# A container has a volume of #18 L# and holds #9 mol# of gas. If the container is compressed such that its new volume is #8 L#, how many moles of gas must be released from the container to maintain a constant temperature and pressure?

When pressure and temperature are held constant, the number of moles is proportional to the volume of the container.

Keep in mind that the quantity of moles in this example is precisely half that of liters.

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The ideal gas law, (PV = nRT), where (P) is pressure, (V) is volume, (n) is the number of moles, (R) is the gas constant, and (T) is temperature, can be rearranged to (n_1V_1 = n_2V_2), where (n_1) and (V_1) are the initial moles and volume, and (n_2) and (V_2) are the final moles and volume.

[ n_2 = \frac{n_1 \cdot V_1}{V_2} ]

Given that the initial volume (V_1) is 18 L, initial moles (n_1) is 9 mol, and the final volume (V_2) is 8 L, the calculation yields:

[ n_2 = \frac{9 , \text{mol} \cdot 18 , \text{L}}{8 , \text{L}} ]

[ n_2 = 20.25 , \text{mol} ]

Therefore, 20.25 moles of gas must be released from the container to maintain a constant temperature and pressure.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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