# A container has a volume of #2 L# and holds #4 mol# of gas. If the container is expanded such that its new volume is #15 L#, how many moles of gas must be injected into the container to maintain a constant temperature and pressure?

30 moles of gas must be injected into the container.

The answer can be determined by using Avogadro's law:

The number 1 represents the initial conditions and the number 2 represents the final conditions.

Identify your known and unknown variables:

Rearrange the equation to solve for the final number of moles:

Plug in your given values to obtain the final number of moles:

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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, (R) is the gas constant, and (T) is temperature, we can rearrange the equation to solve for moles:

(n = \frac{{PV}}{{RT}})

Given that the temperature and pressure are constant, we can use the initial conditions to find the number of moles of gas:

(n_1 = \frac{{P_1V_1}}{{RT_1}})

Then, we can use the final volume to find the new number of moles:

(n_2 = \frac{{P_1V_2}}{{RT_1}})

Subtracting (n_1) from (n_2) will give us the number of moles to be injected:

(n_{\text{injected}} = n_2 - n_1)

Substituting the given values:

(n_{\text{injected}} = \frac{{P_1V_2}}{{RT_1}} - \frac{{P_1V_1}}{{RT_1}})

(n_{\text{injected}} = \frac{{P_1}}{{RT_1}} (V_2 - V_1))

Now, we can plug in the values:

(n_{\text{injected}} = \frac{{P}}{{RT}} (V_2 - V_1))

(n_{\text{injected}} = \frac{{P}}{{RT}} (15 , \text{L} - 2 , \text{L}))

(n_{\text{injected}} = \frac{{4}}{{0.0821 \times 298}} (15 - 2))

(n_{\text{injected}} \approx 0.269 , \text{mol})

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