# 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?

The number of moles to be injected is

The Ideal Gas Law is

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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.

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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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