $ L
$ n_2 $ is the unknown number of moles to be found.

$$ \frac{21}{27} = \frac{18}{n_2} $$

Solve for $ n_2 $:

$$ n_2 = \frac{18 \times 27}{21} $$

$$ n_2 \approx 23.14 \, \text{mol} $$

To find the number of moles released, subtract the initial number of moles from $ n_2 $:

$$ \text{Moles released} = n_2 - n_1 $$

$$ \text{Moles released} \approx 23.14 \, \text{mol} - 27 \, \text{mol} $$

$$ \text{Moles released} \approx -3.86 \, \text{mol} $$

Since moles cannot be negative, the negative sign indicates that the gas was released from the container. Therefore, approximately 3.86 moles of gas must be released from the container to maintain constant temperature and pressure.