# A container has a volume of #4 L# and holds #5 mol# of gas. If the container is compressed such that its new volume is #12 L#, how many moles of gas must be released to maintain a constant temperature and pressure?

15 moles of gas must be released

Applying Avogadro's law here:

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:

• Rewrite the equation to find the total number of moles in the end:

• Enter the provided values to determine the total number of moles:

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Using 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, we can rearrange the equation to solve for the number of moles: (n = \frac{PV}{RT}). Since temperature and pressure are constant, we can set up a ratio of initial to final volumes: (\frac{V_i}{n_i} = \frac{V_f}{n_f}). Solving for (n_f) gives us (n_f = \frac{V_i}{V_f} \times n_i). Substituting the given values, (V_i = 4 L), (n_i = 5 mol), and (V_f = 12 L), we find (n_f = \frac{4}{12} \times 5 = \frac{5}{3} mol). Therefore, (n_f = 1.67 mol). Since the number of moles must be an integer, we round to the nearest whole number. Thus, 2 moles of gas must be released.

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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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