A container has a volume of #9 L# and holds #15 mol# of gas. If the container is compressed such that its new volume is #8 L#, how many moles of gas must be released to maintain a constant temperature and pressure?

Question

A container has a volume of #9   L# and holds #15   mol# of gas.  If the container is compressed such that its new volume is #8 L#, how many moles of gas must be released to maintain a constant temperature and pressure?

Isabella Alvarez · Accepted Answer

13.3 moles of gas must be released.

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(orange)("Knowns:"# #v_1#= 9 L #v_2#= 8 L #n_1#= 15 mol #color(magenta) ("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=(8cancelLxx15mol)/(9\cancel"L")# = # 13.3 mol#

Layla Ahmed · Answer

undefined Six moles of gas must be released to maintain a constant temperature and pressure when the container is compressed from 9 L to 8 L.

Layla Ahmed · Answer

undefined To find the number of moles of gas that must be released to maintain a constant temperature and pressure when the volume is compressed, you can use Boyle's Law, which states that the product of pressure and volume is constant for a given amount of gas at constant temperature.

Initially, the pressure and volume of the gas are related by the equation: $P_1V_1 = n_1RT$, where $P_1$ is the initial pressure, $V_1$ is the initial volume, $n_1$ is the initial number of moles of gas, $R$ is the gas constant, and $T$ is the temperature.

After compression, the pressure remains constant, so the equation becomes: $P_1V_2 = n_2RT$, where $V_2$ is the new volume and $n_2$ is the new number of moles of gas.

We can rearrange the equation to solve for $n_2$: $n_2 = \frac{P_1V_1}{RT}$.

Using the initial conditions, we can calculate $n_2$ using the new volume $V_2$.

Substituting the given values:

$n_2 = \frac{(15 \text{ mol})(9 \text{ L})}{(0.0821 \text{ L} \cdot \text{atm/mol} \cdot \text{K})(T)}$

Then, using the final volume $V_2 = 8 \text{ L}$, we can solve for $T$ using the ideal gas law: $PV = nRT$, rearranging to $T = \frac{PV}{nR}$.

Finally, we plug in the values to find $n_2$.