Consider the apparatus shown in the following drawing. (a) When the valve between the two containers is opened and the gases are allowed to mix, what is the partial pressure of N2 after mixing?

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Step 1: Identify the initial conditions for each gas. For He: Volume (V1) = 1.5 L, Pressure (P1) = 1.0 atm, Temperature (T) = 26°C. For Ar: Volume (V2) = 2.5 L, Pressure (P2) = 1.5 atm, Temperature (T) = 26°C.

Step 2: Calculate the total volume after the valve is opened. Total Volume (V_total) = V1 + V2 = 1.5 L + 2.5 L.

Step 3: Use the ideal gas law to find the number of moles of N2 in each container before mixing. For He: n1 = (P1 * V1) / (R * T). For Ar: n2 = (P2 * V2) / (R * T).

Step 4: Calculate the total number of moles of N2 after mixing. Total moles (n_total) = n1 + n2.

Step 5: Use the ideal gas law to find the partial pressure of N2 after mixing. P_total = (n_total * R * T) / V_total.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Partial Pressure

Partial pressure is the pressure exerted by a single gas in a mixture of gases. According to Dalton's Law of Partial Pressures, the total pressure of a gas mixture is the sum of the partial pressures of each individual gas. This concept is crucial for determining the behavior of gases when they are allowed to mix, as it helps in calculating the contribution of each gas to the overall pressure.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law assumes that gases behave ideally, meaning they occupy no volume and have no intermolecular forces. Understanding this law is essential for solving problems involving gas mixtures, as it allows for the calculation of changes in pressure and volume when gases are combined.

Gas Mixture Calculations

When dealing with gas mixtures, it is important to apply the principles of gas laws to determine the final conditions after mixing. This involves calculating the total volume and using the initial pressures and volumes of the individual gases to find their new partial pressures. These calculations are fundamental in predicting how gases will behave when they are allowed to mix in a closed system.

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